IEEJ International Workshop on Sensing, Actuation, Motion Control, and Optimization

Advanced Motion Control for Next-Generation Precision Mechatronics:Challenges for Control, Identification, and Learning

Tom Oomen⇤a) Non-member

Manufacturing equipment and scientific instruments, including wafer scanners, printers, microscopes, and medicalimaging scanners, require accurate and fast motions. Increasing requirements necessitate enhanced control performance.The aim of this paper is to identify several challenges for advanced motion control originating from these increasing accu-racy, speed, and cost requirements. For instance, flexible mechanics must be explicitly addressed through overactuation,oversensing, inferential control, and position-dependent control. This in turn requires suitable models of appropriatecomplexity, which are identified and learned from inexpensive experimental data. Several ongoing developments areoutlined that constitute a part of an overall framework for control, identification, and learning of complex motionsystems. In turn, this may pave the way for new mechatronic design principles, leading to fast lightweight machineswhere the spatio-temporal flexible mechanics are explicitly compensated through advanced motion control.

Keywords: Mechatronics, motion control, robust control, multivariable control, system identification, iterative learning control.

1. IntroductionPositioning systems are a key enabling technology in manu-

facturing machines and scientific instruments. A state-of-the-art example of such a mechatronic system is a wafer scanner,which is used in the lithographic production of integrated cir-cuits (ICs), see Fig. 1(a)-1(b), and achieves sub-nanometerpositioning accuracy with extreme speed and acceleration (59).Also, in semiconductor assembly processes, including wire-bonders and diebonders, products have to be positioned withvarying trajectories, up to 72000 products per hour (9). Further-more, for printing systems, ranging from desktop printers toindustrial printers and 3D printing, see Fig. 1, printing accu-racy and speed are essential. In scientific instruments, suchas atomic force microscopes (AFMs) and scanning electronmicroscopes (SEM), the sample needs to be accurately posi-tioned (1) (31), whereas in CT scanners the detector is positionedfor medical imaging, see also Fig. 1. The accuracy and speedof these positioning systems hinges on the motion control de-sign (65) (87) and determines the capabilities and market positionof the manufacturing machines and scientific instruments.

Control of these positioning systems is traditionally sim-plified by an excellent mechanical design. In particular, themechanical design is such that the system is sti↵ and highlyreproducible. In conjunction with moderate performance re-quirements, the bandwidth is well-below the resonance fre-quencies of the flexible mechanics. As a result, the systemcan often be completely decoupled (90) in the frequency rangerelevant for control. Consequently, the control design is di-vided into well-manageable SISO control loops, for whichstandard guidelines exist for their manual tuning by controlengineers for both feedback and feedforward, see (63) (33) (87) andSec. 2.2. In addition, SISO learning control approaches that

a) Correspondence to: t.a.e.oomen@tue.nl⇤ Eindhoven University of Technology, Department of Mechanical

Engineering, Eindhoven, The Netherlands.

are suitable for motion control are well-developed, see (86) (19).Although motion control design is well-developed,

presently available techniques mainly apply to positioningsystems that behave as a rigid body in the relevant frequencyrange. On the one hand, increasing performance requirementshamper the validity of this assumption, since the bandwidth,i.e., the frequency range over which control is e↵ective, hasto increase, leading to flexible dynamics in the cross-over re-gion (5) (53) (74). On the other hand, the requirement for rigid-bodybehavior puts high requirements on the mechatronic systemdesign, e.g., in terms of exotic and sti↵ materials and hencecost. The aim of this paper is to sketch the present state of thepractice (Sec. 2) and to identify challenges arising in precisionmotion control (Sec. 3). Recent results that address these chal-lenges in motion feedback control are then outlined (Sec. 4),revealing the need for system identification techniques. Next,feedforward and learning control are addressed (Sec. 5).

(a) Experimental wafer stage. (b) Prototype reticle stage.

(c) Arizona flatbed printer. (d) Wire bonder.

Fig. 1. Example state-of-the-art positioning systems.

c� 2017 The Institute of Electrical Engineers of Japan. 1

36�

Advanced Motion Control for Next-Generation Precision Mechatronics: Challenges for Control, Identification, and Learning (Tom Oomen)

2. Traditional motion control2.1 Motion systems Mechatronic positioning sys-

tems consist of mechanics, actuators, and sensors (63) (32). Inthe frequency range that is relevant for control, mainly themechanics have a relevant dynamical behavior. In particular,the mechanics can typically be described as (37)

Gm =

nRBX

i=1

cibTi

s2

| {z }rigid�body modes

+

nsX

i=Nrb+1

cibTi

s2 + 2⇣i!i s + !2i| {z }

flexible modes

, · · · · (1)

where nRB is the number of rigid-body modes, the vectorsci 2 Rny , bi 2 Rnu are associated with the mode shapes, and⇣i,!i 2 R+. Here, ns 2 N may be very large and even in-finite (52). Note that in (1), it is assumed that the rigid-bodymodes are not suspended, i.e., the term 1

s2 relates to Newton’slaw. In the case of suspended rigid-body modes, e.g., in caseof flexures as in (33) (69), (1) can directly be extended.

In traditional positioning systems, the number of actuatorsnu and sensors ny equals nRB, and are positioned such that thematrix

PnRBi=1 cibT

i is invertible. In this case, matrices Tu and Tycan be selected such that

G = TyGmTu =1s2 InRB +Gflex, · · · · · · · · · · · · · · · · · · · (2)

where Ty is typically selected such that the transformed outputy equals the performance variable z, as is defined in Sec. 3.3.Importantly, the selection of these matrices Tu and Ty canbe done directly on the basis of frequency response function(FRF) data, e.g., (90). Such frequency response data is inexpen-sive, fast, and accurate to obtain and its importance is furtherclarified in Sec. 4.8.

2.2 Traditional control architecture The motioncontrol architecture in Fig. 2 is standard, where

e = S (r �G f ) � S v, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (3)

with S = (I +GK)�1. Typically, r is a prespecified referencetrajectory for the output y, e is the error vector to be mini-mized, f is a feedforward signal, K is the feedback controller,and v represents disturbances. It is remarked that these aretacitly used for both continuous and discrete time systems.Indeed, for manual tuning often the continuous time domainis used as in (1) - (2). For automated algorithms, as developedin Sec. 4 and Sec. 5, the discrete time domain is more natural.These domains can be directly linked, see (71) for details.

In view of (2), G is decoupled in the relevant frequencyranges, in which case the elements e may be minimized stepby step. This is investigated in the following subsections.

2.2.1 Traditional feedforward design Feedforwardcan e↵ectively compensate for reference-induced error signals.In particular, f should be selected such that r � G f is mini-mized. In the low-frequency range, the system is decoupledand Gflex can be ignored in (2), in which case f = G�1r = s2r,which is the Laplace transformation of the acceleration profile.Note that in (2), the mass of the rigid-body mode is normal-ized to unity. In practice, the feedforward signal is selectedas f = ms2r, which is tuned in the time domain by decorre-lating the measured error signal in (3) and the accelerationprofile, details of which can be found in (12). Furthermore, the

K G�

r

f

e

v

y

Fig. 2. Traditional motion control architecture.

SensorFig. 3. Envisaged lightweight motion system in lithog-raphy. Top right: reticle stage containing reticle. Bottomleft: envisaged lightweight wafer stage with spatio-tempo-ral deformations due to flexible dynamics.

compliance of the higher-order modes Gflex can be addressedin a snap term, as well as friction terms, all of which can bedirectly tuned manually in a straightforward manner (12).

2.2.2 Traditional feedback design For an appropri-ately designed feedforward signal, � = r �G f is small. In thiscase, the feedback controller has to minimize S (� � v), whereS is subject to a number of constraints and limitations (83), andhence cannot be made zero in general. Due to rigid-body de-coupling, S is diagonal at low frequencies for a decentralizedcontroller C. As a result, each diagonal element of C maybe tuned independently. Typically, due to the low-frequencyrigid-body behavior, a PID controller is tuned through manualloopshaping, followed by notch filters to account for thoseflexible modes in Gflex that hamper stability and/or perfor-mance.

2.2.3 Traditional learning control In the case wherethe setpoint r does not vary, the feedforward f may be ob-tained or improved using learning techniques. For SISO sys-tems, these are fairly well-developed, see, e.g., (86) (19) for anapproach that relates to the design approach in Sec. 2.2.2.

2.2.4 Traditional design procedure Traditional mo-tion control design divides the multivariable control designproblems into subproblems that are manageable by manualcontrol design. The traditional procedure consists of the fol-lowing steps:• identify an FRF of Gm, i.e., Gm(!i), for frequencies !i;• decouple the plant to obtain an FRF of G;• design C using manual loopshaping on the basis of the

FRF, consisting of a PID with notches; and• tune a feedforward controller, e.g., f = mr, using correla-

tion techniques, optionally followed by learning control.

3. Precision motion control developments3.1 Future mechatronic designs A radically new

lightweight mechatronic system design is envisaged to meetthe requirements imposed by innovations in manufacturingmachines and scientific instruments in terms of throughput,accuracy, and cost for the following reasons.

( 1 ) Increased throughput is directly related to faster move-ments. The acceleration is directly determined by Newton’slaw F = ma. Here, the forces F that the actuators can de-liver are bounded due to size and thermal aspects. Hence,throughput is increased by reducing the moving mass m.

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Advanced Motion Control for Next-Generation Precision Mechatronics: Challenges for Control, Identification, and Learning (Tom Oomen)

( 2 ) Increased accuracy is enabled by contactless motion,e.g., through magnetic levitation (25), since this avoids frictionand enhances reproducibility. In addition, in certain applica-tions, including EUV lithography, motion has to be performedin a vacuum environment. Contactless motion is then essentialto avoid pollution caused by mechanical wear and lubricants.

( 3 ) Reduced cost can be enabled by reducing the require-ments on material properties. In particular, present state-of-the-art systems involve exotic materials that provide highsti↵ness in conjunction with good thermal behavior.Combining these aspects reveals that a lightweight systemdesign is highly promising for next-generation motion sys-tems. Such lightweight systems exhibit predominant flexibledynamical behavior, as is schematically illustrated in Fig. 3,as well as an increased susceptibility to disturbances (63, Sec. 9.5.2).The prime reason why such systems are not yet feasible isthe lack of control methodologies that handle the increasedcomplexity, since the overall control design problem cannot bedivided into subproblems as in Sec. 2, which are manageableby manual tuning techniques.

In particular, the envisaged future designs of next-generation systems lead to several challenges for motion con-trol design, as are outlined next.

3.2 Advanced motion control challenges for futuremechatronic systems The envisaged mechatronic de-signs in Sec. 3.1 lead to several challenges for motion controldesign, including the following.

( 1 ) Unmeasured performance variables are introducedby spatio-temporal deformations. In particular, the locationwhere the performance is desired may not be directly mea-sured. For example, performance in lithographic wafer stagesis required at the spot of exposure, whereas sensors typicallymeasure the edge of the stage, see Fig. 3. A key challenge liesin inferring the unmeasured performance variables.

( 2 ) Many additional inputs and outputs can be exploited toactively control the flexible dynamical behavior. In particular,the presence of spatio-temporal deformations and spatiallydistributed disturbances lead to highly complex deformations.A large number of sensors, which is enabled by the availabil-ity of inexpensive sensors and ubiquitous computing power,enable a high quality estimation of the dynamical behavior.Subsequently, spatially distributed actuators, including inex-pensive smart materials such as piezos, will actively providesti↵ness and damping to the mechanical deformations. Suchan oversensed and overactuated situation is in sharp contrastto the present rigid-body situation, as is outlined in Sec. 2,and a key challenge lies in dealing with a large number ofmeasured variables and manipulated variables.

( 3 ) Position-dependent behavior is almost unavoidable inthe case of spatio-temporal deformations, since motion sys-tems perform motion by definition. For instance, for thesingle-mass system in Fig. 3, the spatio-temporal deforma-tions are observed di↵erently if the sensor is not moving.In addition, in certain systems, including H-drive designs,mass distributions change due to motion, leading to additionalposition-dependent behavior. A key challenge lies in handlingthe position dependence of future systems.

( 4 ) A systems-of-systems perspective on motion controldesign provides a strong potential for performance enhance-ment of the overall system. In particular, typical manufac-

Fig. 4. Example of flexible tasks in 2D and 3D printing.

K

P

w z

yu

Fig. 5. Standard plant setup, where P(G). Note that Kcan be equal as in Fig. 2, but can also be extended togenerate the signal f in Fig. 2.

turing machines and scientific instruments involve multiplecontrolled subsystems, e.g., in the schematic illustration ofa wafer scanner in Fig. 3, the wafer stage and reticle stagehave to move relative to each other. In the design approach ofSec. 2, the overall goal is first divided into subsystems with acertain error budget. As a result, performance limitations (83) ineach subsystem will directly negatively impact the overall per-formance. A joint design enables that individual subsystemswill be able to compensate each other’s limitations. However,a main challenge lies in a doubling of the complexity of thecontrol problem.

( 5 ) Thermal dynamics, in addition to mechanical deforma-tions, are expected to become substantially more importantdue to increasing performance specifications, the use of lessexotic materials for cost reduction, etc. A key challenge liesin the joint thermo-mechanical control design.

( 6 ) Vibrations, including flow-induced vibrations of cool-ing liquids, floor vibrations, and immersion-hood in lithog-raphy, have to be attenuated. These are expected to increaseproportionally to mass reduction (63, Sec. 9.5.2) and must be explic-itly compensated.

( 7 ) Flexible tasks are foreseen to become much moreimportant in future manufacturing machines. For in-stance, ( a ) additive manufacturing allows for a large user-customization of products, ( b ) wafer scanners compensate forsurface roughness (63, Sec. 9.4.1) ( c ) die-bonders and wire-bondersperform pick-and-place tasks based on actual product loca-tions (9), and ( d ) 2D printing tasks involve varying referencesand media width (18). As a result, the positioning systems insuch machines have to perform a class of tasks, see also Fig. 4.

3.3 A standard plant approach A standard plantframework allows for a systematic way to address the fu-ture challenges in advanced motion control. In particular, theenvisaged developments on future mechatronic system design,as described in Sec. 3.1, lead to challenges for motion controldesign, as are identified in Sec. 3.2.

The standard plant is depicted in Fig. 5. The standardplant is by no means new, and is at the basis of commonoptimization-based control algorithms (84). However, it encom-passes the identified challenges in Sec. 3.2 in a unified manner,whereas the traditional architecture in Fig. 2, which directlyfits in the setup of Fig. 5, cannot deal with these. Here, zare the performance variables, addressing Challenge 1, whicharises in addition to the already present measured variablesy. Indeed, y and u are the measured variables and manipu-lated variables, respectively, the dimensions of which will

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Advanced Motion Control for Next-Generation Precision Mechatronics: Challenges for Control, Identification, and Learning (Tom Oomen)

drastically increase in view of Challenge 2. The variable wcontains the exogenous inputs, typically including both refer-ence signals and disturbances (Challenge 6), i.e., r and d inFig. 2. Now, these variables may all be position-dependent(Challenge 3), an in addition, the variable r may vary foreach task (Challenge 7). Furthermore, if multiple systemsare addressed simultaneously, either due to their interaction,or their interaction due to a shared, overall machine controlgoal (Challenge 4), then this substantially increases the signaldimensions. Similarly, a joint thermal-mechanical controldesign (Challenge 5) involves signals and systems in both thethermal domain and the positioning domain.

The standard plant approach in Fig. 5 directly reveals theadditional complexity arising from the challenges outlined inSec. 3.2. Here P(G) denotes the standard plant, which con-tains the input-output plant G as well as the interconnectionstructure, e.g., Fig. 2. These increased complexity and accu-racy requirements necessitate new developments in controlalgorithms, since these undermine the basic assumptions onwhich the approach in Sec. 2 relies on. Indeed, the standardplant is a conceptual framework to pose the overall problem,the actual design of motion controllers requires substantiallymore steps. Importantly, the controller K in Fig. 5 can beeither a feedback controller, a feedforward controller, or both.Due to the fundamentally di↵erent objectives of these con-trollers, these are investigated sequentially in the forthcomingsections.

4. Feedback and identification for controlFeedback control, i.e., K in Fig. 2, is essential to deal with

uncertainty in the system dynamics G and disturbances v. Inparticular, the prime goal of feedback is to render the systeminsensitive to such uncertainties. Note that the commonlyimposed requirement of stability is only a direct consequenceof the presence of uncertainties. In this section, the design offeedback controllers is investigated in view of the challengesoutlined in Sec. 3.2.

4.1 Norm-based control In view of feedback, amodel-based design is foreseen to be able to systematicallyaddress the challenges in Sec. 3.2. Here, model-based con-trol refers to the use of parametric models using optimizationalgorithms (84). For example, model-based optimal controllersynthesis enables a systematic control design procedure formultivariable systems, enabling centralized controller struc-tures. Also, a model-based design enables the estimationof unmeasured performance variables through the use of amodel. It is emphasized that such a design is far from standardin industry, where the procedure in Sec. 2.2.2 is still mostcommonly used in state-of-the-art positioning systems.

To specify the control goal, the criterion

J(G,K) = kFl(P(G),K)k · · · · · · · · · · · · · · · · · · · · · · · · (4)

is posed, where the goal is to compute

Kopt = arg minK

J(Go,K). · · · · · · · · · · · · · · · · · · · · · · · · · (5)

Here, k.k denotes a suitable norm, e.g., H2 or H1. Also, Fldenotes a lower linear fractional transformation (LFT), i.e.,

Fl(G,K) = P11 + P12K(I � P22K)�1P21, · · · · · · · · · · (6)

where P(G) is the interconnection structure and contains G. Inparticular, Fl(G,K) is typically a closed-loop transfer function,e.g., the general four-block problem

Fl(G,K) = W"

GI

#(I + KG)�1

hK I

iV, · · · · · (7)

where W and V are user-chosen weighting filters of suitabledimensions. For instance, these can be chosen such that (7)reduces to

G(I + KG)�1. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (8)

Finally, and very importantly, Go in (5) denotes the true sys-tem, e.g., one of the systems depicted in Fig. 1.

4.2 Nominal modeling for control: motivation Toarrive at a mathematically tractable optimization problem in(5), knowledge of the true system is represented through amodel G. The central question is how to obtain such a modelthat is suitable for controller design. System identification, orexperimental modeling as opposed to first principles modeling,is an inexpensive, fast, and accurate approach to obtain such amodel, see (55) (75) (50) for a general overview of such approaches.Indeed, the positioning system often is already built, enablingdirect experimentation.

The model G that results from system identification is anapproximation of the true system Go for several reasons i) mo-tion systems, typically of the form (2), often contain an infi-nite number of modes ns, while a model of limited complexitymay be desirable from a control perspective; ii) parasitic non-linearities are present, including nonlinear damping (85); andiii) identification experiments are based on finite time dis-turbed observations, leading to variance errors on estimatedparameters, e.g., ⇣i and !i in (2).

Although a large variety of system identification approachesand algorithms have been developed, many of these do notdirectly deliver a model that is suitable for designing a high-performance controller when implemented on the true systemin view of (5). The main reason is that most identification tech-niques deliver a model that predicts the open-loop response aswell as possible, instead of the desired closed-loop response,which is unknown before the controller is actually synthesized.This is illustrated in the following example.Example 1 Consider the true system

Go =1s2 +

1s2 + 2 · 0.1 · (2⇡100)s + (2⇡100)2 · · · · · (9)

and the modelsG1 =

1s2 �

1s2+2·0.1·(2⇡100)s+(2⇡100)2 ·(10)

G2 =1

s2+2·1s·(2⇡0.2)+(2⇡0.2)2 +1

s2+2·0.1·(2⇡100)s+(2⇡100)2 , ·(11)see Fig. 6 for a Bode plot.

Next, an input

f (t) =(

1 0.1 t 0.20 elsewhere

· · · · · · · · · · · · · · · · · · (12)

is applied to the true system Go as well as to both models G1and G2, all of which are in open-loop, i.e., K = 0 in Fig. 2.In addition, r and v are zero in Fig. 2. The responses aredepicted in Fig. 6. It is observed that G1 matches the trueresponse accurately, while G2 shows a very di↵erent response.In particular, Go and G1 show an unbounded response due tothe rigid-body behavior, while G2 shows a bounded response.The Bode plots in Fig. 6 support this, since the model G2 does

4

Advanced Motion Control for Next-Generation Precision Mechatronics: Challenges for Control, Identification, and Learning (Tom Oomen)

100

f [Hz]

-150

-100

-50

0

50

100

150

|.|[dB]

Bode magnitude

100

f [Hz]

-180

-90

0

90

180

!(.)[!]

Bode phase

0 0.2 0.4 0.6 0.8 1t

0

0.02

0.04

0.06

0.08

0.1

y

Step open-loop

0 0.2 0.4 0.6 0.8 1t

-3

-2

-1

0

1

2

3y

Step closed-loop

Fig. 6. Example 1: true system Go in (9) (solid blue),model G1 in (10) (dashed red), model G2 in (11) (dash–dotted green). Left: Bode plot. Right top: open-loopresponse to the input f in (12). The model G1 in (10)(dashed red) closely matches the true system Go. How-ever, model G2 in (11) (dash-dotted green) shows a strongdeviation. Right bottom: closed-loop response to the in-put f in (12) with optimal controller K = 105. The modelG2 in (11) (dash-dotted green) now closely matches thetrue system Go. In contrast, the model G1 in (10) (dashedred), which accurately predicted the open-loop response,performs poorly in closed-loop.

have not a �2 slope at low frequencies.The key point is that most system identification techniques

deliver a model that compares to G1, which is of course de-sired if the goal is to simulate Go in open-loop as in Fig. 6.

Now, suppose that the optimal controller (5) is given byK = 105, i.e., a proportional controller to illustrate the mainidea. When applying the same input (12), yet with K = 105

implemented as in Fig. 2, then the results in Fig. 6 are ob-tained. The di↵erence of these closed-loop results are strikingcompared to Fig. 6: when the optimal controller K = 105

is implemented on the model G1, this does not even give abounded response. In contrast, the model G2, that seeminglyperformed poorly in the open-loop response in Fig. 6, is verysuitable for predicting the closed-loop response. ⇤

The main conclusion to be drawn from Example 1 is thatthe quality of models should be evaluated in view of their sub-sequent goal. The main goal of the models here is to deliver acontroller that performs well on the true system.

4.3 Control-relevant nominal identification Thequality of models depends on their goal. Here, the goal isgiven by (5). In particular, a model G is used to determine

K(G) = arg minK

J(G,K) · · · · · · · · · · · · · · · · · · · · · · · · (13)

which is then implemented on the true system Go, leading tothe achieved cost J(Go,K(G), with upper bound

J(Go,Kopt) J(Go,K(G)). · · · · · · · · · · · · · · · · · · · · · (14)

The main question now is how to identify models that de-liver a good controller in the sense that the bound (14) is tight.In addition, these models should preferably be of limited com-plexity, since the order of the controller is directly related

to the order of the model G. In contrast, in manually-tunedcontrollers, cf. Sec. 2.2.2, notch filters are only added for themodes in (1) that endanger stability and performance. Hence,the complexity of the model has to be justified by the controlrequirements.

A strategy to obtain such control-relevant models is to notethat J(Go,K) involves a norm. Hence, by rewriting and apply-ing the triangle inequality for a certain K,

J(Go,K)= J(G,K) + J(Go,K) � J(G,K) · · · · · · · · · (15) J(G,K) + kFl(P(Go),K) � Fl(P(G),K)k(16)

Here, the first term J(G,K) can be minimized, which in factequals the model-based design (13). The second term is afunction of Go, G, and K. To arrive at a well-posed identifi-cation problem, assume that a reasonable feedback controllerKexp is already designed and implemented, e.g., following theprocedure in Sec. 2.2.2. In fact, such a controller is typicallyrequired for identification experiments, since the open-loopsystem is often unstable, see (1). Then, Fl(P(Go),Kexp) issimply the closed-loop system with Kexp implemented.

In this case, a suitable identification criterion is to substituteKexp into the term in (16), leading to

GCR = arg minGkFl(P(Go),Kexp)�Fl(P(G),Kexp)k.(17)

Essentially, in (17) a model is identified that aims at repre-senting closed-loop behavior. Note that (17) depends on thecontroller. If K is chosen equal to Kopt, then typically thebest result is obtained. Since Kopt is unknown, the result willdepend on the quality of Kexp. To mitigate this dependence,the controller synthesis (13) and control-relevant identifica-tion (17) can be solved alternately, aiming to minimize theupper bound (16). Such an iterative procedure is at the basisof many approaches, including (82) (39) (91) (3). Unfortunately, suchan approach does not work, since the triangle inequality in(16) only holds valid for a fixed K, and does not allow for iter-ative updating of the controller. Still, (17) is a very valuablecriterion for model identification, as will be shown in Sec. 4.5.

4.4 Toward robust motion control The key reasonwhy alternating between control-relevant identification (17)and model-based control design (13) does not work is the lackof robustness. Indeed, if K(G) is designed solely based on G,there is no reason to assume that it achieves a suitable levelof performance on Go. In fact, there are no guarantees that itactually stabilizes Go in closed-loop. This motivates a robustcontrol design, where the model quality is explicitly addressedduring controller synthesis, as is outlined next.

In a robust control design (84), the true system behavior isrepresented by a model set G such that

Go 2 G. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (18)

Throughout, this model set is constructed by considering aperturbation around the nominal model G, see Sec. 4.3, i.e.,

G =nG���G = Fu(H,�u),�u 2 �u

o, · · · · · · · · · · · · · · · (19)

with the upper linear fractional transformation (LFT)

Fu(H,�u) = H22 + H21�u(I � H11�u)�1H12 · · · · · (20)

and H contains the nominal model G and the model uncer-tainty structure. Note that G is recovered if the uncertainty is

5

Advanced Motion Control for Next-Generation Precision Mechatronics: Challenges for Control, Identification, and Learning (Tom Oomen)

zero, so that G = Fu(H, 0).It remains to specify �u in more detail. In view of the

considered motion control objectives, anH1 norm, i.e.,

kHk1 = sup!�(H( j!)), · · · · · · · · · · · · · · · · · · · · · · · · · (21)

with � denoting maximum singular value, is selected for thefollowing reasons.( 1 ) H1-norm-bounded uncertainty enables a frequency-

dependent characterization of dynamic uncertainty, whichis very well suited for representing lightly damped modesin systems of the form (1). This is in sharp contrast toparameter uncertainty as is used in, e.g., (40).

( 2 ) The H1 norm provides a suitable means to quantifyperformance objectives for motion systems in (4). In par-ticular, theH1 norm allows a loopshaping-based design,see (60) (29) for a general perspective and (87) (88) (80) (93) (13). Inaddition, controller synthesis is typically most straightfor-ward if a single norm is used for representing uncertaintyand specifying the performance objectives.

Hence,

�u =n�u 2 H1

��� k�uk1 �o, · · · · · · · · · · · · · · · · · · (22)

� 2 R+. Associated with G is the worst-case criterion

JWC = supG2G

J(G,K). · · · · · · · · · · · · · · · · · · · · · · · · · · · · (23)

Hence, by minimizing the worst-case performance

KRP = arg minK

JWC(G,K) · · · · · · · · · · · · · · · · · · · · · · · (24)

this leads by using (18) to the guaranteed upper bound

J(Go,KRP) JWC(G,KRP). · · · · · · · · · · · · · · · · · · · · · (25)

Hence, this leads to a performance guarantee when KRP isimplemented on the true system Go. This is in sharp contrastto (14), which may actually be unbounded.

4.5 Modeling for robust motion control Robustcontrol provides a performance guarantee when implementingthe controller KRP on the true system Go. The question onhow to minimize the upper bound (25) hinges on the modelset G. Essentially, this involves the robust-control-relevantidentification of a model set, which is the counterpart of thenominal control-relevant identification problem in Sec. 4.3.

The main idea is to follow a very similar approach as inSec. 4.3. In particular, assume again that a controller Kexp isalready implemented. Then, instead of minimizing (4) over Kas in (24), it is minimized for the entire set G, i.e.,

minG

JWC(G,Kexp), · · · · · · · · · · · · · · · · · · · · · · · · · · · · (26)

subject to (18).

Combining the arguments implies that

J(Go,KRP) JWC(G,KRP) JWC(G,Kexp), · · · · · (27)

hence guaranteed performance enhancement is achieved. Al-though this also depends on Kexp, it can be iterated, leading tomonotonous performance enhancement (21), which is in sharpcontrast to the suggested iterative procedure in Sec. 4.3.

The key question is how to actually determine the model

set (26). The approach pursued here is to continue along thepath in Sec. 4.3, i.e., to determine a control-relevant model asin (17). In a second step, it is aimed to extend the model with�u such that (26) is actually addressed. Very many techniqueshave been developed for selecting the structure of uncertainty,e.g., (95, Table 9.1), as well as quantifying its size (76) (23). However,the closed-loop aspect of the identified models, as in Exam-ple 1, has important consequences.( 1 ) Constraint (18) has to be satisfied for (25) to hold. Al-

though this may seem trivially satisfied by increasing thesize of �u, note that typical uncertainty structures arebased on open-loop reasoning. In particular, suppose thatin Example 1G =nG���G = G2 + �u, k�uk1 �

o. · · · · · · · · · (28)

Then, since G2 2 H1, G ⇢ H1. However, sinceGo < H1, (18) cannot be satisfied. The main reasonis that Go contains a rigid-body mode, which is neitherincluded in G2, nor in anH1-norm-bounded perturbation�u. This is confirmed by Fig. 6, where G2 and �u have abounded magnitude, yet Go ! 1 for !! 0.

( 2 ) Suppose that (1) is successfully overcome, and a certainbound � guarantees that (18) is satisfied, the next questionis how this actually minimizes JWC(G,Kexp) in (26). In-deed, often G satisfies (18), yet contains an element thatis not stabilized by Kexp, in which case (26) is unbounded,see, e.g., (73, Table 1).

( 3 ) Suppose that Aspect 1 and 2 are addressed, the finalquestion is how JWC(G,Kexp) in (26) can be actually min-imized.

These three aspects are of crucial importance to avoid conser-vatism in the entire robust control design procedure. Indeed,robust control is often experienced to lead to conservativeresults or may need a very large user-interaction, e.g., (93) (22),due to inappropriately dealing with Aspects 1 - 3, above.

The main trick to address aspects 1 and 2 has a very longhistory in control and is known as the dual form of the Youlaparameterization. The Youla parameterization (4) parameter-izes all controllers that stabilize a certain system. The dualform, as is considered here, see also (57) (43) (64) (21) (28), parame-terizes all candidate systems that are closed-loop stable withKexp implemented. In particular,• the dual-Youla uncertainty structure is generated around

the nominal model G obtained from Sec. 4.3,• Go is stabilized by Kexp, hence (18) is satisfied for a su�-

ciently large �,• all elements in G are stabilized, hence JWC(G,Kexp) in

(26) remains bounded.The remaining step to obtain a robust-control-relevant modelset in the sense of (26) is to appropriately define the distancemetric. Indeed, there is a large amount of freedom left in thedual-Youla parameterization. Recently, in (68), this freedom isexploited through a new coprime factorization, which directlyconnects the size of uncertainty � in (22) and the control-relevant identification criterion (17). The underlying theoryclosely connects to recent developments in, e.g., (54). A keyconsequence of this approach is that it provides an automaticscaling of the uncertainty, both in input/output directions andfrequency, enabling the nonconservative use of unstructureduncertainty in (22).

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Advanced Motion Control for Next-Generation Precision Mechatronics: Challenges for Control, Identification, and Learning (Tom Oomen)

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Fig. 7. Sec. 4.7.1: identified model set of the systemin Fig. 1(a), with G (solid blue), G (cyan). Robust-con-trol-relevance emphasizes the bandwidth region around90 Hz, as well as the first two resonance phenomena.

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Fig. 8. Sec. 4.7.2: original system (dashed red), the useof overactuation adds damping and sti↵ness to the firstflexible mode (solid blue).

4.6 Identification procedure for robust motion controlCombining the developments in the preceding sections leadsto the following design procedure.( 1 ) Specify a control objective J in (4) using theH1 norm,

e.g., using loop-shaping design as in Sec. 2.2.2.( 2 ) Identify a nominal model G by minimizing (17) using

data collected while Kexp is implemented.( 3 ) Extend the nominal model with the dual-Youla uncer-

tainty structure as is outlined in Sec. 4.5, and determinethe size of � using any model uncertainty quantificationprocedure that delivers the minimal � such that (18) issatisfied, e.g., (72) (38) (67).

( 4 ) Compute and implement the optimal robust controller(24). If the performance is not satisfactory, repeat theprocedure from Step 1.

The overall design procedure leads to nonconservative robustmotion controllers and applies to highly complex systems. Itenables new developments in motion control and addressesthe challenges in Sec. 3.2 as is illustrated next.

4.7 Case studies The procedure in Sec. 4.6 allowsthe design of advanced motion controllers that address thechallenges in Sec. 3.2. These are elaborated on next.

4.7.1 Case 1: multivariable modeling for robust con-trol. To show that the approach in Sec. 4.6 can deal with

multivariable dynamics, a robust-control-relevant model setin the sense of (26) of the wafer stage in Fig. 1(a) is identified.The control goal in (4) is set to a bandwidth (84, Sec. 2.4.5) of 90 Hzwith PID characteristics.

The identification results are depicted in Fig. 7. The modelG is of order 8, corresponding to nRB = 2 and ns = 2 in (1).In addition, the uncertainty is tuned towards the control ob-jective: the uncertainty is small in the bandwidth region andthe first two resonances, which typically need notches in thetraditional manual design procedure in Sec. 2.2.2. In addition,at low and high frequencies, a very large uncertainty is toler-ated. The model set has been shown to lead to a factor twoerror reduction after 1 design cycle, see (73) for details. Thiserror can be further reduced by repeating the design cycle inSec. 4.6, as well as an error-based redesign (71).

4.7.2 Case 2: overactuation. The closed-loop band-width is often limited by resonance phenomena (48), even ifmultivariable loopshaping techniques (13) are used that addressthe directionality of Gflex in (2). In view of the ideas in Sec. 3.2,additional actuators and sensors can be exploited. From a prac-tical perspective, these can be employed to add active dampingand sti↵ness. This technique has been successfully applied toa prototype wafer stage, where in the result of Fig. 8 a singleactuator and sensor pair address the torsion mode, leading toa 35% bandwidth increase compared to the traditional input-output situation. These techniques are being extended to the14 input-14 output prototype reticle stage in Fig. 1(b), whichcan potentially achieve a significant accuracy and throughputenhancement by lightweight stage design, see Sec. 3.1.

4.7.3 Case 3: inferential control The procedure inSec. 4.6 can be directly extended towards dealing with un-measurable performance variables, in which case z containsvariables that are not contained in y. The main idea is that amodel is made that enables prediction of the unmeasurableperformance variables, e.g., using temporary sensors. This re-quires an extension of the controller structure in Fig. 2, detailsand an experimental example are provided in (69).

4.7.4 Case 4: position-dependent control. Motionsystems perform motions by definition. Hence, it can be ex-pected that the system in Fig. 3 is position dependent, sincethe sensor observes the mode-shapes di↵erently for changingpositions. Such dependence can be directly seen as linearparameter-varying (LPV) behavior (41), for which reliable syn-thesis techniques are available. However, the identificationof such systems from data is challenging (56). Recently, a newapproach has been developed (79) to model position-dependentsystems for LPV control, which consists of two steps.( 1 ) Identify the system at a large number of frozen positions

n✓, which are considered as ny ·n✓ auxiliary outputs. Iden-tify the high-dimensional nu input ny · n✓ output systemusing the procedure in Sec. 4.3 and Sec. 4.5.

( 2 ) Interpolate the modeshapes to obtain a model with acontinuous position dependence.

Experimental results are very promising, see Fig. 9.4.7.5 Case 5: systems of systems. The overall con-

trol of the wafer stage in Fig. 3 involves several subsystems,including the wafer stage and the reticle stage. The overallcontrol problem is the relative positioning of the wafer withrespect to the reticle. Instead of dividing the overall controlproblem in independent subproblems, the overall framework

7

Advanced Motion Control for Next-Generation Precision Mechatronics: Challenges for Control, Identification, and Learning (Tom Oomen)

xy

z

xy

Fig. 9. Sec. 4.7.4: identification of position-dependentmotion systems: 5th and 9th estimated mode of the proto-type lightweight motion system of Sec. 4.7.2.

( 1 ) Interaction analysis. Decoupled?

• yes: independent SISO design (Sec. 2.2.2). No: next step

( 2 ) Static decoupling (Equation (2)). Decoupled?

• yes: independent SISO design (Sec. 2.2.2). No: next step

( 3 ) Decentralized MIMO design: loop closing procedures (70, Sec. 1.3.3)

• robustness for interaction, e.g., using factorized Nyquist• design for interaction, e.g., sequential loop closing

Not successful? Next step

( 4 ) Optimal & robust control (Sec. 4.6)

• centralized controller with typically best performance

Fig. 10. Design procedure for advanced motion control.The blue steps can be based on an nonparametric FRF,while the red step requires a parametric model.

of Fig. 5 enables the direct solution of the overall problemthrough the approach in Sec. 4.6. Interestingly, the theorydeveloped in Sec. 4.4-Sec. 4.5 also allows for a systematicadd-on, see (30) for results in this direction.

4.7.6 Case 6: thermomechanical systems. So far,the focus has mainly been on motion control. However, ther-mal aspects are becoming significant for increasing accuracy.These directly fit in the setup of Fig. 5, and the approach inSec. 4.6 has recently been applied to a thermal control sys-tem with thermal actuators and sensors (42). This also enablescompensating for thermal deformations in motion control.

4.7.7 Case 7: Vibrations. The presence of exoge-nous disturbances is essential and addressed in various as-pects, including the use of active vibration isolation systems(AVIS) (72), compensation through disturbance observers (92),and disturbance-based redesign (71).

4.8 Discussion and overall design procedure InSec. 4.7, several successful case studies of the approach inSec. 4.6 are presented. This raises the question whether theapproach in Sec. 4.6 has disadvantages compared to the tradi-tional approach in Sec. 2.2.2. Although the theory is laid out,the algorithms still require significant user interaction. Also,numerical aspects are highly challenging (20) (49) (47), especiallyfor complex systems as arising from the challenges in Sec. 3.2.

Taking into account the present level of maturity of the toolsdescribed in this section and based on significant experiencewith multivariable motion systems, the general procedure inFig. 10 has proven to perfectly balance e↵ort vs. control re-quirements (70). Indeed, the e↵ort in terms of user interventionand modeling are only increased if necessitated by the controlrequirements. Interestingly, the first three steps are all basedon FRF data, whereas the latter step, i.e., the procedure ofSec. 4.6 involves the use of a parametric model.

Note that all four steps in Fig. 10 are based on FRF data.Indeed, Step 4 in Fig. 10 involves the identification problemSec. 4.3, which is again based on FRFs. This has led toa renewed interest in identifying FRFs of complex mecha-tronic systems, where traditionally noise excitation has been

used (87) (93). These have been extended towards periodic exci-tation (73), and more recently substantial advancements havebeen made using local parametric modeling techniques (81) (58).

5. Feedforward and learningFeedforward and learning control are essential for high

performance motion control. In this section, first learning con-trol is investigated, the connection to feedforward is furtheroutlined in Sec. 5.1.5.

5.1 Learning control Iterative learning control (ILC)(19) is particularly promising for positioning systems that per-form repeating tasks. Typically, the feedforward signal f inFig. 2 is updated based on past experiments or trials j, e.g.,

f j+1 = Q( f j + Le j), · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (29)

with Q and L appropriate learning filters. Essentially, (29)involves a trial-domain feedback, hence the resulting systemis a 2D system (77). For SISO systems, a well-developed de-sign framework is available (86), yet in view of the challenges inSec. 3.2, ILC algorithms of the form (29) are not directly appli-cable. The challenges in Sec. 3.2 are now briefly investigatedin the context of ILC, see (7) for a more detailed overview.

5.1.1 Inferential ILC for unmeasurable feedback sig-nals. Often, the performance variables are not directlyaccessible to the feedback controller, but they can be mea-sured after a task is completed. For instance, in printinginvisible markers can be used (17, Sec. 5.3). However, this requiresa major extension to traditional ILC structures (16).

5.1.2 Multivariable ILC with additional inputs andoutputs. ILC for multivariable systems is significantlymore challenging compared to feedback. Although ILC isfairly robust with respect to modeling errors, it is e↵ectiveup to the Nyquist frequency, imposing model quality require-ments over the entire frequency range, which is in sharp con-trast to the results in Fig. 7. In (8), the ILC analogue of theadvanced motion feedback control design procedure in Fig. 10is developed. In addition, in (98), the potential of additional in-puts for ILC is established.

5.1.3 ILC for position-dependent systems. SinceILC is e↵ective over a much larger frequency range com-pared to feedback, the e↵ect of position-dependent dynamicsis amplified. These are e↵ectively addressed though an LTVapproach in (96) and an LPV approach in (78).

5.1.4 Systems of systems. The design procedure in (8)

can directly be applied to such systems, whereas a systematicILC add-on as in Sec. 4.7.5 is developed in (61).

5.1.5 Flexible tasks. One of the largest drawbacks ofILC is that it requires the reference r in Fig. 2 to be constant.This is in sharp contrast to traditional feedforward control asis outlined in Sec. 2.2.1. The main goal of recent research,including (94) (44) (51) (17) has been to combine the performanceadvantages of learning control with the extrapolation capa-bilities of the feedforward structures in Sec. 2.2.1. This isfurther extended towards input shaping (11) and rational feed-forward structures in (15) (97), which have as key advantage thatthese can exactly compensate non-minimum phase dynamics,e.g., (26) (66) (96). These are successfully applied to the printersystem of Fig. 1(c) (18) and the wire bonder of Fig. 1(d) in (9).

A related approach that further connects to system identifi-cation in Sec. 4.3 is developed in (12) (10), see also (6).

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Advanced Motion Control for Next-Generation Precision Mechatronics: Challenges for Control, Identification, and Learning (Tom Oomen)

6. ConclusionAdvanced motion control is a highly challenging area. Sev-

eral issues arising from ongoing developments in applicationshave been identified, along with several solution strategiesthat are being developed. Many of these exciting control chal-lenges are still ahead of us, and several open problems havenot been addressed in the present paper, including (27) (62) (24) (31) (2).Furthermore, nonlinear control techniques have been inves-tigated in, e.g., (36) (46) (89). Implementation aspects are inves-tigated in (2) (99) (35). Finally, data-driven techniques to avoidmodeling altogether are being investigated in, e.g., (89) (34) (45) forfeedback control and (14) for ILC.

In the near future, developments in advanced motion controlmay enable a paradigm shift in mechatronic system design. In-deed, a very lightweight design is foreseen, see Fig. 3, wheresti↵ness is obtained through active control. In addition, ther-mal behavior will be actively controlled. These future systemsmay achieve unprecedented accuracy, speed, and cost.

AcknowledgementsI would like to thank many collaborators over the past decade, both in academia

and industry, and in particular Lennart Blanken, Frank Boeren, Joost Bolder, EnzoEvers, Egon Geerardyn, Robbert van Herpen, Robin de Rozario, Robbert Voorhoeve,and Jurgen van Zundert, as well as Maarten Steinbuch and Okko Bosgra.

References

( 1 ) D. Abramovitch, S. Andersson, L. Pao, and G. Schitter. A tutorial on themechanics, dynamics, and control of atomic force microscopes. In Proc. 2007Americ. Contr. Conf., pages 3488–3502, New York, NY, USA, 2007.

( 2 ) D. Y. Abramovitch. Trying to keep it real: 25 years of trying to get the stu↵I learned in grad school to work on mechatronic systems. In Proc. 2015Multi-conf. Syst. Contr., pages 223–250, Syndey, Australia, 2015.

( 3 ) P. Albertos and A. Sala. Multivariable Control Systems: An EngineeringApproach. Springer-Verlag, London, UK, 2004.

( 4 ) B. D. O. Anderson. From Youla-Kucera to identification, adaptive and nonlin-ear control. Automatica, 34(12):1485–1506, 1998.

( 5 ) G. J. Balas and J. C. Doyle. Control of lightly damped, flexible modes in thecontroller crossover region. J. Guid., Contr., Dyn., 17(2):370–377, 1994.

( 6 ) L. Blanken, F. Boeren, D. Bruijnen, and T. Oomen. Batch-to-batch rationalfeedforward control: from iterative learning to identification approaches, withapplication to a wafer stage. IEEE Trans. Mech..

( 7 ) L. Blanken, R. de Rozario, J. van Zundert, S. Koekebakker, M. Steinbuch, andT. Oomen. Advanced feedforward and learning control for mechatronic sys-tems. In Proc. 3rd DSPE Conf. Prec. Mech., pages 79–86, Sint-Michielsgestel,The Netherlands, 2016.

( 8 ) L. Blanken, S. Koekebakker, and T. Oomen. Design and modeling aspects inmultivariable iterative learning control. In Proc. 55th Conf. Dec. Contr., pages5502–5507, Las Vegas, NV, USA, 2016.

( 9 ) F. Boeren, A. Bareja, T. Kok, and T. Oomen. Frequency-domain ILC approachfor repeating and varying tasks: With application to semiconductor bondingequipment. IEEE Trans. Mech., 21(6):2716–2727, 2016.

(10 ) F. Boeren, D. Bruijnen, and T. Oomen. Enhancing feedforward controllertuning via instrumental variables: With application to nanopositioning. Int. J.Contr., To appear.

(11 ) F. Boeren, D. Bruijnen, N. van Dijk, and T. Oomen. Joint input shaping andfeedforward for point-to-point motion: Automated tuning for an industrialnanopositioning system. Mechatronics, 24(6):572–581, 2014.

(12 ) F. Boeren, T. Oomen, and M. Steinbuch. Iterative motion feedforward tuning:a data-driven approach based on instrumental variable identification. Contr.Eng. Prac., 37:11–19, 2015.

(13 ) F. Boeren, R. van Herpen, T. Oomen, M. van de Wal, and M. Steinbuch.Non-diagonal H1 weighting function design: Exploiting spatial-temporaldeformations for precision motion control. Contr. Eng. Prac., 35:35–42, 2015.

(14 ) J. Bolder, S. Kleinendorst, and T. Oomen. Data-driven multivariable ILC:Enhanced performance by eliminating L and Q filters. Int. J. Rob. Nonlin.Contr., To appear.

(15 ) J. Bolder and T. Oomen. Rational basis functions in iterative learning control -

with experimental verification on a motion system. IEEE Trans. Contr. Syst.Techn., 23(2):722–729, 2015.

(16 ) J. Bolder and T. Oomen. Inferential iterative learning control: A 2D-systemapproach. Automatica, 71:247–253, 2016.

(17 ) J. Bolder, T. Oomen, S. Koekebakker, and M. Steinbuch. Using iterativelearning control with basis functions to compensate medium deformation in awide-format inkjet printer. Mechatronics, 24(8):944–953, 2014.

(18 ) J. Bolder, J. van Zundert, S. Koekebakker, and T. Oomen. Enhancing flatbedprinter accuracy and throughput: Optimal rational feedforward controllertuning via iterative learning control. IEEE Trans. Ind. Electr., To appear.

(19 ) D. A. Bristow, M. Tharayil, and A. G. Alleyne. A survey of iterative learn-ing control: A learning-based method for high-performance tracking control.IEEE Contr. Syst. Mag., 26(3):96–114, 2006.

(20 ) A. Bultheel, M. van Barel, Y. Rolain, and R. Pintelon. Numerically robusttransfer function modeling from noisy frequency domain data. IEEE Trans.Automat. Contr., 50(11):1835–1839, 2005.

(21 ) R. A. de Callafon and P. M. J. Van den Hof. Suboptimal feedback controlby a scheme of iterative identification and control design. Math. Mod. Syst.,3(1):77–101, 1997.

(22 ) R. A. de Callafon and P. M. J. Van den Hof. Multivariable feedback relevantsystem identification of a wafer stepper system. IEEE Trans. Contr. Syst.Techn., 9(2):381–390, 2001.

(23 ) J. Chen and G. Gu. Control-Oriented System Identification: AnH1 Approach.John Wiley & Sons, New York, NY, USA, 2000.

(24 ) G. Cherubini, C. C. Chung, W. C. Messner, and S. Moheimani. Introductionto the special section on advanced servo control for emerging data storagesystems. IEEE Trans. Contr. Syst. Techn., 20(2):292–295, 2012.

(25 ) J. C. Compter. Electro-dynamic planar motor. Prec. Eng., 28(2):171–180,2004.

(26 ) S. Devasia, D. Chen, and B. Paden. Nonlinear inversion-based output tracking.IEEE Trans. Automat. Contr., 41(7):930–942, 1996.

(27 ) S. Devasia, E. Eleftheriou, and S. Moheimani. A survey of control issues innanopositioning. IEEE Trans. Contr. Syst. Techn., 15(5):802–823, 2007.

(28 ) S. G. Douma and P. M. J. Van den Hof. Relations between uncertainty struc-tures in identification for robust control. Automatica, 41(3):439–457, 2005.

(29 ) J. C. Doyle and G. Stein. Multivariable feedback design: Concepts for aclassical/modern synthesis. IEEE Trans. Automat. Contr., 26(1):4–16, 1981.

(30 ) E. Evers, M. van de Wal, and T. Oomen. Synchronized stage motion controlusing a youla approach to bi-directional controller coupling. In Submitted.

( 31 ) R. Findeisen, M. A. Grover, C. Wagner, M. Maiworm, R. Temirov, F. S. Tautz,M. V. Salapaka, S. Salapaka, R. D. Braatz, and S. O. R. Moheimani. Controlon a molecular scale: a perspective. In Proc. 2016 Americ. Contr. Conf., pages3069–3076, Boston, MA, USA, 2016.

(32 ) A. J. Fleming. Measuring and predicting resolution in nanopositioning sys-tems. Mechatronics, 24(6):605–618, 2014.

(33 ) A. J. Fleming and K. K. Leang. Design, Modeling and Control of Nanoposi-tioning Systems. Springer, 2014.

(34 ) S. Formentin, K. van Heusden, and A. Karimi. A comparison of model-based and data-driven controller tuning. Int. J. Adapt. Contr. Sign. Proc.,28(10):882–897, 2014.

(35 ) H. Fujimoto, Y. Hori, and A. Kawamura. Perfect tracking control based onmultirate feedforward control with generalized sampling periods. IEEE Trans.Ind. Electr., 48(3):636–644, 2001.

(36 ) S. Galeani, S. Tarbouriech, M. Turner, and L. Zaccarian. A tutorial on modernanti-windup design. Eur. J. Contr., 15(3-4):418–440, 2009.

(37 ) W. K. Gawronski. Advanced Structural Dynamics and Active Control ofStructures. Springer, New York, NY, USA, 2004.

(38 ) E. Geerardyn, T. Oomen, and J. Schoukens. EnhancingH1 norm estimationusing local LPM/LRM modeling: Applied to an AVIS. In IFAC 19th TriennialWorld Congress, pages 10856–10861, Cape Town, South Africa, 2014.

(39 ) M. Gevers. Towards a joint design of identification and control ? In H. L.Trentelman and J. C. Willems, editors, Essays on Control : Perspectives in theTheory and its Applications, chapter 5, pages 111–151. Birkhauser, Boston,MA, USA, 1993.

(40 ) M. Gevers, X. Bombois, B. Codrons, G. Scorletti, and B. D. O. Anderson.Model validation for control and controller validation in a prediction erroridentification framework - part I: Theory. Automatica, 39(3):403–415, 2003.

(41 ) M. Groot Wassink, M. van de Wal, C. Scherer, and O. Bosgra. LPV control fora wafer stage: Beyond the theoretical solution. Contr. Eng. Prac., 13:231–245,2003.

(42 ) J. Guo. Positioning performance enhancement via identification and con-trol of thermal dynamics: A MIMO wafer table case study. Master’s thesis,Eindhoven University of Technology, 2014.

(43 ) F. Hansen, G. Franklin, and R. Kosut. Closed-loop identification via the frac-tional representation: Experiment design. In Proc. 8th Americ. Contr. Conf.,pages 1422–1427, Pittsburgh, PA, USA, 1989.

9

Advanced Motion Control for Next-Generation Precision Mechatronics: Challenges for Control, Identification, and Learning (Tom Oomen)

(44) M. Heertjes, D. Hennekens, and M. Steinbuch. MIMO feed-forward design inwafer scanners using a gradient approximation-based algorithm. Contr. Eng.Prac., 18(5):495–506, 2010.

(45 ) M. Heertjes, B. van der Velden, and T. Oomen. Constrained iterative feedbacktuning for robust control of a wafer stage system. IEEE Trans. Contr. Syst.Techn., 24(1):56–66, 2016.

(46 ) M. F. Heertjes. Variable gain motion control of wafer scanners. IEEJ Journalof Industry Applications, 5(2):90–100, 2016.

(47 ) R. van Herpen, O. Bosgra, and T. Oomen. Bi-orthonormal polynomial basisfunctions for improved frequency-domain system identification. IEEE Trans.Automat. Contr., 61(11):3285–3300, 2016.

(48 ) R. van Herpen, T. Oomen, E. Kikken, M. van de Wal, W. Aangenent, andM. Steinbuch. Exploiting additional actuators and sensors for nano-positioningrobust motion control. In Proc. 2014 Americ. Contr. Conf., pages 984–990,Portland, OR, USA, 2014.

(49 ) R. van Herpen, T. Oomen, and M. Steinbuch. Optimally conditioned in-strumental variable approach for frequency-domain system identification.Automatica, 50(9):2281–2293, 2014.

(50 ) H. Hjalmarsson. From experiment design to closed-loop control. Automatica,41:393–438, 2005.

(51 ) D. J. Hoelzle, A. G. Alleyne, and A. J. Wagoner Johnson. Basis task approachto iterative learning control with applications to micro-robotic deposition.IEEE Trans. Contr. Syst. Techn., 19(5):1138–1148, 2011.

(52 ) P. C. Hughes. Space structure vibration modes: How many exist? Which onesare important? IEEE Contr. Syst. Mag., 7(1):22–28, 1987.

(53 ) D. Hyland, J. Junkins, and R. Longman. Active control technology for largespace structures. J. Guid., Contr., Dyn., 16(5):801–821, 1993.

(54 ) A. Lanzon and G. Papageorgiou. Distance measures for uncertain linearsystems: A general theory. IEEE Trans. Automat. Contr., 54(7):1532–1547,2009.

(55 ) L. Ljung. System Identification: Theory for the User. Prentice Hall, UpperSaddle River, NJ, USA, second edition, 1999.

(56 ) P. Lopes des Santos, A. Perdicoulis, C. Novara, J. A. Ramos, and D. E. Rivera,editors. Linear Parameter-Varying System Identification: New Developmentsand Trends. World Scientific, 2011.

(57 ) C. C. H. Ma. Comments on “A necessary and su�cient condition for stabilityof a perturbed system”. IEEE Trans. Automat. Contr., 33(8):796–797, 1988.

(58 ) R. van der Maas, A. van der Maas, R. Voorhoeve, and T. Oomen. AccurateFRF identification of LPV systems: nD-LPM with application to a medicalX-ray system. To appear in IEEE Trans. Contr. Syst. Techn..

( 59 ) V. M. Martinez and T. F. Edgar. Control of lithography in semiconductormanufacturing. IEEE Contr. Syst. Mag., 26(6):46–55, 2006.

(60 ) D. C. McFarlane and K. Glover. Robust Controller Design Using NormalizedCoprime Factor Plant Descriptions, volume 138 of LNCIS. Springer-Verlag,Berlin, Germany, 1990.

(61 ) S. Mishra, W. Yeh, and M. Tomizuka. Iterative learning control design forsynchronization of wafer and reticle stages. In Proc. 2008 Americ. Contr.Conf., 2008.

(62 ) S. Moheimani and E. Eleftheriou. Dynamics and control of micro- andnanoscale systems. IEEE Contr. Syst. Mag., 33(6):42–45, 2013.

(63 ) R. Munnig Schmidt, G. Schitter, and J. van Eijk. The Design of High Perfor-mance Mechatronics. Delft University Press, Delft, The Netherlands, 2011.

(64 ) H. Niemann. Dual Youla parameterisation. IEE Proc.-Control Theory Appl.,150(5):493–497, 2003.

(65 ) K. Ohnishi, M. Shibata, and T. Murakami. Motion control for advancedmechatronics. IEEE Trans. Mech., 1(1):56–67, 1996.

(66 ) W. Ohnishi and H. Fujimoto. Tracking control method for plant with continu-ous time unstable zeros - stable inversion by time axis reversal and multiratefeedforward -. In IEE of Japan Technical Meeting Record, pages 109–114,2015. MEC-15-047.

(67 ) T. Oomen and O. Bosgra. Well-posed model uncertainty estimation by designof validation experiments. In 15th IFAC Symp. Sys. Id., pages 1199–1204,Saint-Malo, France, 2009.

(68 ) T. Oomen and O. Bosgra. System identification for achieving robust perfor-mance. Automatica, 48(9):1975–1987, 2012.

(69 ) T. Oomen, E. Grassens, and F. Hendriks. Inferential motion control: An iden-tification and robust control framework for unmeasured performance variables.IEEE Trans. Contr. Syst. Techn., 23(4), 2015.

(70 ) T. Oomen and M. Steinbuch. Model-based control for high-tech mechatronicsystems. In The Handbook on Electrical Engineering Technology and Systems,Volume 5 – Factory and Industrial Automated Systems. CRC Press/Taylor &Francis, 2017.

(71 ) T. Oomen, M. van de Wal, and O. Bosgra. Design framework for high-performance optimal sampled-data control with application to a wafer stage.Int. J. Contr., 80(6):919–934, 2007.

(72 ) T. Oomen, R. van der Maas, C. R. Rojas, and H. Hjalmarsson. Iterative data-

drivenH1 norm estimation of multivariable systems with application to robustactive vibration isolation. IEEE Trans. Contr. Syst. Techn., 22(6):2247–2260,2014.

(73 ) T. Oomen, R. van Herpen, S. Quist, M. van de Wal, O. Bosgra, and M. Stein-buch. Connecting system identification and robust control for next-generationmotion control of a wafer stage. IEEE Trans. Contr. Syst. Techn., 22(1):102–118, 2014.

(74 ) I. R. Petersen and A. Lanzon. Feedback control of negative-imaginary systems.IEEE Contr. Syst. Mag., 30(5):54–72, 2010.

(75 ) R. Pintelon and J. Schoukens. System Identification: A Frequency DomainApproach. IEEE Press, New York, NY, USA, second edition, 2012.

(76 ) W. Reinelt, A. Garulli, and L. Ljung. Comparing di↵erent approaches tomodel error modeling in robust identification. Automatica, 38(5):787–803,2002.

(77 ) E. Rogers, K. Galkowski, and D. H. Owens. Control Systems Theory andApplications for Linear Repetitive Processes. Number 349 in LNCIS. Springer,Berlin, Germany, 2007.

(78 ) R. de Rozario, T. Oomen, and M. Steinbuch. ILC and feedforward controlfor LPV systems: with application to a position-dependent motion system. InProc. 2017 Americ. Contr. Conf., Seattle, WA, USA.

(79 ) R. de Rozario, R. Voorhoeve, W. Aangenent, and T. Oomen. Spatio-temporalidentification of mechanical systems: With application to global feedforwardcontrol of an industrial wafer stage. In Submitted for conference publication.

( 80 ) U. Schonho↵ and R. Nordmann. AH1-weighting scheme for PID-like motioncontrol. In Proc. 2002 Conf. Contr. Appl., pages 192–197, Glasgow, Scotland,2002.

(81 ) J. Schoukens, G. Vandersteen, K. Barbe, and R. Pintelon. Nonparametricpreprocessing in system identification: A powerful tool. Eur. J. Contr., 3-4:260–274, 2009.

(82 ) R. J. P. Schrama. Accurate identification for control: The necessity of aniterative scheme. IEEE Trans. Automat. Contr., 37(7):991–994, 1992.

(83 ) M. M. Seron, J. H. Braslavsky, and G. C. Goodwin. Fundamental Limitationsin Filtering and Control. Springer-Verlag, London, UK, 1997.

(84 ) S. Skogestad and I. Postlethwaite. Multivariable Feedback Control: Analysisand Design. John Wiley & Sons, West Sussex, UK, second edition, 2005.

(85 ) R. S. Smith. Closed-loop identification of flexible structures: An experimentalexample. J. Guid., Contr., Dyn., 21(3):435–440, 1998.

(86 ) M. Steinbuch and R. v. d. Molengraft. Iterative learning control of industrialmotion systems. In 1st IFAC Symp, Mech. Syst., Darmstadt, Germany, 2000.

(87 ) M. Steinbuch and M. L. Norg. Advanced motion control: An industrialperspective. Eur. J. Contr., 4(4):278–293, 1998.

(88 ) M. Steinbuch and M. L. Norg. Industrial perspective on robust control: Appli-cation to storage systems. Annual Reviews in Control, 22:47–58, 1998.

(89 ) M. Steinbuch, J. van Helvoort, W. Aangenent, B. de Jager, and R. van deMolengraft. Data-based control of motion systems. In Proc. 2005 Americ.Contr. Conf., pages 529–534, Toronto, Canada, 2005.

(90 ) J. Stoev, T. Oomen, and J. Schoukens. Tensor methods for MIMO decouplingusing frequency response functions. In 7th IFAC Symposium on MechatronicSystems & 1st Mechatronics Forum International Conference, pages 447–453,Loughborough, UK, 2016.

(91 ) P. M. J. Van den Hof. Closed-loop issues in system identification. AnnualReviews in Control, 22:173–186, 1998.

(92 ) R. Voorhoeve, N. Dirkx, T. Melief, W. Aangenent, and T. Oomen. Estimatingstructural deformations for inferential control: A disturbance observer ap-proach. In 7th IFAC Symposium on Mechatronic Systems & 1st MechatronicsForum International Conference, pages 642–648, Loughborough, UK, 2016.

(93 ) M. van de Wal, G. van Baars, F. Sperling, and O. Bosgra. MultivariableH1/µfeedback control design for high-precision wafer stage motion. Contr. Eng.Prac., 10(7):739–755, 2002.

(94 ) J. van de Wijdeven and O. Bosgra. Using basis functions in iterative learningcontrol: Analysis and design theory. Int. J. Contr., 83(4):661–675, 2010.

(95 ) K. Zhou, J. C. Doyle, and K. Glover. Robust and Optimal Control. PrenticeHall, Upper Saddle River, NJ, USA, 1996.

(96 ) J. van Zundert, J. Bolder, S. Koekebakker, and T. Oomen. Resource e�cientILC for LTI/LTV systems through LQ tracking and stable inversion: Enablinglarge tasks on a position-dependent industrial printer. Mechatronics, 38:76–90,2016.

(97 ) J. van Zundert, J. Bolder, and T. Oomen. Optimality and flexibility in iterativelearning control for varying tasks. Automatica, 67:295–302, 2016.

(98 ) J. van Zundert and T. Oomen. On inversion-based approaches for feedforwardand ILC. Submitted for publication.

( 99 ) J. van Zundert, T. Oomen, D. Goswami, and W. Heemels. On the potential oflifted domain feedforward controllers with a periodic sampling sequence. InProc. 2016 Americ. Contr. Conf., pages 4227–4232, Boston, MA, USA.

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