research article design of telerobotic drilling...

Hindawi Publishing CorporationJournal of Control Science and EngineeringVolume 2013 Article ID 901610 15 pageshttpdxdoiorg1011552013901610

Research ArticleDesign of Telerobotic Drilling Control System withHaptic Feedback

Faraz Shah and Ilia G Polushin

Department of Electrical and Computer Engineering Western University London ON Canada N6A 5B9

Correspondence should be addressed to Ilia G Polushin ipolushiuwoca

Received 24 May 2013 Revised 17 August 2013 Accepted 19 August 2013

Academic Editor Wen Yu

Copyright copy 2013 F Shah and I G Polushin This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The paper deals with the design of control algorithms for virtual reality based telerobotic system with haptic feedback that allowsfor the remote control of the vertical drilling operation The human operator controls the vertical penetration velocity using ahaptic device while simultaneously receiving the haptic feedback from the locally implemented virtual environment The virtualenvironment is rendered as a virtual spring with stiffness updated based on the estimate of the stiffness of the rock currentlybeing cut Based on the existing mathematical models of drill stringdrive systems and rock cuttingpenetration process a robustservo controller is designed which guarantees the tracking of the reference vertical penetration velocity of the drill bit A schemefor on-line estimation of the rock intrinsic specific energy is implemented Simulations of the proposed control and parameterestimation algorithms have been conducted consequently the overall telerobotic drilling systemwith a human operator controllingthe process using PHANTOM Omni haptic device is tested experimentally where the drilling process is simulated in real time invirtual environment

1 Introduction

Drilling a borehole is a common method for extracting oilgas and natural resources from beneath the surface of theearth Conventional oil well drilling has made significantprogress over recent years and currently is one of the mostautomated processes in the oil and gas industry Howeverthere are still some fundamental challenges associated withthe drilling One of the challenges is the choice of verticalpenetration velocity of the drill bit For efficient drillingoperation this velocity must depend upon the type of rockbeds drilled In particular the velocitymust be adjusted whenmechanical characteristics of rock strata change Often it isdifficult to estimate in real time the relative position of thedrill bit with respect to different rock layers and thereforehard to predict the mechanical characteristics of the rockformations

The goal of this research is to design a telerobotic systemwith haptic feedback for control of the drilling processTelerobotics for drilling well is a relatively novel idea and itis substantial endeavor to automate one of the fundamental

processes in the extraction of energy and resources Astelerobotics is integrated with drilling it can greatly decreasethe number of people working and monitoring operationon the site This in particular can reduce the work sitehazards Also telerobotics can bring actual analysis of insitu conditions (underground drilling environment) in realtime to the human operator that works remotely where(s)he will be able to monitor the current drilling conditionsand in particular promptly enforce changes in the verticalspeed of penetration of the drill bit in the oil well Real-timecontrol and optimization of the drilling speed are crucial fortodayrsquos drilling industry as it can reduce time and immensecost associated with the drilling an oil well Introduction ofhaptic feedback would allow the human operator to feel thechanges in mechanical characteristics of the rock and adjustthe vertical velocity of penetration accordingly

In this paper we address the problem of design of controlalgorithms for virtual reality based telerobotic system withhaptic feedback that allows for the remote control of thevertical drilling operation Based on a simplified mathe-matical model of the drilling process control algorithms

2 Journal of Control Science and Engineering

are designed which allow to achieve a desired rate of thevertical penetration regardless of the mechanical propertiesof the rock The control design includes an online parameterestimator of the intrinsic specific energy which is a parameterthat describes the hardness of the rock All these algorithmsare consequently used in the design of a telerobotic drillingsystem with virtual environment-based haptic feedback thatallows the human operator to feel the stiffness of the rock incontact with the drill bit Simulations and semiexperimentalresults are performed which confirm the validity of thetheoretical developments

The potential application domain of this research is notlimited to onshoreoffshore oil well drilling but the sameprinciples can be applied in particular to different typesof mining robots [1] telerobotic systems for dredging andmining ocean [2ndash5] surgical drilling [6] and teleroboticsystems for drilling the extraterrestrial terrain to discover andresearch the minerals and composition beneath [5 7]

The structure of the paper is as follows In Section 2 amathematical model of the drilling process is derived whichis subsequently used for the control design Section 3 dealswith the design of control algorithms for rotational and trans-lationalmotion of the drilling systems as well as the design ofan online parameter estimator of the intrinsic specific energyof the rock In Section 4 the structure of a telerobotic drillingsystem is described and the corresponding experimentalresults are presented Finally in Section 5 some conclusionsare given and possible future directions are formulated

2 Mathematical Model of Drilling System

In this section mathematical models that describe thedrilling system are presented Specifically the mathematicalmodel of drill string and drive system is described inSection 21 while the model of rock cutting and penetrationis the subject of Section 22

21 Mathematical Model of the Drill String and Drive SystemThe drill string is the assembly of rotating pipes which areresponsible for transmitting rotation and weight to the bitand bridge up a connection between the bottom hole tools[8] The components of a drill string along with drill pipesand the bottom hole assembly (BHA) are shown in Figure 1A number of simplified mathematical models for drill stringand drive systems were proposed in the literature such as[9ndash12] The model used in our work was developed in [9]This model describes the drill string as a simple torsionalpendulum where the drill pipes are represented as torsionalsprings and the bottom hole assembly is described as a rigidbody with inertia The model is based on the followingsimplifying assumptions

(1) The bottom hole assembly and the drill bits behavelike rigid bodies

(2) The moment of inertia of the drill pipe is consideredto be small in comparisonwith themoments of inertiaof the bottom hole assembly and the rotary table andtherefore neglected

DC

HWDP

Bit

BHA

Dril

l pip

e

Dril

l str

ing

Figure 1 Drill string components [8]

Gearboxand bevel gear

Jr

k

J1

c2

c1 minusTb

1206011

1206012

R

minus

+

V Motor

LI

Jm

Rotary table

Drill pipes

Drill collars

1 n

Figure 2 Representation of drill stringdrive system with mechan-ical and electrical components [9]

(3) The nonzero time propagation of the torsional forcedisturbances along the drill string is neglected Theforces assume to propagate instantaneously along thedrill string

Under the above described assumptions 1ndash3 the wholedrill string and drive system with equivalent electro-mechanical components can be represented by its structuraldiagram shown in Figure 2 This system is described by thefollowing mathematical model [9] First the motion of thedrill string is described by the following equation

11986911206011+ 11988811206011+ 119896 (120601

1minus 1206012) minus 119879 = 0 (1)

Journal of Control Science and Engineering 3

Here 1206011is the angular displacement of bit and drill collars

(BHA) 1206012is the angular displacement of the rotary table

1198691is the equivalent moment of inertia of the collars (BHA)

and the drill pipes coefficient 1198881represents equivalent viscous

damping 119896 is the equivalent torsional stiffness of the drillpipes and 119879 is the torque-on-bit (TOB) generated during therock cutting process (see Section 22 below)The dynamics ofthe rotary table and drive system is described by the followingequation

11986921206012+ 11988821206012minus 119896 (120601

1minus 1206012) minus 119899119879

119898= 0 (2)

where 1198692is combined moment of inertia of the rotary table

and of the rotor of the electric motor coupled together witha gearbox that has 1 119899 gear ratio 119888

2is aggregated damping

of all the components of the drive system and 119879119898

is themotor torque Finally the electric motor is described by thefollowing equations

119871 119868 + 119877119868 + 119881119887minus 119881 = 0 119881

119887= 119870 1206013= 119870119899 120601

2

119879119898= 119870119868

(3)

where 119868 is the armature current 119871 is an equivalent armatureinductance 119877 is an equivalent armature resistance 119881

119887is the

back emf 119881 is the armature voltage 1206013is the rotor angular

velocity and 119870 is a constant that depends upon the motorcharacteristics

By combining all the above equations the complete drillstringdrive system can be written in the following state spaceform

[[[[[[[[

[

1206011

1

1206012

2

119868

]]]]]]]]

]

=

[[[[[[[[[[[[[

[

0 1 0 0 0

minus119896

1198691

minus1198881

1198691

119896

1198691

0 0

0 0 0 1 0

119896

1198692

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]]]]]

]

[[[[[[

[

1206011

1205961

1206012

1205962

119868

]]]]]]

]

+

[[[[[[[[[[

[

0

minus119879

1198691

0

0

119881

119871

]]]]]]]]]]

]

(4)

Here 1205961and 120596

2are the angular velocities of the drill bit and

the rotary table respectively Equation (4) is valid when thedrill bit rotational velocity is greater than zero that is 120596

1gt 0

In order to reduce the number of equations a variable 120601 isintroduced as the difference of 120601

2and 120601

1 In this case the

original system can be rewritten in the following reducedstate space form

[[[[[

[

1

120601

2

119868

]]]]]

]

=

[[[[[[[[[[

[

minus1198881

1198691

119896

1198691

0 0

minus1 0 1 0

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]]

]

[[[[[

[

1205961

120601

1205962

119868

]]]]]

]

+

[[[[[[[[

[

minus119879

1198691

0

0

119881

119871

]]]]]]]]

]

(5)

Ω

zU(t minus tn)

U(t)

dn(t)

Φ(t minus tn)2120587n

Φ(t)

1 2

985747n

Figure 3 Section of the bottom hole profile located between twosuccessive blades [10]

Equation (5) defines the reduced order model of the drillstring and drive systemThemodel (5) is used for the controldesign below

22 RockCutting andVertical PenetrationModels Astandarddrill bit usually exhibits two kinds of motions rotationalalong its axis of rotation and vertical motion while penetrat-ing through the rocks As described in [13] in the normalmode of operation of the drill bit the bit rotational velocity 120596is parallel to its axis of rotation and the penetration velocity Vis directed vertically straight through the rocks Similarly theweight-on-bit119882 acts in the vertical direction and the torque-on-bit 119879 is applied in parallel to the direction of rotationof drill bit The cutting components of the weight-on-bitand torque-on-bit depend on the radius of PDC drill bit 119886intrinsic specific energy 120598 a parameter 120577 gt 0which representsthe ratio of the vertical force to the horizontal force betweenrock and cutter contact surfaces and the depth of cut 119889 Thedepth of cut 119889 plays significant role in the equations to followthat describe the cutting components of the torque-on-bit 119879and the weight-on-bit119882The equations for these two cuttingcomponents are as follows [13]

119879119888=1

21198862120598119889 (6)

119882119888= 119886120577120598119889 (7)

In this work the system is developed under simplifyingassumption that the friction effects are negligible In this caseboth variables 119879 asymp 119879

119888 and 119882 asymp 119882119888 are proportional to

the depth of cut 119889 according to (6) and (7) As illustrated inFigure 3 the depth of cut 119889 is the thickness of rock ridge infront of the blade It is assumed that the drill bit has 119899 numberof identical blades and the difference of angular positions ofthese two successive blades is (2120587119899) In this case 119889 is thecombined depth of cut of all 119899 blades in each revolution ofdrill bit according to the formula

119889 (119905) = 119899119889119899(119905) (8)


where 119889119899is the depth of cut of each blade The depth of cut

for each blade is in turn defined according to the formula

119889119899(119905) = 119880 (119905) minus 119880 (119905 minus 119905

119899) (9)

where119880(119905) and119880(119905 minus 119905119899) are the vertical positions of the drill

bit at current time instant 119905 and a certain previous instant 119905 minus119905119899 respectively [10 11] The delay 119905

119899in the above formula is

exactly the time that is required for the drill bit to rotate byan angle 2120587119899 to achieve its current angular position 120601

1(119905) in

other words it also satisfies the following equation

120601 (119905) minus 120601 (119905 minus 119905119899) =

2120587

119899 (10)

Using (9) and (10) for calculating 119889(119905)would significantlycomplicate the control design In this work we simplify thisproblem by assuming that both the vertical and angularvelocities change slowly specifically it is assumed that bothV(120591) equiv (120591) and 120596

1(120591) equiv 120601

1(120591) are approximately constant

during each period 120591 isin [119905 minus 119905119899 119905] Using this assumptions (9)

and (10) can be rewritten as follows

119889 (119905) asymp 119899 sdot V (119905) sdot 119905119899 (11)

1205961(119905) sdot 119905119899asymp2120587

119899 (12)

Combining (11) (12) and assuming 1205961(119905) = 0 one gets the

following approximate expression for 119889(119905)

119889 (119905) asymp2120587 sdot 119905 (119905)

1205961(119905)

(13)

The above formula has a singularity at 1205961(119905) = 0 To

remove this singularity note that the drilling occurs whenboth 120596

1(119905) gt 0 and V(119905) gt 0 On the contrary 120596

1(119905) le 0

the drill bits do not cut the rock and therefore 119889(119905) equiv 0

in this case Based on the above considerations one canapproximately define the depth of cut according to theformula

119889 (119905) asymp2120587 sdot V (119905)

max 1205961(119905) 1205980 (14)

where 1205980gt 0 is sufficiently small positive constant The

formula (14) does not have singularity at 1205961(119905) = 0 it will be

occasionally used for calculations of 119889(119905) instead of (13) in thecases where avoiding singularity is important (in simulationsetc)

Finally the vertical motion of the drill bit is described bythe following equation [12]

119872119889V

119889119905= 119882119904minus119882 minus119867

0minus 119870119891V (15)

Here V is the vertical velocity of the drill bit 119872 is thecombinedmass of the drill string and BHA119867

0is the constant

upward force applied from the top of drilling rig and119882119904is

the submerged weight of the drill string and Bottom HoleAssembly (BHA) In this model it is assumed that 119882

119904and

1198670to be constants and defined their difference with another

constant1198820such that119882

0= 119882119904minus 1198670 Also119882 is the applied

weight on bit from the interaction of rock defined by (7) and119870119891gt 0 is the coefficient of viscous friction

Vertical motion

Rotational motion

Cutting process

W(t)

V(t)

(t)

T(t)

d(t)

d(t)

d(t)

1205961(t)

W = a120577120598d

T =1

2a2120598d

Figure 4 The block diagram of the drilling system

3 Controller Design

The block diagram of the overall drilling system is shownin Figure 4 As it can be seen from this figure the blockdiagram has a complex structure and consists of severalinterconnected subsystems Specifically the vertical motionsubsystem is described by (15) the output of this subsystemis the vertical velocity of penetration V(119905) The subsystemthat represents the rotational motion is described by (5)this subsystem has one control input which is the armaturevoltage 119881(119905) and one output which is the angular velocityof the drill bits 120596

1(119905) Both V(119905) and 120596

1(119905) are the inputs of

the nonlinear static block that represents the cutting processthis subsystem generates the depth of cut 119889(119905) accordingto (13) Both the torque-on-bit 119879 and weight-on-bit 119882 areproportional to 119889 they are fed back to rotational motion andvertical motion subsystems respectively

Our goal is to design a control system that maintains adesired rate of drilling Specifically we are looking for thecontrol algorithm for the armature voltage119881 that would guar-antee that the velocity of the vertical penetration V(119905) tendsasymptotically to an arbitrary positive desired value Vref gt 0We start designing a control algorithm by considering theequation of vertical motion (15) in some detail

31 Control of the Vertical Motion of a Drill Bit The verticalmotion of the drilling system is described by (15) Forconvenience this equation is rewritten below in a slightlymodified form as follows

V = minus119870119891

119872V minus

(119882119904minus 1198670)

119872minus119882

119872 (16)

The idea of the controller developed in this work is to use theweight-on-bit119882 as the control input to the vertical motionsubsystem (16) More specifically combining formulas (7)and (13) one get the following expression for119882

119882 = 1198861205771205982120587

1205961

V (17)

which essentially indicates that 119882 is proportional to thevertical velocity V(119905) and inversely proportional to the angular


velocity of the rotational motion 1205961(119905) Substituting the last

formula into (16) one gets

V =119882119904minus 1198670

119872minus1

119872(119886120577120598

2120587

1205961

+ 119870119891) V (18)

Equation (18) is a linear differential equation with respect toV which assuming 120596

1gt 0 has one stable equilibrium V = V

0

defined by the formula

119882119904minus 1198670

119872minus1

119872(119886120577120598

2120587

1205961

+ 119870119891) V0= 0 (19)

Solving the above equation with respect to V0 one gets

V0=

119882119904minus 1198670

(119886120577120598 (21205871205961) + 119870119891) (20)

The above equation (20) indicates that the location of thestable equilibrium V = V

0of the vertical motion subsystem

(16) can be controlled if one can control the rotational veloc-ity 1205961 Specifically (20) defines one-to-one correspondence

between 1205961from the range (0 +infin) and V

0from the range

(0 (119882119904minus1198670)119870119891) In particular for any given Vref isin (0 (119882119904 minus

1198670)119870119891) there exists an unique 120596ref isin (0 +infin) such that

if the angular velocity satisfies 1205961(119905) equiv 120596ref then Vref is a

globally exponentially stable equilibrium of the translationaldynamics (16) For a given Vref isin (0 (119882

119904minus 1198670)119870119891) the

corresponding 120596ref can be found using formula (20) asfollows

120596ref =2120587119886120577120598

((119882119904minus 1198670) Vref) minus 119870119891

(21)

Therefore the control goal of stabilization of the verticalpenetration velocity V(119905) rarr Vref can be achieved bydesigning a controller for rotational motion that guaranteesa sufficiently fast convergence of 120596

1(119905) rarr 120596ref The design of

such a controlled is presented in the next section

32 Stabilization of the Angular Velocity of the Drilling SystemThe rotational dynamics of the drilling system together withthe electric drive are described by (5) which is repeated belowfor convenience

[[[

[

1

120601

2

119868

]]]

]

=

[[[[[[[[[

[

minus1198881

1198691

119896

1198691

0 0

minus1 0 1 0

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]

]

[[[

[

1205961

120601

1205962

119868

]]]

]

+

[[[[

[

0

0

01

119871

]]]]

]

119881 +

[[[[[

[

minus1

1198691

0

0

0

]]]]]

]

119879

(22)

The above system has one control input which is the armaturevoltage of the electric drive 119881 and one disturbance inputwhich is the torque-on-bit 119879 Our objective in this section isto design a control law for119881which would track the referenceangular velocity of the drill 120596

1rarr 120596ref while rejecting the

disturbance 119879To solve the control problem formulated above one

can use the approach to feedforward robust servo controlproblem presented in [14 15] Below the above approach isdescribed in a simplified manner which however serves ourpurpose well Consider a linear time invariant system of theform

= 119860119909 + 119861119906 + 119863119908

119910 = 119862119909 + 119865119906 + 119867119908(23)

where 119909 isin R119899 is the state 119906 isin R119898 is the control input119910 isin R119901 is the output 119908 isin R119903 are the disturbances and 119860119861 119862 119863 119865 and 119867 are matrices of appropriate dimensionsConsider a control problem described as follows Supposethe disturbances119908(119905) are measurable Given a desired outputsignal 119910ref(119905) design a control algorithm that guarantees119910(119905) rarr 119910ref(119905) as 119905 rarr +infin This problem was addressedin [14 15] in a very general setting In this work a simplecase is addressed where both 119910ref and 119908(119905) are assumed to beconstant signals 119910ref(119905) equiv 119910ref and119908(119905) equiv 119908119898 In this case thefollowing two conditions are necessary and sufficient for theexistence of a linear time-invariant controller that solves theabove described problem

(i) The pair (119860 119861) is stabilizable which means that

rank [119861 119860119861 1198602119861 119860119899minus1119861] = 119899 (24)

(ii) Consider

rank [119860 119861

119862 119865] = 119899 + 119901 (25)

If the above two conditions hold (and only in this case)the linear time-invariant controller that solves the abovedescribed problem is given according to the formula

119906 = 119870119909 +Gdagger119910ref +G

lowast119908119898 (26)

where 119870 isin R119899times119899 is the feedback gain matrix which is tobe chosen such that 119860 minus 119861119870 is stable and has the requireddynamic properties

G = minus119862(119860 minus 119861119870)minus1119861 (27)

Glowast= Gdagger119862(119860 minus 119861119870)

minus1119863 (28)

where Gdagger is the Moore-Penrose pseudoinverse of the matrixG in (27) defined by the formula

Gdagger= G119879(GG119879)minus1

(29)

The above described control approach can be applied tothe problem of stabilization of the angular velocity of drilling


as follows Equations (22) which describe the rotationaldynamics of a drilling system can be rewritten in the form(23) where 119909 = [1205961 120601 120596

2119868]119879

isin R4 119906 = 119881 isin R1119910 = 120596

1isin R1 119908 = 119879 isin R1 and the corresponding matrices

are

119860 =

[[[[[[[[[[[

[

minus1198881

1198691

119896

1198691

0 0

minus1 0 1 0

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]]]

]

119861 =

[[[[

[

0

0

01

119871

]]]]

]

119863 =

[[[[[

[

minus1

1198691

0

0

0

]]]]]

]

(30)

119862 = [1 0 0 0] 119865 = [0] 119867 = [0] (31)

Below we consider the drilling system with specific values ofthe parameters that are listed in Table 1With these values thematrices 119860 119861 and119863 become

119860 =

[[[[[

[

minus01123 12647 0 0

minus1 0 1 0

0 minus02231 minus02005 00204

0 0 minus8640 minus2

]]]]]

]

119861 =

[[[[[

[

0

0

0

200

]]]]]

]

119863 =

[[[[[

[

minus00027

0

0

0

]]]]]

]

(32)

while 119862 119865 and119867 are given by (31)For the above system the necessary and sufficient con-

ditions for stabilization (24) (25) are satisfied Indeed thestabilizability condition (24) is satisfied since

rank [119861 119860119861 1198602119861 119860119899minus1119861]

= rank[[[[[

[

0 0 0 5154273

0 0000000 4075472 minus8968

0 4075 minus8968 minus700339

200 minus400 minus34412 146307

]]]]]

]

= 4

(33)

Table 1 Numerical values for drilling system parameters

Parameter Description Value Unit1198691

BHA + drill string inertia 374 [kgm2]1198692

Rotary table + drive inertia 2120 [kgm2]1198881

BHA damping 42 [Nmsrad]1198882

Rotary table damping 425 [Nmsrad]119896 Drill string stiffness 473 [Nmrad]119877 Motor armature resistance 0010 [Ω]

119871 Motor armature inductance 0005 [H]119870 Motor constant 6 [Vs]

119899Combined gear ratio forbevel and gear box 72 mdash

119886 Drill bit radius 0108 [m]

120577Ratio of drilling strength todrilling specific energy 07 mdash

119872

Mass of drill string(28120Kg) + BHA(25080Kg)

53000 [kg]

119882119904minus 1198670

Submerged weight119882119904minus

applied weight from top ofthe Rig119867

0

100 or 1000 [N]

119870119891 Viscous friction coefficient 20 [Nmrad]

On the other hand the rank condition (25) is also satisfiedbecause

rank [119860 119861

119862 119865]

= rank

[[[[[[[

[

minus0112299 1264706 0 0 0

minus1 0 1 0 0

0 minus0223113 minus0200472 0020377 0

0 0 minus8640 minus2 200

1 0 0 0 0

]]]]]]]

]

= 5

(34)

Therefore a controller of the form (26) (27) (28) and (29)guarantees that the angular velocity of the drill approach thereference angular velocity 120596

1rarr 120596ref as 119905 rarr infin while

rejecting the disturbance 119879119887

The design of controller (26) (27) (28) and (29) beginsby choosing the desired location of the closed-loop systemrsquospoles For the purpose of simulations presented below weconsider two specific set of poles The first set denoted by 119875

1

is chosen as follows

1198751= [minus10 minus2 + 2119894 minus2 minus 2119894 minus4] (35)

The set 1198751consists of two real poles and two complex

conjugate poles On the other hand the set 1198752contains only

poles on the real axis as follows

1198752= [minus55 minus2 minus45 minus1] (36)


The feedback gain matrix 1198701such that the poles of 119860 minus 119861119870

1

are located according to 1198751is

1198701= [3224 5745 minus1941 00784] (37)

The coefficientsGlowastGdagger in (26) are calculated according to theformulas (27)ndash(29) the results are

Glowast

1= 0123497 G

dagger

1= 600844 (38)

On the other hand the feedbackmatrix1198702such that the poles

of 119860 minus 1198611198702are located according to 119875

2is

1198702= [minus5167 16943 minus3062 00534] (39)

The corresponding coefficientsGlowast2Gdagger2are

Glowast

2= 0037286 G

dagger

2= 9603682 (40)

33 Rock Stiffness Estimation In the controller design pre-sented above it was assumed that the ldquohardnessrdquo of the rockrepresented by the intrinsic specific energy 120598 is constant andexactly knownThis knowledge of 120598was used explicitly in thecontroller design in particular in formula (21) In practicalgeological drilling however the hardness of different layersof rock lying underneath the surface can be different andusually is not exactly known beforehand More specificallydifferent characteristics of the rock such as hardness densityand porosity typically remain constant through each layerbut differs from layer to layer On the other hand controlengineers frequently deal with the problem of designinga controller without a priori knowledge of the exact val-ues of one or more parameters involved in the processOften the processes can be robustly controlled without theactual knowledge of some of the parameters In other casesthe unknown parameters can be identified using speciallydesigned estimators Below a simple online estimator of therock intrinsic specific energy 120598 is designed following themethods described in [16] and the resulting estimate is thenused in the controller for for drilling system

Specifically during the cutting process the torque-on-bit 119879 is produced by bit rock interaction according to theformula

119879 =1

21198862120598119889 (41)

where 119886 is the radius of drill bit 119889 is the depth of cutand 120598 gt 0 is the intrinsic specific energy The intrinsicspecific energy 120598 gt 0 depends on the properties of themedia and typically unknownbeforehandHowever since thetorque on bit 119879(119905) can typically be measured with advancedtransducers located in the bottom hole assembly [17] 119886 gt 0is constant and known and 119889(119905) can be calculated accordingto formula (13) one can use the method described in theprevious section to design an online estimation scheme for120598 In particular considering (12)1198862119889(119905) as the input andtorque-on-bit 119879 as the measured output one can follow theprocedure described in the previous section to design anestimator for an unknown parameter 120598The predicted torque-on-bit

119887is defined according to the formula

(119905) =1

21198862120598119889 (119905) (42)

where 120598(119905) is the current estimate of actual rock strength 120598The algorithm for online estimation of the intrinsic specificenergy 120598 has a form

120598 = 1205740(119879 minus )

1

21198862119889 (43)

where 1205740gt 0 is an arbitrary gain

A natural question regarding the algorithm (43) is if itguarantees the convergence of the parameter estimate to thetrue value of the parameter 120598 mathematically is 120598(119905) rarr 120598

as 119905 rarr +infin It is known [16] that the convergence canbe guaranteed if the ldquoinputrdquo signal (12)1198862119889(119905) is persistentlyexciting A signal 119906(119905) is said to be persistently exciting whichis to say that there exist 120572

0gt 0119879

0gt 0 such that the inequality

int

119905+1198790

119905

1199062(120591) 119889120591 ge 120572

01198790

(44)

holds for all 119905 In particular 119906(119905) is persistently exciting if1199062(119905) ge 120572

0for all 119905 Since 119889(119905) is the depth of cut we see

that during normal cutting process 119889(119905) ge 1198890gt 0 which

results in persistent excitation of the input (12)1198862119889(119905) Theparameter convergence 120598(119905) rarr 120598 therefore is guaranteedduring normal cutting process This is also confirmed by thesimulation results presented below

The obtained estimate of the rock strength 120598 is thenused in the control algorithm Specifically in the originalformulation of the control algorithm for a given referencevertical velocity Vref the reference rotational velocity 120596ref iscalculated according to formula (21) which depends on theparameter 120598 In case 120598 is unknown it is substituted by itsestimate 120598(119905) obtained above The new formula for 120596ref hasthe form

120596ref =2120587119886120577120598

((119882119904minus 1198670) Vref) minus 119870119891

(45)

The obtained estimate of the rock stiffness 120598 will also beused to update the stiffness of the virtual spring in the hapticteleoperator drilling system described below

34 Simulation Results In this Section some results of sim-ulations of the drilling control system with intrinsic specificenergy estimator are presented The vertical motion of thedrilling system is described by (15) and it is interconnectedwith the rotational dynamics (5) through nonlinear equa-tion (13) that describes the depth of cut 119889(119905) For a givenreference velocity of the vertical penetration Vref gt 0 thecorresponding reference rotational velocity 120596ref is calculatedaccording to formula (45) The controller (21) (26)ndash(29) hasbeen implemented to guarantee that the angular velocityof the drill bits 120596

1(119905) tracks 120596ref which in turn stabilizes

the vertical penetration velocity V(119905) converges to Vref Thealgorithm (43) provides an estimate of the intrinsic specificenergy parameter 120598 which is then used in the calculationof the reference angular velocity according to formula (45)Specific values of the parameters appearing in these equationsare given in Table 1 The simulations are carried out usingMATLAB where the integration step for each simulation is


0 5 10 15 20 25012345

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

times10minus3

(a)

0 5 10 15 20 25Time (s)

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)

Actual stiffnessEstimated stiffness

times107

(b)

Figure 5 Response of the vertical velocity V(119905) (a) and the intrinsic specific energy estimate 120598(119905) (b) for 1198820= 5000N 120598 = 20MPa and

1205740= 5 sdot 10

9

0 5 10 15 20 25Time (s)

0

5

10

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)Ac

t an

d Es

t to

rque

-on

-bit

(N-m

)

Act torqueEst torque

(b)

34333231

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)

Figure 6 Response of rotational velocity 1205961(119905) (a) torque-on-bit 119879(119905) vresus estimated torque-on-bit (119905) (b) and the depth of cut 119889(119905) (c)

for1198820= 5000N 120598 = 20MPa and 120574

0= 5 sdot 10

9

equal to 0005 s The feedback gain matrix is chosen 119870 = 1198701

where1198701is defined by (37)

In the simulations described below the performanceof the system was evaluated for different values of actualintrinsic specific energy 120598 different gains 120574

0and different

values of the applied weight 1198820= 119882119904minus 1198670 Figures 5 and

6 show the response of the vertical penetration velocity V(119905)the intrinsic specific energy estimate 120598(119905) the torque-on-bit119879(119905) the predicted value of the torque-on-bit (119905) and therotational velocity 120596

1(119905) all for the case where the applied

weight on bit 1198820= 5000N the intrinsic specific energy

120598 = 20MPa and the desired vertical velocity Vref is set to0005ms The estimator gain is set to 120574

0= 5 sdot 10

9 The plotsshow that V(119905) converges to Vref in less than 8 sec whereasthe estimate 120598(119905) converges to the actual value of 120598 in lessthan 4 sec Figures 7 and 8 show the output responses ofdescribed parameters where 119882

0= 2500N and the desired

vertical velocity Vref is set to 001ms It can be clearly seen that

the convergence becomes slower with reducing the appliedweight on the drill string119882

0 specifically both V(119905) and 120598(119905)

approach their reference values in about 12 sec Reducing1198820also results in that 120596

1ref increases the steady-state valueof 119879119887(119905) drops to around 200N and the steady-state value

of 119889(119905) also drops to less than 2mm On the other handFigures 9 and 10 demonstrate the response of the system withthe same parameters except the intrinsic specific energy 120598is reduced to 5MPa This results in decreased convergencetime for V(119905) and 120598(119905) The steady state value of rotationalvelocity 120596

1(119905) is also decreased to under 10 rads and steady

state value of the depth of cut 119889(119905) is increased to 65mmFigures 11 and 12 present the output response for the casewhere the estimator gain is decreased to 120574

0= 5sdot10

8 while therest of the parameters are the same as in the last simulationexcept the intrinsic specific energy is set to 120598 = 10MPaThe resulting response is predictably characterized by muchslower convergence which takes about 25 sec for V(119905) and 120598(119905)


0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 5 10 15 20 25Time (s)

0

105

152

Intr

insic

spec

ific e

nerg

y (P

a)

Act stiffnessEst stiffness

times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 250

20

40

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

1234

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)

Figure 8 Response of rotational velocity 1205961(119905) (a) torque-on-bit 119879(119905) versus estimated torque-on-bit (119905) (b) and the depth of cut 119889(119905) (c)

for1198820= 2500N 120598 = 20MPa and 120574

0= 5 sdot 10

9

0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 05 1 15 2 25 3 35 4 45 5

012345

Intr

insic

spec

ific e

nerg

y (P

a)

Est stiffnessAct stiffness

times106

(b)


1205740= 5 sdot 10

9


0 5 10 150

5

10

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wout

Wref

(a)

0 105 15 2 25 3 35 4 45 50

100

200

Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

0 5 10 15 20 252468

Time (s)

Dep

th o

f cu

t (m

)times10minus3

(c)


for1198820= 2500N 120598 = 5MPa and 120574

0= 5 sdot 10

9

00002000400060008

0010012

Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

0 5 10 15 20 25 30 35 40 45 50Time (s)

Vout

Vref

(a)

0 5 10 15 20 25 30 35 40 45 5002

68

1012

4

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times106

(b)


1205740= 5 sdot 10

8

to approach their steady-state values Finally Figures 13 and14 correspond to to the case where119882

0= 5000N 120598 = 20MPa

and 1205740= 1 sdot 10

8Overall simulation results show that the control system

with intrinsic specific energy estimation demonstrate goodstability and performance characteristics for a wide range ofthe parameters In particular the vertical velocity convergesto the desired value and the estimate of the intrinsic specificenergy 120598(119905) converges to an actual value of 120598

4 Telerobotic Drilling System withHaptic Feedback

In this section a telerobotic drilling system with haptic feed-back is designed and experimentally evaluated Haptics canbe defined as the physical or virtual interaction through touchsensation for the purpose of perception and manipulation ofobjects [18 19] Haptic feedback provides the operator withkinaesthetic clues of the physical features of virtual or real

remote environment The structure of a telerobotic drillingsystem with haptic feedback is shown in Figure 15 In thissystem the human operator controls the drilling processusing a haptic device Specifically the position of an end-effector of the haptic device defines the reference verticalvelocity of the drilling The reference vertical velocity is thentransmitted to the drilling control system designed in abovein Section 3 which stabilizes the actual vertical penetrationvelocity to the level equal to the reference vertical velocityOn the other hand an estimate of the intrinsic specific energy120598(119905) which is generated online by an estimator describedin above in Section 33 is sent back to the haptic deviceThe end-effector of the haptic device interacts with a virtualspring of variable stiffness the stiffness of this virtual spring isupdated in real time proportionally to the current estimate ofthe intrinsic specific energy 120598(119905)Thus the telerobotic drillingsystem provides haptic feedback to the human operatorwhich creates an intuitive feeling of the hardness of theremotely drilled material


0 5 10 15 20 25 30 35 40 45 500

10

20

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wref

Wout

(a)

0

100

200

0 5 10 15 20 25 30 35 40 45 50Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

0 5 10 15 20 25 30 35 40 45 50Time (s)

times10minus3

Dep

th o

f cu

t (m

)

(c)


for1198820= 2500N 120598 = 10MPa and 120574

0= 5 sdot 10

8

0 50 100 1500

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 50 100 150

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)

Figure 13 Response of the vertical velocity V(119905) (a) and the intrinsic specific energy estimate 120598(119905) (b) for1198820= 2500N 120598 = 20MPa and

1205740= 108

41 Experimental Setup The above described teleroboticdrilling system is implemented in a semiexperimental setupas follows The setup consists of a PC based on Intel Pentium4 processor with operational frequency of 1 GHz and RAM of1GB and a PHANTOMOmni Haptic device a product fromSensAble Technologies Inc The PHANTOM Omni Hapticdevice is designed for kinematic interaction with the virtualor real environment while providing the kinesthetic feedbackto the operator The device is equipped with a pen-basedstylus and is able to provide three degrees-of-freedom forcefeedback The human operator uses the haptic device to (i)generate a desired vertical velocity Vref(119905) which is used asan input to the drilling control system and (ii) to hapticallyperceive the stiffness 120598 of the rock layersThe remaining partsof the above described telerobotic system including the drillstring and drive system the drilling process as well as thecontrol and estimation algorithms are simulated in real timein virtual environment which is implemented using theOpenHaptics tool kit and Microsoft Visual C++

The human operator assigns the desired velocity Vref(119905)by controlling the position of the end-effector of the PHAN-TOMdevice along its vertical (119884) axisMore exactly a specificrange along the 119910-axis is assigned to each desired verticalvelocity as follows

Vref(119905) = 0001ms if the position of stylus 119910119899(119905) is

ge80mmVref(119905) = 0003ms if the position of stylus 119910

119899(119905) is

le80mm and ge60mmVref(119905) = 0005ms if the position of stylus 119910

119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is

le10mm and ge0mm


0 50 100 1500

10

20

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0200400

0 50 100 150Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

Dep

th o

f cut

(m

)

0 50 100 150Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 108

Estimator

Controller

Virtual stiffness

Haptic device

R

refL

k

c2

c1

J2

J11205961

1205962

Tb

1 n

Figure 15 The structure of a telerobotic drilling system


le0mm

Another function of the haptic device is to allow thehuman operator to feel the stiffness of the rocks As explainedabove this is achieved by updating the stiffness of the virtualspring proportionally to the current estimate of the rockstiffness (intrinsic specific energy 120598(119905)) The coefficient ofproportionality between the estimate of the intrinsic specificenergy (with units of Pascals) and the stiffness of the virtualspring (with units of is Nm) is set in our experiments equalto 10minus7 The feedback force 119865est(119905) due to the virtual spring istherefore calculated according to the formula

119865est (119905) = 10minus7sdot 120598 (119905) sdot 119910

119899(119905) (46)

42 Experimental Results In this Section some experimen-tal results are presented In these experiments we have

attempted to simulate a real drilling case scenario where thecomposition characteristics and types (which all contributeto the intrinsic specific energy) of various rock strata vary atdifferent depths during drilling Specifically in every exper-iment several layers of rocks with different intrinsic specificenergy 120598 ranging from 4MPa to 60MPa are simulated In allexperiments presented here the applied weight119882

0= 5000N

the rest of the parameters if not explicitly mentioned aresame as in Section 34

In the experiment shown in Figures 16 17 and 18 threelayers of rocks with different intrinsic specific energy 120598 aresimulated The top layer has the stiffness of 5MPa and itsthickness is 20 cm from the surface The second layer has astiffness value of 12MPa and lies between 20 cm and 30 cmfrom the surface (total thickness is 10 cm) The third layerstarts at the depth of 30 cm and continues downward It hasa stiffness value of 20MPa The experiment is performedwith the estimator gain 120574

0= 10

9 Figure 16 shows the


0 10 20 30 40 50 60 70 80 900

105

215

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 900123

Time (s)

Estim

ated

fo

rce (

N)

(b)

Figure 16 Experiment 1 Actual stiffness 120598(119905) versus the estimated stiffness 120598(119905) (a) the reflected force 119865est(119905) (b)

0 10 20 30 40 50 60 70 80 900

02040608

112

Time (s)Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

VrefVout

times10minus2

(a)

0 10 20 30 40 50 60 70 80 90Time (s)

05

101520

Ang

veo

lcity

of

dril

l bit

(Rad

s)

WrefWout

(b)

Figure 17 Experiment 1 Output vertical velocity Vout(119905) versus reference vertical velocity Vref(119905) (a) output rotational velocity of the drill bit1205961(119905) versus reference rotational velocity 120596

1119889(119905) (b)

actual intrinsic specific energy 120598(119905) and its estimate 120598(119905) onthe top graph and the reflected force 119865est(119905) on the bottomgraph Due to high estimator gain 120598(119905) quickly tracks 120598(119905)for all three layers as the drill bit progressed cutting throughthese layers Figure 17 shows the vertical velocity Vout(119905) andthe reference vertical velocity Vref(119905) on the top graph andthe reference rotational velocity 120596

1119889(119905) and the actual drill

bit rotational velocity 1205961(119905) at the bottom graph Finally

Figure 18 shows the behaviour of the actual torque-on-bit119879(119905) and the estimated torque (119905) along with depth ofcut 119889(119905) These plots show that the system is stable anddemonstrates good performance in particular all the outputvariables track their desired (reference) trajectories

Another set of experimental results is presented in Fig-ures 19ndash21 where the estimator gain is increased to 120574

0= 5 sdot

109 and the depth of the rock layers and their corresponding

stiffness values have been altered Specifically the first rocklayer has depth 20 cm and the intrinsic specific energy 120598 isset to 20MPa for this layer Second layer lies between 20 cmand 40 cm with 120598 = 40MPaThe third layer lies below 40 cmand its intrinsic specific energy 120598 = 60MPa Figure 19 showsthe corresponding plots of 120598(119905) 120598(119905) and 119865est(119905) Figure 20shows the response of Vref(119905) and Vout(119905) on the top graphand the responses of 120596

1119889(119905) and 120596

1(119905) on the bottom graph

respectively The response of (119905) and 119879(119905) along with 119889(119905)are shown in Figure 21Overall our experiments demonstratestability and good performance of the designed teleroboticdrilling system with haptic feedback for a wide range ofparameters and control gains

5 Conclusions

This paper deals with control design for a teleoperator systemwith haptic feedback for an oil well drilling process Amathematical model of the drilling process was describedand the control algorithm was designed that guaranteesthe convergence of the vertical penetration velocity to anarbitrary reference value The control algorithm has a cas-caded structure where the velocity of vertical penetration iscontrolled indirectly through stabilization of the rotationalmotion of the drill bit In order to guarantee the convergenceof the angular velocity to a desired value in the presenceof disturbances in the form of torque-on-bit a robustservo controller was designed However the design of suchcontroller depends on the parameter of environment calledthe intrinsic specific energy which is generally unknownbeforehand To solve this issue an online parameter estimatorwas designed that provides an estimate of the intrinsic specificenergy This estimate is substituted for the actual value of theparameter in the control algorithm and the correspondingadaptive control system is evaluated through simulationsFinally a telerobotic drilling system with haptic feedback isdesigned and verified through semi-experiments The hapticfeedback for the human operator is provided by creatinga virtual spring that interacts with the haptic device thestiffness of the spring is adjusted in real time depending onthe current estimate of the intrinsic specific energy Semi-experiments are conducted using PHANTOM Omni Hapticdevice where the drilling process model is implemented


0 10 20 30 40 50 60 70 80 900

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)

Actual torqueEstimated torque

(a)

0 10 20 30 40 50 60 70 80 900

001002003

Time (s)

Dep

th o

f cut

(m)

(b)

Figure 18 Experiment 1 Torque-on-bit 119879(119905) versus estimated torque-on-bit (119905) (a) depth of cut 119889cut(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000246

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

05

1015

Estim

ated

fo

rce (

N)

(b)

Figure 19 Experiment 2 Actual stiffness 120598(119905) versus estimated stiffness 120598(119905) (a) reflected force 119865est(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

0005001

0015

Time (s)Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

020406080

100

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

00002000400060008

001

Dep

th o

f cut

(m)

(b)



in C++ environment and the haptic feedback is provided tothe human operator

There exists a number of challenges associated withthe real-life drilling operation that were not addressed inour paper In particular the frictional forces at the contactwere neglected in our analysis while in reality they mayplay significant role in the drilling process Also in real-lifedrilling systems the rotational velocity and the penetrationrate are typically measured at the surface while the torque-on-bit should ideally be measured above the bit thus thereexists a problem of synchronizing the data obtained atthe surface with those obtained at the bit The issue ofcommunication delay between the haptic device and thedrilling process is also not addressed These as well as moredetailed experimental evaluation of the designed system arethe topics for future research

Conflict of Interests

Theauthors of the paper do not have a direct financial relationwith the commercial identity mentioned in the paper thatmight lead to a conflict of interests for any of the authors

Acknowledgment

This work was supported by the Natural Sciences andEngineering Research Council (NSERC) of Canada underDiscovery Grant RGPIN1510

References

[1] P Corke J Roberts J Cunningham and D HainsworthldquoMining robotsrdquo in Springer Hand-Book of Robotics pp 1127ndash1150 Springer New York NY USA 1st edition 2007

[2] E Jackson andDClarke ldquoSubsea excavation of seafloormassivesuiphidesrdquo in Proceedings of the IEEE Oceans ConferenceVancouver Canada October 2007

[3] N Ridley S Graham and S Kapusniak ldquoSea oor productiontools for the resources of the futurerdquo in Proceedings of theOffshore Technology Conference Houston Tex USA May 2011

[4] M N Wendt and G A Einicke ldquoDevelopment of a water-hydraulic self-propelled robotic drill for underground miningrdquoin Field and Service Robotics vol 25 pp 355ndash366 Springer NewYork NY USA 2006

[5] G Baiden ldquoTelerobotic lunar habitat construction and mininga minerrsquos perspectiverdquo in Proceedings of the 9th InternationalSymposium on Artificial Intelligence Robotics and Automationfor Space (i-SAIRAS rsquo08) Los Angeles Calif USA 2008

[6] J Lee I Hwang K Kim S Choi W K Chung and Y S KimldquoCooperative robotic assistant with drill-by-wire end-effectorfor spinal fusion surgeryrdquo Industrial Robot vol 36 no 1 pp 60ndash72 2009

[7] B Glass H Cannon S Hanagud and J Frank ldquoDrillingautomation for subsurface planetary explorationrdquo in Proceed-ings of the 8th International Symposium on Artificial IntelligenceRobotics and Automation in Space (i-SAIRAS rsquo05) pp 205ndash209Munich Germany September 2005

[8] F Poletto and F Miranda SeismicWhile Drilling Fundamentalsof Drill-Bit Seismic For Exploration vol 35 ofHandbook of Geo-physical Exploration Seismic Exploration Elsevier San DiegoCalif USA 2004

[9] JD Jansen andL van den Steen ldquoActive damping of self-excitedtorsional vibrations in oil well drillstringsrdquo Journal of Sound andVibration vol 179 no 4 pp 647ndash668 1995

[10] T Richard C Germay and E Detournay ldquoSelf-excited stick-slip oscillations of drill bitsrdquo Comptes Rendus vol 332 no 8pp 619ndash626 2004

[11] T Richard CGermay and EDetournay ldquoA simplifiedmodel toexplore the root cause of stick-slip vibrations in drilling systemswith drag bitsrdquo Journal of Sound and Vibration vol 305 no 3pp 432ndash456 2007

[12] M Zamanian S E Khadem and M R Ghazavi ldquoStick-sliposcillations of drag bits by considering damping of drillingmudand active damping systemrdquo Journal of Petroleum Science andEngineering vol 59 no 3-4 pp 289ndash299 2007

[13] E Detournay T Richard and M Shepherd ldquoDrilling responseof drag bits theory and experimentrdquo International Journal ofRock Mechanics and Mining Sciences vol 45 no 8 pp 1347ndash1360 2008

[14] E J Davison ldquoThe feedforward control of linear multivariabletime-invariant systemsrdquo Automatica vol 9 no 5 pp 561ndash5731973

[15] E J Davison ldquoMultivariable tuning regulators the feedforwardand robust control of a general servomechanismproblemrdquo IEEETransactions on Automatic Control vol 21 no 1 pp 35ndash47 1976

[16] P A Ioannou and J SunRobust Adaptive Control PrenticeHallNew York NY USA 1996

[17] B P Peltier ldquoDrilling monitor with downhole torque and axialload transducersrdquo US Patent 4 695 957 September 1987

[18] T H Massie and J K Salisbury ldquoThe PHANTOM hapticinterface a device for probing virtual objectsrdquo in Proceedingsof the ASME Winter Annual Meeting Symposium on HapticInterfaces for Virtual Environment and Teleoperator Systems pp295ndash299 Chicago Ill USA November 1994

[19] K Salisbury F Conti and F Barbagli ldquoHaptic rendering intro-ductory conceptsrdquo IEEE Computer Graphics and Applicationsvol 24 no 2 pp 24ndash32 2004

International Journal of

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Control Scienceand Engineering

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Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


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Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



are designed which allow to achieve a desired rate of thevertical penetration regardless of the mechanical propertiesof the rock The control design includes an online parameterestimator of the intrinsic specific energy which is a parameterthat describes the hardness of the rock All these algorithmsare consequently used in the design of a telerobotic drillingsystem with virtual environment-based haptic feedback thatallows the human operator to feel the stiffness of the rock incontact with the drill bit Simulations and semiexperimentalresults are performed which confirm the validity of thetheoretical developments

The potential application domain of this research is notlimited to onshoreoffshore oil well drilling but the sameprinciples can be applied in particular to different typesof mining robots [1] telerobotic systems for dredging andmining ocean [2ndash5] surgical drilling [6] and teleroboticsystems for drilling the extraterrestrial terrain to discover andresearch the minerals and composition beneath [5 7]

The structure of the paper is as follows In Section 2 amathematical model of the drilling process is derived whichis subsequently used for the control design Section 3 dealswith the design of control algorithms for rotational and trans-lationalmotion of the drilling systems as well as the design ofan online parameter estimator of the intrinsic specific energyof the rock In Section 4 the structure of a telerobotic drillingsystem is described and the corresponding experimentalresults are presented Finally in Section 5 some conclusionsare given and possible future directions are formulated

2 Mathematical Model of Drilling System

In this section mathematical models that describe thedrilling system are presented Specifically the mathematicalmodel of drill string and drive system is described inSection 21 while the model of rock cutting and penetrationis the subject of Section 22

21 Mathematical Model of the Drill String and Drive SystemThe drill string is the assembly of rotating pipes which areresponsible for transmitting rotation and weight to the bitand bridge up a connection between the bottom hole tools[8] The components of a drill string along with drill pipesand the bottom hole assembly (BHA) are shown in Figure 1A number of simplified mathematical models for drill stringand drive systems were proposed in the literature such as[9ndash12] The model used in our work was developed in [9]This model describes the drill string as a simple torsionalpendulum where the drill pipes are represented as torsionalsprings and the bottom hole assembly is described as a rigidbody with inertia The model is based on the followingsimplifying assumptions

(1) The bottom hole assembly and the drill bits behavelike rigid bodies

(2) The moment of inertia of the drill pipe is consideredto be small in comparisonwith themoments of inertiaof the bottom hole assembly and the rotary table andtherefore neglected

DC

HWDP

Bit

BHA

Dril

l pip

e

Dril

l str

ing

Figure 1 Drill string components [8]

Gearboxand bevel gear

Jr

k

J1

c2

c1 minusTb

1206011

1206012

R

minus

+

V Motor

LI

Jm

Rotary table

Drill pipes

Drill collars

1 n

Figure 2 Representation of drill stringdrive system with mechan-ical and electrical components [9]

(3) The nonzero time propagation of the torsional forcedisturbances along the drill string is neglected Theforces assume to propagate instantaneously along thedrill string

Under the above described assumptions 1ndash3 the wholedrill string and drive system with equivalent electro-mechanical components can be represented by its structuraldiagram shown in Figure 2 This system is described by thefollowing mathematical model [9] First the motion of thedrill string is described by the following equation

11986911206011+ 11988811206011+ 119896 (120601

1minus 1206012) minus 119879 = 0 (1)







11986921206012+ 11988821206012minus 119896 (120601

1minus 1206012) minus 119899119879

119898= 0 (2)






119871 119868 + 119877119868 + 119881119887minus 119881 = 0 119881

119887= 119870 1206013= 119870119899 120601

2

119879119898= 119870119868

(3)


119887is the




[[[[[[[[

[

1206011

1

1206012

2

119868

]]]]]]]]

]

=

[[[[[[[[[[[[[

[

0 1 0 0 0

minus119896

1198691

minus1198881

1198691

119896

1198691

0 0

0 0 0 1 0

119896

1198692

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]]]]]

]

[[[[[[

[

1206011

1205961

1206012

1205962

119868

]]]]]]

]

+

[[[[[[[[[[

[

0

minus119879

1198691

0

0

119881

119871

]]]]]]]]]]

]

(4)

Here 1205961and 120596



1gt 0


2and 120601

1 In this case the


[[[[[

[

1

120601

2

119868

]]]]]

]

=

[[[[[[[[[[

[

minus1198881

1198691

119896

1198691

0 0

minus1 0 1 0

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]]

]

[[[[[

[

1205961

120601

1205962

119868

]]]]]

]

+

[[[[[[[[

[

minus119879

1198691

0

0

119881

119871

]]]]]]]]

]

(5)

Ω

zU(t minus tn)

U(t)

dn(t)


Φ(t)

1 2

985747n




119879119888=1

21198862120598119889 (6)

119882119888= 119886120577120598119889 (7)




119889 (119905) = 119899119889119899(119905) (8)




119889119899(119905) = 119880 (119905) minus 119880 (119905 minus 119905

119899) (9)





1(119905) in


120601 (119905) minus 120601 (119905 minus 119905119899) =

2120587

119899 (10)


1(120591) equiv 120601




119889 (119905) asymp 119899 sdot V (119905) sdot 119905119899 (11)

1205961(119905) sdot 119905119899asymp2120587

119899 (12)



119889 (119905) asymp2120587 sdot 119905 (119905)

1205961(119905)

(13)




1(119905) le 0



119889 (119905) asymp2120587 sdot V (119905)

max 1205961(119905) 1205980 (14)





119872119889V

119889119905= 119882119904minus119882 minus119867

0minus 119870119891V (15)


0is the constant



119904and





Vertical motion

Rotational motion

Cutting process

W(t)

V(t)

(t)

T(t)

d(t)

d(t)

d(t)

1205961(t)

W = a120577120598d

T =1

2a2120598d


3 Controller Design


1(119905) Both V(119905) and 120596





V = minus119870119891

119872V minus

(119882119904minus 1198670)

119872minus119882

119872 (16)


119882 = 1198861205771205982120587

1205961

V (17)





V =119882119904minus 1198670

119872minus1

119872(119886120577120598

2120587

1205961

+ 119870119891) V (18)



0


119882119904minus 1198670

119872minus1

119872(119886120577120598

2120587

1205961

+ 119870119891) V0= 0 (19)


V0=

119882119904minus 1198670

(119886120577120598 (21205871205961) + 119870119891) (20)





0from the range





119904minus 1198670)119870119891) the


120596ref =2120587119886120577120598

((119882119904minus 1198670) Vref) minus 119870119891

(21)





[[[

[

1

120601

2

119868

]]]

]

=

[[[[[[[[[

[

minus1198881

1198691

119896

1198691

0 0

minus1 0 1 0

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]

]

[[[

[

1205961

120601

1205962

119868

]]]

]

+

[[[[

[

0

0

01

119871

]]]]

]

119881 +

[[[[[

[

minus1

1198691

0

0

0

]]]]]

]

119879

(22)





= 119860119909 + 119861119906 + 119863119908

119910 = 119862119909 + 119865119906 + 119867119908(23)



rank [119861 119860119861 1198602119861 119860119899minus1119861] = 119899 (24)

(ii) Consider

rank [119860 119861

119862 119865] = 119899 + 119901 (25)


119906 = 119870119909 +Gdagger119910ref +G

lowast119908119898 (26)




minus1119863 (28)



(29)




2119868]119879

isin R4 119906 = 119881 isin R1119910 = 120596


are

119860 =

[[[[[[[[[[[

[

minus1198881

1198691

119896

1198691

0 0

minus1 0 1 0

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]]]

]

119861 =

[[[[

[

0

0

01

119871

]]]]

]

119863 =

[[[[[

[

minus1

1198691

0

0

0

]]]]]

]

(30)

119862 = [1 0 0 0] 119865 = [0] 119867 = [0] (31)


119860 =

[[[[[

[

minus01123 12647 0 0

minus1 0 1 0

0 minus02231 minus02005 00204


]]]]]

]

119861 =

[[[[[

[

0

0

0

200

]]]]]

]

119863 =

[[[[[

[

minus00027

0

0

0

]]]]]

]

(32)



rank [119861 119860119861 1198602119861 119860119899minus1119861]

= rank[[[[[

[

0 0 0 5154273

0 0000000 4075472 minus8968

0 4075 minus8968 minus700339

200 minus400 minus34412 146307

]]]]]

]

= 4

(33)











119872


53000 [kg]

119882119904minus 1198670



0

100 or 1000 [N]



rank [119860 119861

119862 119865]

= rank

[[[[[[[

[

minus0112299 1264706 0 0 0

minus1 0 1 0 0

0 minus0223113 minus0200472 0020377 0


1 0 0 0 0

]]]]]]]

]

= 5

(34)





1









1


1198701= [3224 5745 minus1941 00784] (37)


Glowast

1= 0123497 G

dagger

1= 600844 (38)



2is

1198702= [minus5167 16943 minus3062 00534] (39)


Glowast

2= 0037286 G

dagger

2= 9603682 (40)



119879 =1

21198862120598119889 (41)



(119905) =1

21198862120598119889 (119905) (42)


120598 = 1205740(119879 minus )

1

21198862119889 (43)




0gt 0119879


int

119905+1198790

119905

1199062(120591) 119889120591 ge 120572

01198790

(44)






120596ref =2120587119886120577120598

((119882119904minus 1198670) Vref) minus 119870119891

(45)






0 5 10 15 20 25012345

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

times10minus3

(a)

0 5 10 15 20 25Time (s)

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 25Time (s)

0

5

10

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)Ac

t an

d Es

t to

rque

-on

-bit

(N-m

)


(b)

34333231

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 5000N 120598 = 20MPa and 120574

0= 5 sdot 10

9




0and different






0= 5 sdot 10











0= 5sdot10



0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 5 10 15 20 25Time (s)

0

105

152

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 250

20

40

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

1234

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 5 sdot 10

9

0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 05 1 15 2 25 3 35 4 45 5

012345

Intr

insic

spec

ific e

nerg

y (P

a)


times106

(b)


1205740= 5 sdot 10

9


0 5 10 150

5

10

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wout

Wref

(a)

0 105 15 2 25 3 35 4 45 50

100

200

Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

0 5 10 15 20 252468

Time (s)

Dep

th o

f cu

t (m

)times10minus3

(c)


for1198820= 2500N 120598 = 5MPa and 120574

0= 5 sdot 10

9

00002000400060008

0010012

Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

0 5 10 15 20 25 30 35 40 45 50Time (s)

Vout

Vref

(a)

0 5 10 15 20 25 30 35 40 45 5002

68

1012

4

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times106

(b)


1205740= 5 sdot 10

8


0= 5000N 120598 = 20MPa

and 1205740= 1 sdot 10







0 5 10 15 20 25 30 35 40 45 500

10

20

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wref

Wout

(a)

0

100

200

0 5 10 15 20 25 30 35 40 45 50Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

0 5 10 15 20 25 30 35 40 45 50Time (s)

times10minus3

Dep

th o

f cu

t (m

)

(c)


for1198820= 2500N 120598 = 10MPa and 120574

0= 5 sdot 10

8

0 50 100 1500

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 50 100 150

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 108





119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is

le10mm and ge0mm


0 50 100 1500

10

20

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0200400

0 50 100 150Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

Dep

th o

f cut

(m

)

0 50 100 150Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 108

Estimator

Controller

Virtual stiffness

Haptic device

R

refL

k

c2

c1

J2

J11205961

1205962

Tb

1 n



le0mm



119899(119905) (46)



0= 5000N



0= 10



0 10 20 30 40 50 60 70 80 900

105

215

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 900123

Time (s)

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 900

02040608

112

Time (s)Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

VrefVout

times10minus2

(a)

0 10 20 30 40 50 60 70 80 90Time (s)

05

101520

Ang

veo

lcity

of

dril

l bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)






0= 5 sdot



1119889(119905) and 120596



5 Conclusions



0 10 20 30 40 50 60 70 80 900

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 900

001002003

Time (s)

Dep

th o

f cut

(m)

(b)


0 10 20 30 40 50 60 70 80 90 1000246

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

05

1015

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 90 1000

0005001

0015

Time (s)Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

020406080

100

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

00002000400060008

001

Dep

th o

f cut

(m)

(b)







Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















11986921206012+ 11988821206012minus 119896 (120601

1minus 1206012) minus 119899119879

119898= 0 (2)






119871 119868 + 119877119868 + 119881119887minus 119881 = 0 119881

119887= 119870 1206013= 119870119899 120601

2

119879119898= 119870119868

(3)


119887is the




[[[[[[[[

[

1206011

1

1206012

2

119868

]]]]]]]]

]

=

[[[[[[[[[[[[[

[

0 1 0 0 0

minus119896

1198691

minus1198881

1198691

119896

1198691

0 0

0 0 0 1 0

119896

1198692

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]]]]]

]

[[[[[[

[

1206011

1205961

1206012

1205962

119868

]]]]]]

]

+

[[[[[[[[[[

[

0

minus119879

1198691

0

0

119881

119871

]]]]]]]]]]

]

(4)

Here 1205961and 120596



1gt 0


2and 120601

1 In this case the


[[[[[

[

1

120601

2

119868

]]]]]

]

=

[[[[[[[[[[

[

minus1198881

1198691

119896

1198691

0 0

minus1 0 1 0

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]]

]

[[[[[

[

1205961

120601

1205962

119868

]]]]]

]

+

[[[[[[[[

[

minus119879

1198691

0

0

119881

119871

]]]]]]]]

]

(5)

Ω

zU(t minus tn)

U(t)

dn(t)


Φ(t)

1 2

985747n




119879119888=1

21198862120598119889 (6)

119882119888= 119886120577120598119889 (7)




119889 (119905) = 119899119889119899(119905) (8)




119889119899(119905) = 119880 (119905) minus 119880 (119905 minus 119905

119899) (9)





1(119905) in


120601 (119905) minus 120601 (119905 minus 119905119899) =

2120587

119899 (10)


1(120591) equiv 120601




119889 (119905) asymp 119899 sdot V (119905) sdot 119905119899 (11)

1205961(119905) sdot 119905119899asymp2120587

119899 (12)



119889 (119905) asymp2120587 sdot 119905 (119905)

1205961(119905)

(13)




1(119905) le 0



119889 (119905) asymp2120587 sdot V (119905)

max 1205961(119905) 1205980 (14)





119872119889V

119889119905= 119882119904minus119882 minus119867

0minus 119870119891V (15)


0is the constant



119904and





Vertical motion

Rotational motion

Cutting process

W(t)

V(t)

(t)

T(t)

d(t)

d(t)

d(t)

1205961(t)

W = a120577120598d

T =1

2a2120598d


3 Controller Design


1(119905) Both V(119905) and 120596





V = minus119870119891

119872V minus

(119882119904minus 1198670)

119872minus119882

119872 (16)


119882 = 1198861205771205982120587

1205961

V (17)





V =119882119904minus 1198670

119872minus1

119872(119886120577120598

2120587

1205961

+ 119870119891) V (18)



0


119882119904minus 1198670

119872minus1

119872(119886120577120598

2120587

1205961

+ 119870119891) V0= 0 (19)


V0=

119882119904minus 1198670

(119886120577120598 (21205871205961) + 119870119891) (20)





0from the range





119904minus 1198670)119870119891) the


120596ref =2120587119886120577120598

((119882119904minus 1198670) Vref) minus 119870119891

(21)





[[[

[

1

120601

2

119868

]]]

]

=

[[[[[[[[[

[

minus1198881

1198691

119896

1198691

0 0

minus1 0 1 0

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]

]

[[[

[

1205961

120601

1205962

119868

]]]

]

+

[[[[

[

0

0

01

119871

]]]]

]

119881 +

[[[[[

[

minus1

1198691

0

0

0

]]]]]

]

119879

(22)





= 119860119909 + 119861119906 + 119863119908

119910 = 119862119909 + 119865119906 + 119867119908(23)



rank [119861 119860119861 1198602119861 119860119899minus1119861] = 119899 (24)

(ii) Consider

rank [119860 119861

119862 119865] = 119899 + 119901 (25)


119906 = 119870119909 +Gdagger119910ref +G

lowast119908119898 (26)




minus1119863 (28)



(29)




2119868]119879

isin R4 119906 = 119881 isin R1119910 = 120596


are

119860 =

[[[[[[[[[[[

[

minus1198881

1198691

119896

1198691

0 0

minus1 0 1 0

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]]]

]

119861 =

[[[[

[

0

0

01

119871

]]]]

]

119863 =

[[[[[

[

minus1

1198691

0

0

0

]]]]]

]

(30)

119862 = [1 0 0 0] 119865 = [0] 119867 = [0] (31)


119860 =

[[[[[

[

minus01123 12647 0 0

minus1 0 1 0

0 minus02231 minus02005 00204


]]]]]

]

119861 =

[[[[[

[

0

0

0

200

]]]]]

]

119863 =

[[[[[

[

minus00027

0

0

0

]]]]]

]

(32)



rank [119861 119860119861 1198602119861 119860119899minus1119861]

= rank[[[[[

[

0 0 0 5154273

0 0000000 4075472 minus8968

0 4075 minus8968 minus700339

200 minus400 minus34412 146307

]]]]]

]

= 4

(33)











119872


53000 [kg]

119882119904minus 1198670



0

100 or 1000 [N]



rank [119860 119861

119862 119865]

= rank

[[[[[[[

[

minus0112299 1264706 0 0 0

minus1 0 1 0 0

0 minus0223113 minus0200472 0020377 0


1 0 0 0 0

]]]]]]]

]

= 5

(34)





1









1


1198701= [3224 5745 minus1941 00784] (37)


Glowast

1= 0123497 G

dagger

1= 600844 (38)



2is

1198702= [minus5167 16943 minus3062 00534] (39)


Glowast

2= 0037286 G

dagger

2= 9603682 (40)



119879 =1

21198862120598119889 (41)



(119905) =1

21198862120598119889 (119905) (42)


120598 = 1205740(119879 minus )

1

21198862119889 (43)




0gt 0119879


int

119905+1198790

119905

1199062(120591) 119889120591 ge 120572

01198790

(44)






120596ref =2120587119886120577120598

((119882119904minus 1198670) Vref) minus 119870119891

(45)






0 5 10 15 20 25012345

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

times10minus3

(a)

0 5 10 15 20 25Time (s)

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 25Time (s)

0

5

10

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)Ac

t an

d Es

t to

rque

-on

-bit

(N-m

)


(b)

34333231

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 5000N 120598 = 20MPa and 120574

0= 5 sdot 10

9




0and different






0= 5 sdot 10











0= 5sdot10



0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 5 10 15 20 25Time (s)

0

105

152

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 250

20

40

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

1234

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 5 sdot 10

9

0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 05 1 15 2 25 3 35 4 45 5

012345

Intr

insic

spec

ific e

nerg

y (P

a)


times106

(b)


1205740= 5 sdot 10

9


0 5 10 150

5

10

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wout

Wref

(a)

0 105 15 2 25 3 35 4 45 50

100

200

Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

0 5 10 15 20 252468

Time (s)

Dep

th o

f cu

t (m

)times10minus3

(c)


for1198820= 2500N 120598 = 5MPa and 120574

0= 5 sdot 10

9

00002000400060008

0010012

Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

0 5 10 15 20 25 30 35 40 45 50Time (s)

Vout

Vref

(a)

0 5 10 15 20 25 30 35 40 45 5002

68

1012

4

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times106

(b)


1205740= 5 sdot 10

8


0= 5000N 120598 = 20MPa

and 1205740= 1 sdot 10







0 5 10 15 20 25 30 35 40 45 500

10

20

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wref

Wout

(a)

0

100

200

0 5 10 15 20 25 30 35 40 45 50Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

0 5 10 15 20 25 30 35 40 45 50Time (s)

times10minus3

Dep

th o

f cu

t (m

)

(c)


for1198820= 2500N 120598 = 10MPa and 120574

0= 5 sdot 10

8

0 50 100 1500

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 50 100 150

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 108





119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is

le10mm and ge0mm


0 50 100 1500

10

20

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0200400

0 50 100 150Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

Dep

th o

f cut

(m

)

0 50 100 150Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 108

Estimator

Controller

Virtual stiffness

Haptic device

R

refL

k

c2

c1

J2

J11205961

1205962

Tb

1 n



le0mm



119899(119905) (46)



0= 5000N



0= 10



0 10 20 30 40 50 60 70 80 900

105

215

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 900123

Time (s)

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 900

02040608

112

Time (s)Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

VrefVout

times10minus2

(a)

0 10 20 30 40 50 60 70 80 90Time (s)

05

101520

Ang

veo

lcity

of

dril

l bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)






0= 5 sdot



1119889(119905) and 120596



5 Conclusions



0 10 20 30 40 50 60 70 80 900

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 900

001002003

Time (s)

Dep

th o

f cut

(m)

(b)


0 10 20 30 40 50 60 70 80 90 1000246

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

05

1015

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 90 1000

0005001

0015

Time (s)Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

020406080

100

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

00002000400060008

001

Dep

th o

f cut

(m)

(b)







Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119889119899(119905) = 119880 (119905) minus 119880 (119905 minus 119905

119899) (9)





1(119905) in


120601 (119905) minus 120601 (119905 minus 119905119899) =

2120587

119899 (10)


1(120591) equiv 120601




119889 (119905) asymp 119899 sdot V (119905) sdot 119905119899 (11)

1205961(119905) sdot 119905119899asymp2120587

119899 (12)



119889 (119905) asymp2120587 sdot 119905 (119905)

1205961(119905)

(13)




1(119905) le 0



119889 (119905) asymp2120587 sdot V (119905)

max 1205961(119905) 1205980 (14)





119872119889V

119889119905= 119882119904minus119882 minus119867

0minus 119870119891V (15)


0is the constant



119904and





Vertical motion

Rotational motion

Cutting process

W(t)

V(t)

(t)

T(t)

d(t)

d(t)

d(t)

1205961(t)

W = a120577120598d

T =1

2a2120598d


3 Controller Design


1(119905) Both V(119905) and 120596





V = minus119870119891

119872V minus

(119882119904minus 1198670)

119872minus119882

119872 (16)


119882 = 1198861205771205982120587

1205961

V (17)





V =119882119904minus 1198670

119872minus1

119872(119886120577120598

2120587

1205961

+ 119870119891) V (18)



0


119882119904minus 1198670

119872minus1

119872(119886120577120598

2120587

1205961

+ 119870119891) V0= 0 (19)


V0=

119882119904minus 1198670

(119886120577120598 (21205871205961) + 119870119891) (20)





0from the range





119904minus 1198670)119870119891) the


120596ref =2120587119886120577120598

((119882119904minus 1198670) Vref) minus 119870119891

(21)





[[[

[

1

120601

2

119868

]]]

]

=

[[[[[[[[[

[

minus1198881

1198691

119896

1198691

0 0

minus1 0 1 0

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]

]

[[[

[

1205961

120601

1205962

119868

]]]

]

+

[[[[

[

0

0

01

119871

]]]]

]

119881 +

[[[[[

[

minus1

1198691

0

0

0

]]]]]

]

119879

(22)





= 119860119909 + 119861119906 + 119863119908

119910 = 119862119909 + 119865119906 + 119867119908(23)



rank [119861 119860119861 1198602119861 119860119899minus1119861] = 119899 (24)

(ii) Consider

rank [119860 119861

119862 119865] = 119899 + 119901 (25)


119906 = 119870119909 +Gdagger119910ref +G

lowast119908119898 (26)




minus1119863 (28)



(29)




2119868]119879

isin R4 119906 = 119881 isin R1119910 = 120596


are

119860 =

[[[[[[[[[[[

[

minus1198881

1198691

119896

1198691

0 0

minus1 0 1 0

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]]]

]

119861 =

[[[[

[

0

0

01

119871

]]]]

]

119863 =

[[[[[

[

minus1

1198691

0

0

0

]]]]]

]

(30)

119862 = [1 0 0 0] 119865 = [0] 119867 = [0] (31)


119860 =

[[[[[

[

minus01123 12647 0 0

minus1 0 1 0

0 minus02231 minus02005 00204


]]]]]

]

119861 =

[[[[[

[

0

0

0

200

]]]]]

]

119863 =

[[[[[

[

minus00027

0

0

0

]]]]]

]

(32)



rank [119861 119860119861 1198602119861 119860119899minus1119861]

= rank[[[[[

[

0 0 0 5154273

0 0000000 4075472 minus8968

0 4075 minus8968 minus700339

200 minus400 minus34412 146307

]]]]]

]

= 4

(33)











119872


53000 [kg]

119882119904minus 1198670



0

100 or 1000 [N]



rank [119860 119861

119862 119865]

= rank

[[[[[[[

[

minus0112299 1264706 0 0 0

minus1 0 1 0 0

0 minus0223113 minus0200472 0020377 0


1 0 0 0 0

]]]]]]]

]

= 5

(34)





1









1


1198701= [3224 5745 minus1941 00784] (37)


Glowast

1= 0123497 G

dagger

1= 600844 (38)



2is

1198702= [minus5167 16943 minus3062 00534] (39)


Glowast

2= 0037286 G

dagger

2= 9603682 (40)



119879 =1

21198862120598119889 (41)



(119905) =1

21198862120598119889 (119905) (42)


120598 = 1205740(119879 minus )

1

21198862119889 (43)




0gt 0119879


int

119905+1198790

119905

1199062(120591) 119889120591 ge 120572

01198790

(44)






120596ref =2120587119886120577120598

((119882119904minus 1198670) Vref) minus 119870119891

(45)






0 5 10 15 20 25012345

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

times10minus3

(a)

0 5 10 15 20 25Time (s)

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 25Time (s)

0

5

10

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)Ac

t an

d Es

t to

rque

-on

-bit

(N-m

)


(b)

34333231

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 5000N 120598 = 20MPa and 120574

0= 5 sdot 10

9




0and different






0= 5 sdot 10











0= 5sdot10



0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 5 10 15 20 25Time (s)

0

105

152

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 250

20

40

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

1234

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 5 sdot 10

9

0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 05 1 15 2 25 3 35 4 45 5

012345

Intr

insic

spec

ific e

nerg

y (P

a)


times106

(b)


1205740= 5 sdot 10

9


0 5 10 150

5

10

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wout

Wref

(a)

0 105 15 2 25 3 35 4 45 50

100

200

Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

0 5 10 15 20 252468

Time (s)

Dep

th o

f cu

t (m

)times10minus3

(c)


for1198820= 2500N 120598 = 5MPa and 120574

0= 5 sdot 10

9

00002000400060008

0010012

Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

0 5 10 15 20 25 30 35 40 45 50Time (s)

Vout

Vref

(a)

0 5 10 15 20 25 30 35 40 45 5002

68

1012

4

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times106

(b)


1205740= 5 sdot 10

8


0= 5000N 120598 = 20MPa

and 1205740= 1 sdot 10







0 5 10 15 20 25 30 35 40 45 500

10

20

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wref

Wout

(a)

0

100

200

0 5 10 15 20 25 30 35 40 45 50Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

0 5 10 15 20 25 30 35 40 45 50Time (s)

times10minus3

Dep

th o

f cu

t (m

)

(c)


for1198820= 2500N 120598 = 10MPa and 120574

0= 5 sdot 10

8

0 50 100 1500

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 50 100 150

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 108





119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is

le10mm and ge0mm


0 50 100 1500

10

20

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0200400

0 50 100 150Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

Dep

th o

f cut

(m

)

0 50 100 150Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 108

Estimator

Controller

Virtual stiffness

Haptic device

R

refL

k

c2

c1

J2

J11205961

1205962

Tb

1 n



le0mm



119899(119905) (46)



0= 5000N



0= 10



0 10 20 30 40 50 60 70 80 900

105

215

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 900123

Time (s)

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 900

02040608

112

Time (s)Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

VrefVout

times10minus2

(a)

0 10 20 30 40 50 60 70 80 90Time (s)

05

101520

Ang

veo

lcity

of

dril

l bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)






0= 5 sdot



1119889(119905) and 120596



5 Conclusions



0 10 20 30 40 50 60 70 80 900

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 900

001002003

Time (s)

Dep

th o

f cut

(m)

(b)


0 10 20 30 40 50 60 70 80 90 1000246

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

05

1015

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 90 1000

0005001

0015

Time (s)Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

020406080

100

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

00002000400060008

001

Dep

th o

f cut

(m)

(b)







Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












V =119882119904minus 1198670

119872minus1

119872(119886120577120598

2120587

1205961

+ 119870119891) V (18)



0


119882119904minus 1198670

119872minus1

119872(119886120577120598

2120587

1205961

+ 119870119891) V0= 0 (19)


V0=

119882119904minus 1198670

(119886120577120598 (21205871205961) + 119870119891) (20)





0from the range





119904minus 1198670)119870119891) the


120596ref =2120587119886120577120598

((119882119904minus 1198670) Vref) minus 119870119891

(21)





[[[

[

1

120601

2

119868

]]]

]

=

[[[[[[[[[

[

minus1198881

1198691

119896

1198691

0 0

minus1 0 1 0

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]

]

[[[

[

1205961

120601

1205962

119868

]]]

]

+

[[[[

[

0

0

01

119871

]]]]

]

119881 +

[[[[[

[

minus1

1198691

0

0

0

]]]]]

]

119879

(22)





= 119860119909 + 119861119906 + 119863119908

119910 = 119862119909 + 119865119906 + 119867119908(23)



rank [119861 119860119861 1198602119861 119860119899minus1119861] = 119899 (24)

(ii) Consider

rank [119860 119861

119862 119865] = 119899 + 119901 (25)


119906 = 119870119909 +Gdagger119910ref +G

lowast119908119898 (26)




minus1119863 (28)



(29)




2119868]119879

isin R4 119906 = 119881 isin R1119910 = 120596


are

119860 =

[[[[[[[[[[[

[

minus1198881

1198691

119896

1198691

0 0

minus1 0 1 0

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]]]

]

119861 =

[[[[

[

0

0

01

119871

]]]]

]

119863 =

[[[[[

[

minus1

1198691

0

0

0

]]]]]

]

(30)

119862 = [1 0 0 0] 119865 = [0] 119867 = [0] (31)


119860 =

[[[[[

[

minus01123 12647 0 0

minus1 0 1 0

0 minus02231 minus02005 00204


]]]]]

]

119861 =

[[[[[

[

0

0

0

200

]]]]]

]

119863 =

[[[[[

[

minus00027

0

0

0

]]]]]

]

(32)



rank [119861 119860119861 1198602119861 119860119899minus1119861]

= rank[[[[[

[

0 0 0 5154273

0 0000000 4075472 minus8968

0 4075 minus8968 minus700339

200 minus400 minus34412 146307

]]]]]

]

= 4

(33)











119872


53000 [kg]

119882119904minus 1198670



0

100 or 1000 [N]



rank [119860 119861

119862 119865]

= rank

[[[[[[[

[

minus0112299 1264706 0 0 0

minus1 0 1 0 0

0 minus0223113 minus0200472 0020377 0


1 0 0 0 0

]]]]]]]

]

= 5

(34)





1









1


1198701= [3224 5745 minus1941 00784] (37)


Glowast

1= 0123497 G

dagger

1= 600844 (38)



2is

1198702= [minus5167 16943 minus3062 00534] (39)


Glowast

2= 0037286 G

dagger

2= 9603682 (40)



119879 =1

21198862120598119889 (41)



(119905) =1

21198862120598119889 (119905) (42)


120598 = 1205740(119879 minus )

1

21198862119889 (43)




0gt 0119879


int

119905+1198790

119905

1199062(120591) 119889120591 ge 120572

01198790

(44)






120596ref =2120587119886120577120598

((119882119904minus 1198670) Vref) minus 119870119891

(45)






0 5 10 15 20 25012345

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

times10minus3

(a)

0 5 10 15 20 25Time (s)

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 25Time (s)

0

5

10

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)Ac

t an

d Es

t to

rque

-on

-bit

(N-m

)


(b)

34333231

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 5000N 120598 = 20MPa and 120574

0= 5 sdot 10

9




0and different






0= 5 sdot 10











0= 5sdot10



0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 5 10 15 20 25Time (s)

0

105

152

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 250

20

40

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

1234

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 5 sdot 10

9

0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 05 1 15 2 25 3 35 4 45 5

012345

Intr

insic

spec

ific e

nerg

y (P

a)


times106

(b)


1205740= 5 sdot 10

9


0 5 10 150

5

10

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wout

Wref

(a)

0 105 15 2 25 3 35 4 45 50

100

200

Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

0 5 10 15 20 252468

Time (s)

Dep

th o

f cu

t (m

)times10minus3

(c)


for1198820= 2500N 120598 = 5MPa and 120574

0= 5 sdot 10

9

00002000400060008

0010012

Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

0 5 10 15 20 25 30 35 40 45 50Time (s)

Vout

Vref

(a)

0 5 10 15 20 25 30 35 40 45 5002

68

1012

4

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times106

(b)


1205740= 5 sdot 10

8


0= 5000N 120598 = 20MPa

and 1205740= 1 sdot 10







0 5 10 15 20 25 30 35 40 45 500

10

20

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wref

Wout

(a)

0

100

200

0 5 10 15 20 25 30 35 40 45 50Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

0 5 10 15 20 25 30 35 40 45 50Time (s)

times10minus3

Dep

th o

f cu

t (m

)

(c)


for1198820= 2500N 120598 = 10MPa and 120574

0= 5 sdot 10

8

0 50 100 1500

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 50 100 150

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 108





119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is

le10mm and ge0mm


0 50 100 1500

10

20

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0200400

0 50 100 150Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

Dep

th o

f cut

(m

)

0 50 100 150Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 108

Estimator

Controller

Virtual stiffness

Haptic device

R

refL

k

c2

c1

J2

J11205961

1205962

Tb

1 n



le0mm



119899(119905) (46)



0= 5000N



0= 10



0 10 20 30 40 50 60 70 80 900

105

215

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 900123

Time (s)

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 900

02040608

112

Time (s)Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

VrefVout

times10minus2

(a)

0 10 20 30 40 50 60 70 80 90Time (s)

05

101520

Ang

veo

lcity

of

dril

l bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)






0= 5 sdot



1119889(119905) and 120596



5 Conclusions



0 10 20 30 40 50 60 70 80 900

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 900

001002003

Time (s)

Dep

th o

f cut

(m)

(b)


0 10 20 30 40 50 60 70 80 90 1000246

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

05

1015

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 90 1000

0005001

0015

Time (s)Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

020406080

100

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

00002000400060008

001

Dep

th o

f cut

(m)

(b)







Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











2119868]119879

isin R4 119906 = 119881 isin R1119910 = 120596


are

119860 =

[[[[[[[[[[[

[

minus1198881

1198691

119896

1198691

0 0

minus1 0 1 0

0minus119896

1198692

minus1198882

1198692

119870119899

1198692

0 0minus119870119899

119871

minus119877

119871

]]]]]]]]]]]

]

119861 =

[[[[

[

0

0

01

119871

]]]]

]

119863 =

[[[[[

[

minus1

1198691

0

0

0

]]]]]

]

(30)

119862 = [1 0 0 0] 119865 = [0] 119867 = [0] (31)


119860 =

[[[[[

[

minus01123 12647 0 0

minus1 0 1 0

0 minus02231 minus02005 00204


]]]]]

]

119861 =

[[[[[

[

0

0

0

200

]]]]]

]

119863 =

[[[[[

[

minus00027

0

0

0

]]]]]

]

(32)



rank [119861 119860119861 1198602119861 119860119899minus1119861]

= rank[[[[[

[

0 0 0 5154273

0 0000000 4075472 minus8968

0 4075 minus8968 minus700339

200 minus400 minus34412 146307

]]]]]

]

= 4

(33)











119872


53000 [kg]

119882119904minus 1198670



0

100 or 1000 [N]



rank [119860 119861

119862 119865]

= rank

[[[[[[[

[

minus0112299 1264706 0 0 0

minus1 0 1 0 0

0 minus0223113 minus0200472 0020377 0


1 0 0 0 0

]]]]]]]

]

= 5

(34)





1









1


1198701= [3224 5745 minus1941 00784] (37)


Glowast

1= 0123497 G

dagger

1= 600844 (38)



2is

1198702= [minus5167 16943 minus3062 00534] (39)


Glowast

2= 0037286 G

dagger

2= 9603682 (40)



119879 =1

21198862120598119889 (41)



(119905) =1

21198862120598119889 (119905) (42)


120598 = 1205740(119879 minus )

1

21198862119889 (43)




0gt 0119879


int

119905+1198790

119905

1199062(120591) 119889120591 ge 120572

01198790

(44)






120596ref =2120587119886120577120598

((119882119904minus 1198670) Vref) minus 119870119891

(45)






0 5 10 15 20 25012345

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

times10minus3

(a)

0 5 10 15 20 25Time (s)

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 25Time (s)

0

5

10

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)Ac

t an

d Es

t to

rque

-on

-bit

(N-m

)


(b)

34333231

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 5000N 120598 = 20MPa and 120574

0= 5 sdot 10

9




0and different






0= 5 sdot 10











0= 5sdot10



0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 5 10 15 20 25Time (s)

0

105

152

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 250

20

40

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

1234

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 5 sdot 10

9

0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 05 1 15 2 25 3 35 4 45 5

012345

Intr

insic

spec

ific e

nerg

y (P

a)


times106

(b)


1205740= 5 sdot 10

9


0 5 10 150

5

10

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wout

Wref

(a)

0 105 15 2 25 3 35 4 45 50

100

200

Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

0 5 10 15 20 252468

Time (s)

Dep

th o

f cu

t (m

)times10minus3

(c)


for1198820= 2500N 120598 = 5MPa and 120574

0= 5 sdot 10

9

00002000400060008

0010012

Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

0 5 10 15 20 25 30 35 40 45 50Time (s)

Vout

Vref

(a)

0 5 10 15 20 25 30 35 40 45 5002

68

1012

4

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times106

(b)


1205740= 5 sdot 10

8


0= 5000N 120598 = 20MPa

and 1205740= 1 sdot 10







0 5 10 15 20 25 30 35 40 45 500

10

20

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wref

Wout

(a)

0

100

200

0 5 10 15 20 25 30 35 40 45 50Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

0 5 10 15 20 25 30 35 40 45 50Time (s)

times10minus3

Dep

th o

f cu

t (m

)

(c)


for1198820= 2500N 120598 = 10MPa and 120574

0= 5 sdot 10

8

0 50 100 1500

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 50 100 150

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 108





119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is

le10mm and ge0mm


0 50 100 1500

10

20

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0200400

0 50 100 150Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

Dep

th o

f cut

(m

)

0 50 100 150Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 108

Estimator

Controller

Virtual stiffness

Haptic device

R

refL

k

c2

c1

J2

J11205961

1205962

Tb

1 n



le0mm



119899(119905) (46)



0= 5000N



0= 10



0 10 20 30 40 50 60 70 80 900

105

215

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 900123

Time (s)

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 900

02040608

112

Time (s)Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

VrefVout

times10minus2

(a)

0 10 20 30 40 50 60 70 80 90Time (s)

05

101520

Ang

veo

lcity

of

dril

l bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)






0= 5 sdot



1119889(119905) and 120596



5 Conclusions



0 10 20 30 40 50 60 70 80 900

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 900

001002003

Time (s)

Dep

th o

f cut

(m)

(b)


0 10 20 30 40 50 60 70 80 90 1000246

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

05

1015

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 90 1000

0005001

0015

Time (s)Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

020406080

100

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

00002000400060008

001

Dep

th o

f cut

(m)

(b)







Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1


1198701= [3224 5745 minus1941 00784] (37)


Glowast

1= 0123497 G

dagger

1= 600844 (38)



2is

1198702= [minus5167 16943 minus3062 00534] (39)


Glowast

2= 0037286 G

dagger

2= 9603682 (40)



119879 =1

21198862120598119889 (41)



(119905) =1

21198862120598119889 (119905) (42)


120598 = 1205740(119879 minus )

1

21198862119889 (43)




0gt 0119879


int

119905+1198790

119905

1199062(120591) 119889120591 ge 120572

01198790

(44)






120596ref =2120587119886120577120598

((119882119904minus 1198670) Vref) minus 119870119891

(45)






0 5 10 15 20 25012345

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

times10minus3

(a)

0 5 10 15 20 25Time (s)

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 25Time (s)

0

5

10

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)Ac

t an

d Es

t to

rque

-on

-bit

(N-m

)


(b)

34333231

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 5000N 120598 = 20MPa and 120574

0= 5 sdot 10

9




0and different






0= 5 sdot 10











0= 5sdot10



0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 5 10 15 20 25Time (s)

0

105

152

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 250

20

40

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

1234

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 5 sdot 10

9

0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 05 1 15 2 25 3 35 4 45 5

012345

Intr

insic

spec

ific e

nerg

y (P

a)


times106

(b)


1205740= 5 sdot 10

9


0 5 10 150

5

10

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wout

Wref

(a)

0 105 15 2 25 3 35 4 45 50

100

200

Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

0 5 10 15 20 252468

Time (s)

Dep

th o

f cu

t (m

)times10minus3

(c)


for1198820= 2500N 120598 = 5MPa and 120574

0= 5 sdot 10

9

00002000400060008

0010012

Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

0 5 10 15 20 25 30 35 40 45 50Time (s)

Vout

Vref

(a)

0 5 10 15 20 25 30 35 40 45 5002

68

1012

4

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times106

(b)


1205740= 5 sdot 10

8


0= 5000N 120598 = 20MPa

and 1205740= 1 sdot 10







0 5 10 15 20 25 30 35 40 45 500

10

20

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wref

Wout

(a)

0

100

200

0 5 10 15 20 25 30 35 40 45 50Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

0 5 10 15 20 25 30 35 40 45 50Time (s)

times10minus3

Dep

th o

f cu

t (m

)

(c)


for1198820= 2500N 120598 = 10MPa and 120574

0= 5 sdot 10

8

0 50 100 1500

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 50 100 150

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 108





119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is

le10mm and ge0mm


0 50 100 1500

10

20

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0200400

0 50 100 150Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

Dep

th o

f cut

(m

)

0 50 100 150Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 108

Estimator

Controller

Virtual stiffness

Haptic device

R

refL

k

c2

c1

J2

J11205961

1205962

Tb

1 n



le0mm



119899(119905) (46)



0= 5000N



0= 10



0 10 20 30 40 50 60 70 80 900

105

215

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 900123

Time (s)

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 900

02040608

112

Time (s)Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

VrefVout

times10minus2

(a)

0 10 20 30 40 50 60 70 80 90Time (s)

05

101520

Ang

veo

lcity

of

dril

l bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)






0= 5 sdot



1119889(119905) and 120596



5 Conclusions



0 10 20 30 40 50 60 70 80 900

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 900

001002003

Time (s)

Dep

th o

f cut

(m)

(b)


0 10 20 30 40 50 60 70 80 90 1000246

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

05

1015

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 90 1000

0005001

0015

Time (s)Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

020406080

100

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

00002000400060008

001

Dep

th o

f cut

(m)

(b)







Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15 20 25012345

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

times10minus3

(a)

0 5 10 15 20 25Time (s)

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 25Time (s)

0

5

10

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)Ac

t an

d Es

t to

rque

-on

-bit

(N-m

)


(b)

34333231

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 5000N 120598 = 20MPa and 120574

0= 5 sdot 10

9




0and different






0= 5 sdot 10











0= 5sdot10



0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 5 10 15 20 25Time (s)

0

105

152

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 250

20

40

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

1234

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 5 sdot 10

9

0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 05 1 15 2 25 3 35 4 45 5

012345

Intr

insic

spec

ific e

nerg

y (P

a)


times106

(b)


1205740= 5 sdot 10

9


0 5 10 150

5

10

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wout

Wref

(a)

0 105 15 2 25 3 35 4 45 50

100

200

Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

0 5 10 15 20 252468

Time (s)

Dep

th o

f cu

t (m

)times10minus3

(c)


for1198820= 2500N 120598 = 5MPa and 120574

0= 5 sdot 10

9

00002000400060008

0010012

Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

0 5 10 15 20 25 30 35 40 45 50Time (s)

Vout

Vref

(a)

0 5 10 15 20 25 30 35 40 45 5002

68

1012

4

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times106

(b)


1205740= 5 sdot 10

8


0= 5000N 120598 = 20MPa

and 1205740= 1 sdot 10







0 5 10 15 20 25 30 35 40 45 500

10

20

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wref

Wout

(a)

0

100

200

0 5 10 15 20 25 30 35 40 45 50Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

0 5 10 15 20 25 30 35 40 45 50Time (s)

times10minus3

Dep

th o

f cu

t (m

)

(c)


for1198820= 2500N 120598 = 10MPa and 120574

0= 5 sdot 10

8

0 50 100 1500

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 50 100 150

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 108





119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is

le10mm and ge0mm


0 50 100 1500

10

20

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0200400

0 50 100 150Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

Dep

th o

f cut

(m

)

0 50 100 150Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 108

Estimator

Controller

Virtual stiffness

Haptic device

R

refL

k

c2

c1

J2

J11205961

1205962

Tb

1 n



le0mm



119899(119905) (46)



0= 5000N



0= 10



0 10 20 30 40 50 60 70 80 900

105

215

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 900123

Time (s)

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 900

02040608

112

Time (s)Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

VrefVout

times10minus2

(a)

0 10 20 30 40 50 60 70 80 90Time (s)

05

101520

Ang

veo

lcity

of

dril

l bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)






0= 5 sdot



1119889(119905) and 120596



5 Conclusions



0 10 20 30 40 50 60 70 80 900

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 900

001002003

Time (s)

Dep

th o

f cut

(m)

(b)


0 10 20 30 40 50 60 70 80 90 1000246

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

05

1015

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 90 1000

0005001

0015

Time (s)Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

020406080

100

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

00002000400060008

001

Dep

th o

f cut

(m)

(b)







Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 5 10 15 20 25Time (s)

0

105

152

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 5 sdot 10

9

0 5 10 15 20 250

20

40

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0

200

400

0 5 10 15 20 25Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

1234

Dep

th o

f cut

(m)

0 5 10 15 20 25Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 5 sdot 10

9

0 5 10 15 20 250

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 05 1 15 2 25 3 35 4 45 5

012345

Intr

insic

spec

ific e

nerg

y (P

a)


times106

(b)


1205740= 5 sdot 10

9


0 5 10 150

5

10

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wout

Wref

(a)

0 105 15 2 25 3 35 4 45 50

100

200

Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

0 5 10 15 20 252468

Time (s)

Dep

th o

f cu

t (m

)times10minus3

(c)


for1198820= 2500N 120598 = 5MPa and 120574

0= 5 sdot 10

9

00002000400060008

0010012

Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

0 5 10 15 20 25 30 35 40 45 50Time (s)

Vout

Vref

(a)

0 5 10 15 20 25 30 35 40 45 5002

68

1012

4

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times106

(b)


1205740= 5 sdot 10

8


0= 5000N 120598 = 20MPa

and 1205740= 1 sdot 10







0 5 10 15 20 25 30 35 40 45 500

10

20

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wref

Wout

(a)

0

100

200

0 5 10 15 20 25 30 35 40 45 50Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

0 5 10 15 20 25 30 35 40 45 50Time (s)

times10minus3

Dep

th o

f cu

t (m

)

(c)


for1198820= 2500N 120598 = 10MPa and 120574

0= 5 sdot 10

8

0 50 100 1500

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 50 100 150

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 108





119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is

le10mm and ge0mm


0 50 100 1500

10

20

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0200400

0 50 100 150Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

Dep

th o

f cut

(m

)

0 50 100 150Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 108

Estimator

Controller

Virtual stiffness

Haptic device

R

refL

k

c2

c1

J2

J11205961

1205962

Tb

1 n



le0mm



119899(119905) (46)



0= 5000N



0= 10



0 10 20 30 40 50 60 70 80 900

105

215

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 900123

Time (s)

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 900

02040608

112

Time (s)Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

VrefVout

times10minus2

(a)

0 10 20 30 40 50 60 70 80 90Time (s)

05

101520

Ang

veo

lcity

of

dril

l bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)






0= 5 sdot



1119889(119905) and 120596



5 Conclusions



0 10 20 30 40 50 60 70 80 900

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 900

001002003

Time (s)

Dep

th o

f cut

(m)

(b)


0 10 20 30 40 50 60 70 80 90 1000246

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

05

1015

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 90 1000

0005001

0015

Time (s)Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

020406080

100

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

00002000400060008

001

Dep

th o

f cut

(m)

(b)







Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 150

5

10

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wout

Wref

(a)

0 105 15 2 25 3 35 4 45 50

100

200

Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

0 5 10 15 20 252468

Time (s)

Dep

th o

f cu

t (m

)times10minus3

(c)


for1198820= 2500N 120598 = 5MPa and 120574

0= 5 sdot 10

9

00002000400060008

0010012

Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

0 5 10 15 20 25 30 35 40 45 50Time (s)

Vout

Vref

(a)

0 5 10 15 20 25 30 35 40 45 5002

68

1012

4

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times106

(b)


1205740= 5 sdot 10

8


0= 5000N 120598 = 20MPa

and 1205740= 1 sdot 10







0 5 10 15 20 25 30 35 40 45 500

10

20

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wref

Wout

(a)

0

100

200

0 5 10 15 20 25 30 35 40 45 50Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

0 5 10 15 20 25 30 35 40 45 50Time (s)

times10minus3

Dep

th o

f cu

t (m

)

(c)


for1198820= 2500N 120598 = 10MPa and 120574

0= 5 sdot 10

8

0 50 100 1500

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 50 100 150

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 108





119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is

le10mm and ge0mm


0 50 100 1500

10

20

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0200400

0 50 100 150Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

Dep

th o

f cut

(m

)

0 50 100 150Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 108

Estimator

Controller

Virtual stiffness

Haptic device

R

refL

k

c2

c1

J2

J11205961

1205962

Tb

1 n



le0mm



119899(119905) (46)



0= 5000N



0= 10



0 10 20 30 40 50 60 70 80 900

105

215

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 900123

Time (s)

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 900

02040608

112

Time (s)Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

VrefVout

times10minus2

(a)

0 10 20 30 40 50 60 70 80 90Time (s)

05

101520

Ang

veo

lcity

of

dril

l bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)






0= 5 sdot



1119889(119905) and 120596



5 Conclusions



0 10 20 30 40 50 60 70 80 900

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 900

001002003

Time (s)

Dep

th o

f cut

(m)

(b)


0 10 20 30 40 50 60 70 80 90 1000246

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

05

1015

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 90 1000

0005001

0015

Time (s)Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

020406080

100

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

00002000400060008

001

Dep

th o

f cut

(m)

(b)







Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15 20 25 30 35 40 45 500

10

20

Time (s)

Ang

velo

city

of

dril

l bit

(Rad

s)

Wref

Wout

(a)

0

100

200

0 5 10 15 20 25 30 35 40 45 50Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

0 5 10 15 20 25 30 35 40 45 50Time (s)

times10minus3

Dep

th o

f cu

t (m

)

(c)


for1198820= 2500N 120598 = 10MPa and 120574

0= 5 sdot 10

8

0 50 100 1500

0002000400060008

0010012

Time (s)

Out

put v

ertic

al v

eloc

ity

of d

rill b

it (m

s)

VrefVout

(a)

Time (s)0 50 100 150

0

05

1

15

2

Intr

insic

spec

ific e

nerg

y (P

a)


times107

(b)


1205740= 108





119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is


119899(119905) is

le10mm and ge0mm


0 50 100 1500

10

20

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0200400

0 50 100 150Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

Dep

th o

f cut

(m

)

0 50 100 150Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 108

Estimator

Controller

Virtual stiffness

Haptic device

R

refL

k

c2

c1

J2

J11205961

1205962

Tb

1 n



le0mm



119899(119905) (46)



0= 5000N



0= 10



0 10 20 30 40 50 60 70 80 900

105

215

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 900123

Time (s)

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 900

02040608

112

Time (s)Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

VrefVout

times10minus2

(a)

0 10 20 30 40 50 60 70 80 90Time (s)

05

101520

Ang

veo

lcity

of

dril

l bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)






0= 5 sdot



1119889(119905) and 120596



5 Conclusions



0 10 20 30 40 50 60 70 80 900

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 900

001002003

Time (s)

Dep

th o

f cut

(m)

(b)


0 10 20 30 40 50 60 70 80 90 1000246

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

05

1015

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 90 1000

0005001

0015

Time (s)Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

020406080

100

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

00002000400060008

001

Dep

th o

f cut

(m)

(b)







Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 50 100 1500

10

20

Time (s)

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(a)

0200400

0 50 100 150Time (s)


Act

and

Est

torq

ue-o

n -b

it (N

-m)

(b)

31323334

Dep

th o

f cut

(m

)

0 50 100 150Time (s)

times10minus3

(c)


for1198820= 2500N 120598 = 20MPa and 120574

0= 108

Estimator

Controller

Virtual stiffness

Haptic device

R

refL

k

c2

c1

J2

J11205961

1205962

Tb

1 n



le0mm



119899(119905) (46)



0= 5000N



0= 10



0 10 20 30 40 50 60 70 80 900

105

215

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 900123

Time (s)

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 900

02040608

112

Time (s)Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

VrefVout

times10minus2

(a)

0 10 20 30 40 50 60 70 80 90Time (s)

05

101520

Ang

veo

lcity

of

dril

l bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)






0= 5 sdot



1119889(119905) and 120596



5 Conclusions



0 10 20 30 40 50 60 70 80 900

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 900

001002003

Time (s)

Dep

th o

f cut

(m)

(b)


0 10 20 30 40 50 60 70 80 90 1000246

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

05

1015

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 90 1000

0005001

0015

Time (s)Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

020406080

100

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

00002000400060008

001

Dep

th o

f cut

(m)

(b)







Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30 40 50 60 70 80 900

105

215

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 900123

Time (s)

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 900

02040608

112

Time (s)Out

put v

ertic

al v

eloc

ity o

f dril

l bit

(ms

)

VrefVout

times10minus2

(a)

0 10 20 30 40 50 60 70 80 90Time (s)

05

101520

Ang

veo

lcity

of

dril

l bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)






0= 5 sdot



1119889(119905) and 120596



5 Conclusions



0 10 20 30 40 50 60 70 80 900

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 900

001002003

Time (s)

Dep

th o

f cut

(m)

(b)


0 10 20 30 40 50 60 70 80 90 1000246

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

05

1015

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 90 1000

0005001

0015

Time (s)Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

020406080

100

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

00002000400060008

001

Dep

th o

f cut

(m)

(b)







Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30 40 50 60 70 80 900

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 900

001002003

Time (s)

Dep

th o

f cut

(m)

(b)


0 10 20 30 40 50 60 70 80 90 1000246

Time (s)

Intr

insic

spec

ific

ener

gy (P

a)


times107

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

05

1015

Estim

ated

fo

rce (

N)

(b)


0 10 20 30 40 50 60 70 80 90 1000

0005001

0015

Time (s)Out

put v

ertic

al v

eloc

ity o

f dr

ill b

it (m

s)

VrefVout

(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

020406080

100

Ang

velo

city

of

drill

bit

(Rad

s)

WrefWout

(b)


1119889(119905) (b)

0 10 20 30 40 50 60 70 80 90 1000

200400600800

1000

Time (s)

Act

and

Est

Tb (N

-m)


(a)

0 10 20 30 40 50 60 70 80 90 100Time (s)

00002000400060008

001

Dep

th o

f cut

(m)

(b)







Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article design of telerobotic drilling...

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