disturbance observer

8/12/2019 Disturbance Observer

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Advanced Motion Control by Multi-Sensor

based Disturbance Observer

Kouhei Irie, Seiichiro Katsura, and Kiyoshi OhishiDepartment of Electrical Engineering, Nagaoka University of Technology, Nagaoka, Niigata, Japan

[email protected]; [email protected]; [email protected]

Abstract Motion control has been widely used in in-dustry applications. One of the key technologies of motioncontrol is a disturbance observer, which quarries a dis-turbance torque of a motion system and realizes a robustacceleration control. The disturbance observer can observeand suppress the disturbance torque within its bandwidth.Recent motion systems begin to spread in the society andthey are required to have ability to contact with unknownenvironment. Such a haptic motion requires much wider

bandwidth. However, since the conventional disturbanceobserver attains the acceleration response by the secondorder derivative of position response, the bandwidth islimited due to the derivative noise.

This paper proposes a novel structure of a disturbanceobserver. The proposed disturbance observer uses an accel-eration sensor for enlargement of bandwidth. Generally, thebandwidth of an acceleration sensor is from 1 Hz to morethan 1 kHz. To cover DC range, the conventional positionsensor based disturbance observer is integrated. Thus, theperformance of the proposed multi-sensor based disturbanceobserver (MSDO) is superior to the conventional one. TheMSDO is applied to position control (infinity stiffness) andforce control (zero stiffness).

The numerical and experimental results show viability of

the proposed method.

I. INTRODUCTION

Motion control technology [1], [2] has been widely

used in industry applications. The software servoing

technology is now common in machine tools, robotics,

and mechatronics. It has been intensively developed for

the numerical control (NC) machines and disturbance

rejection. Since the ideal position control has the infinite

gain against the position error, it has the infinite stiffness.

The position control is effective and robust for the rel-

atively simple task with low degrees-of-freedom (DOF)

applications, such as X Y table of machine tool, joint

control of industrial robot and so on. Such applications

exist in the closed space, and the motion area is limited

in a small space.

However, a robot will be expected to play the role of

a humans partner in aging society with fewer children

[3]. Human-friendly robots begin to spread in the society.

Pet robots, welfare robots, and home robots can be

considered as human-friendly robots. Such robots will

move in open space rather than in limited space. They

will contact various environments and do their tasks. The

recent robots are required to have ability to contact with

unknown environment. Conventional motion control isnot always suitable for future applications due to the

lack of adaptive capability to the environment. A more

sophisticated ability in motion control is necessary for

compliant contact with environment.

Acceleration control is only solution for compliant

motion to unknown environment [4] [5]. The acceleration

control can make a motion system to be a zero stiff-

ness system without losing the robustness. A disturbance

observer is a good candidate to achieve the acceleration

control [6]. The disturbance observer quarries the distur-

bance torque of a motion system by using the currentreference and the acceleration response. The disturbance

observer can realize a robust acceleration control within

its bandwidth.

The bandwidth of the disturbance observer is very

important especially to haptic motion control. Narrow

bandwidth of the disturbance observer has much influence

not only on the contact performance but also on the stabil-

ity of the whole control system [7]. Thus, the bandwidth

should be enlarged for realization of contact motion. How-

ever, since the conventional disturbance observer attains

the acceleration response by the second order derivative of

position response, which is sensed by a position encoder,the bandwidth is limited due to the derivative noise [8].

This paper proposes a novel structure of a distur-

bance observer. The proposed disturbance observer uses

an acceleration sensor for enlargement of bandwidth.

Generally, the bandwidth of an acceleration sensor is

from 1 Hz to more than 1 kHz. To cover DC range, the

conventional position sensor based disturbance observer is

integrated. Thus, the performance of the proposed multi-

sensor based disturbance observer (MSDO) is superior to

the conventional one. The MSDO will be useful for future

haptic motion control.

This paper is organized as follows. The following

section shows an importance of the acceleration control

in motion control. In Section III, the conventional archi-

tecture of the disturbance observer with position sensor is

introduced. The proposed multi-sensor based disturbance

observer (MSDO) is proposed in Section IV. The proposed

MSDO is applied to a position control (infinity stiffness)

system and a force control (zero stiffness) system in

Section V and VI. At the last section, this paper is

summarized.

II. ACCELERATION C ONTROL IN M OTION C ONTROL

A. Target of Motion Control

A motion controller in open environment will require

various stiffness corresponding to the task. The control

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stiffness [2] is defined in the following equation,

=f

x (1)

where denotes a control stiffness. f denotes generated

force and x denotes position. The ideal position control

should have infinite stiffness; however, the ideal forcecontrol should have zero stiffness. Modern motion system

requires an ability to be compliant with contact environ-

ment. The motion control should take plural modes of

environment into account. The environmental information

is a key to be compliant to unknown environment. Motion

control taking environmental information into account

will make various machines including robots more adap-

tive and versatile.

B. Robustness in Motion Systems

High-performance motion controller is a requisite for

more skillful and dexterous motion. To attain such highperformance, motion systems should be robust against

the load change and parameter variation. A conventional

minor control loop structure has been effective in one

degree-of-freedom motion.

The improvement ratio of the performance to the ve-

locity reference tracking and the disturbance rejection

is basically the same in such system. The increase of

forward gain leads to more robust performance and makes

the control stiffness higher. At the same time, high gain

often excites the lowest mechanical resonance mode and

makes the total system unstable. There is a limit of the

forward gain.On the other hand, recent dexterous motion requires

wide range of control stiffness. For example, an electronic

parts inserting machine needs some compliant motion at

the tip of the machine. This case requires low or no

control stiffness. The conventional controller will have

very low forward gain, for such a purpose, and will lose

robustness as a result. To satisfy such varied requirements,

the controller should have variable control stiffness keep-

ing the system highly robust.

Sabanovic mentioned that acceleration controller makes

a motion system robust by analyzing sliding mode control

[4]. Acceleration control can set the control stiffness

independent of robustness. A disturbance observer [1],

[6] which was proposed by Ohishi et al. is a good

candidate for attainment of robust acceleration control.

A disturbance observer identifies the total mechanical

load torque and parameter change. In other words, the

identification of disturbance torque is essential for motion

control robustness to realize various applications.

C. Integration of Multi-Degree-of-Freedom Motion

Acceleration control is essential also for integration of

multi-degree-of-freedom motion. Usually, the relationship

between the work space and the joint space is veryimportant for control of a multi-degree-of-freedom ma-

nipulator. For instance, the relation ship of a three-degree-

of-freedom manipulator is defined as follows; xy

z

= Jaco

12

3

(2)

X = Jaco (3)

where Jaco denotes the Jacobian matrix. Xand denotesthe velocity response with respect to the work space and

the joint space, respectively.

As the hybrid position/force control [9], [10], [11]

is installed to the three-degree-of-freedom manipulator,

motion with respect to the Z axis is constrained by the

environment and the other motion with respect to the

XYplane is controlled by position servoing. Hence the

control stiffness with respect to the Z axis should be 0;

and the control stiffness with respect to the XY plane

should be . It is difficult for a conventional motion

controller to realize the various control stiffness in each

joint. To integrate the various control stiffness in thejoint space, each motion reference with respect to the

work space should be transformed into the acceleration

reference, 12

3

= J1aco

xy

z

(4)

= J1aco X (5)

where X and denotes the acceleration response with

respect to the work space and the joint space, respectively.

Acceleration control is essential technique also for

realization of bilateral teleoperation. The goals of bilateralteleoperation are considered as the following two points

xm xs = 0 (6)

Fm+Fs = 0 (7)

where the positions of the master and the slave are defined

as xm and xs. The operational force and reaction force

from the environment are defined as Fm and Fs. Since

the above two goals are opposite control stiffness, it is

difficult to realize at the same time. Here, to achieve the

above to goals, the above two equations are transformed

into the acceleration dimension

xm xs 0 (8)

xm+ xs = 0. (9)

Since the (8) and (9) are represented in the common

and the differential modes of the master and the slave,

respectively, it is possible to integrate the opposite control

stiffness in each system [12] xcxd

=

1 11 1

xmxs

= H2

xmxs

(10)

where H2 denotes the second-order Hadamard matrix.xc and xd denotes the common mode and the differentialmode of the acceleration responses, respectively. Since

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there is no interference between the two modes, the law

of action and reaction is realized as a result.

As mentioned above, acceleration control is fundamen-

tal technology for modal system design of multi-degree-

of-freedom motion [13], [14].

III. POSITIONS ENSOR BASED D ISTURBANCEOBSERVER

This section introduces a conventional architecture of

a disturbance observer by using a position encoder. A

disturbance observer is designed to cancel the disturbance

torque as quickly as possible. The estimated disturbance

torque is obtained from the velocity responsem and the

current referenceIref as shown in Fig. 1. The velocity re-

sponse is calculated by the derivative of position response,

which is sensed by the position encoder. gpd denotes the

cut-off frequency of the pseudo-derivation.

The disturbance torque dis is represented as (11)

dis = (Jm Jmn)m+ (Ktn Kt)Iref

+Fc+Dmm+ext (11)

where

Jm : Motor inertia

Kt : Torque constant

Fc : Coulomb friction

Dmm : Viscous frictionext : External torque

(subscript) n : Nominal value.

In (11), the first term is the torque due to the self-inertiavariation. The second term is torque pulsations due to the

variation of the torque coefficient.

Equation (12) shows that the disturbance torque is

estimated through the first-order low-pass filter

dis =

JmnJm

gdis

s+ KtKtn

JmnJm

gdisdis (12)

wheregdis denotes the cut-off frequency of the low-pass

filter. The disturbance torque estimated by (12) is used for

a realization of robust motion control. And robust motion

controller makes a motion system to be an accelerationcontrol system as shown in Fig. 2. As shown in Fig. 2,

the effect of the disturbance torque is represented as a

transfer function Gs,

Gs = s

s+gdisdis (13)

gdis = Kt

Ktn

Jmn

Jmgdis. (14)

Gs represents a sensitivity showing how the disturbance

torque influences the motion system and is called a

sensitivity function. Since the conventional disturbance

observer attains the acceleration response by the secondorder derivative of position response, the bandwidth is

limited due to the derivative noise.

dis

dis

s gg

+

sJm

1

s

1

extmmc DF ++

+

refItK

tnK mndisJg++

dism

mndisJg+

tnK1

+

+

cmpI

pd

pd

s

s

g

g

+

.

.

^

.

m

m m

Fig. 1. Block diagram of disturbance observer

dism

+

*diss

s

g+

ref

nJ

1

dismn

tn

tdis

JJ

KK gg =**diss

s

g+

nJ

1

*diss

s

g+ *

nJ

1

mJ

1

disg*

.. ..

m

m m

Fig. 2. Robust acceleration control system

IV. MULTI-S ENSOR BASED D ISTURBANCE O BSERVER

This paper proposes a novel structure of a disturbance

observer. The proposed disturbance observer uses an

acceleration sensor for enlargement of bandwidth. Gener-

ally, the bandwidth of an acceleration sensor is from 1 Hz

to more than 1 kHz. To cover DC range, the conventional

position sensor based disturbance observer is integrated.

The block diagram of the proposed multi-sensor based

disturbance observer (MSDO) is shown in Fig. 3.

dis

dis

s g

g

+

Jm

1

s

1+refItK

tnK mndisJg++

mndisJg+

tnK

1

+

+

cmpI

pd

pd

s

s

g

g

+

dism^

extmmc DF ++

.

.

m

.m m

s

1

..m

tnK mnJ+

diss

s

g+

+

+

Fig. 3. Block diagram of multi-sensor based disturbance observer

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dis

dis

s g

g

+

mJ

1

s

1+refI

tK

tnK mndisJg++

mndisJg+

tnK

1

+

+

cmpI

pd

pd

s

s

g

g

+

dism^

extmmc DF ++ .

.

m

.

m m

s

1..

m

tnK mnJ+

diss

s

g+

+

+

t

mn

K

J

ref..

m

fC+

cmd

reac

reac

s g

g

+

tnK mnreac Jg++

mnreacJg+

tnK mnJ+

reacs

s

g+

+

+

mmc DF + .

ext^

mmc DF + .

Fig. 6. Block diagram of force control with multi-sensor baseddisturbance observer

TABLE II

PARAMETERS OF FORCE CONTROL

Cf Force servoing 2.0

Ze Environmental impedance = Ke +DesKe Environmtntal stiffness 50000 N/mDe Environmental damping 10 N/(m/s)

gpd Cut-off frequency of pseudo-derivation 100 Hzgdis Cut-off frequency of disturbance observer 50 Hz

ga Cut-off frequency of acceleration sensor 1 kHz

Each parameter of the force control is shown in TABLE

II.

A. Simulation Results

The simulation results of the force control are shown

in Fig. 7. The force results with the conventional dis-

turbance observer are shown in Fig. 7 (1). Since the

bandwidth is too low relative to the stiffness of the hard

environment, it is unstable to contact. Fig. 7 (2) shows

the force response with only acceleration sensor baseddisturbance observer. Since the acceleration sensor cannot

sense the DC acceleration response, the force response is

uncontrolled. The proposed MSDO method is shown in

Fig. 7 (3). It turns out that it is possible to contact to the

hard environment, where the conventional method cannot

contact. As a result, the advantage in bandwidth of the

proposed MSDO is very useful for haptic motion control.

VII. EXPERIMENT

A. Experimental Setup

The proposed MSDO is applied for a rod type linear

motor system, which is shown in Fig. 8. The accelerationsensor is implemented to the mover of the linear motor.

The experimental parameters are listed in TABLE III. The

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Force[N]

Time [s]

commandresponse

0

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Position[m]

Time [s]

(a) Force response (b) Position response

(1) Position sensor

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Force[N]

Time [s]

commandresponse

0

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Position[m]

Time [s]


(2) Acceleration sensor

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Force[N]

Time [s]

command

response

0

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Position[m]

Time [s]


(3) Multi sensor

Fig. 7. Simulation results of force control

Fig. 8. Experimental system

control software is written in C language under RTLinux

3.2. The sampling time is 100 s.

B. Experimental Results

The experimental results show the force control re-

sponses, and the following bandwidth is selected to com-

pare the proposed MSDO with the conventional distur-

bance observer;

Case. 1 2000 rad/s;

Case. 2 6280 rad/s.

The mixed bandwidth of the position sensor and the

acceleration sensor is 200 rad/s.

Fig. 9 shows the experimental results when the band-

width is set to 2000 rad/s. Since the same bandwidth is

selected to both observers, it turns out the almost same

force response is obtained. Fig. 10 shows the experimentalresults when the bandwidth is set to 6280 rad/s. When

the bandwidth is raised to 6280 rad/s, the derivative

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TABLE III

PARAMETERS OF EXPERIMENTAL SYSTEM

Mass of mover 0.18 KgForce constant 3.3 N/AThe resolution of position encoder 0.1 m

Bandwidth of acceleration sensor 1 10 kHzSize of the acceleratio n sensor 3.6 mm (H)

11.4 mm (L) 6.4 mm (W)

Weight of the acceleration sensor 0.5 g

noise is observed in force response of the conventional

disturbance observer. It is the limit of the conventional

observer for practical use. In Fig. 10 (2), force response of

the proposed MSDO is stable and there is no observation

noise. Since the bandwidth is superior to the bandwidth

of human sensing, it is suitable for haptic motion control.

VIII. CONCLUSIONS

Acceleration control is essential technique for motion

control. Acceleration control is only solution for compli-

ant motion to unknown environment since it can make a

motion system to be a zero stiffness system without losing

the robustness. A disturbance observer is a good candidate

to achieve the acceleration control. The bandwidth of the

disturbance observer is very important especially to haptic

motion control.

This paper proposed a novel structure of a disturbance

observer for enlargement of the bandwidth of robustness.

To cover bandwidth from DC to high frequency, both a

position encoder and an acceleration sensor were imple-mented to compose the disturbance observer. The pro-

posed multi-sensor based disturbance observer (MSDO)

can estimate the disturbance torque perfectly. The MSDO

was applied to position control (infinity stiffness) and

force control (zero stiffness). The numerical and exper-

imental results showed viability of the proposed method.

The proposed MSDO will be a fundamental technology

for future advanced motion control.

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