Advanced Motion Control for Precision Mechatronics: … Motion Control for Precision Mechatronics: Control, Identiﬁcation, and Learning of Complex Systems (Tom Oomen) (a) Experimental

IEEJ Transactions on xxVol.137 No.xx pp.1–14 DOI: 10.1541/ieejxxs.137.1

Paper

Advanced Motion Control for Precision Mechatronics:Control, Identification, and Learning of Complex Systems

Tom Oomen∗a) Non-member

Manufacturing equipment and scientific instruments, including wafer scanners, printers, microscopes, and medicalimaging scanners, require accurate and fast motions. An increase in such requirements necessitates enhanced controlperformance. The aim of this paper is to identify several challenges for advanced motion control originating fromthese increasing accuracy, speed, and cost requirements. For instance, flexible mechanics must be explicitly addressedthrough overactuation, oversensing, inferential control, and position-dependent control. This in turn requires suitablemodels of appropriate complexity. One of the main advantages of such motion systems is the fact that experimentingand collecting large amounts of accurate data is inexpensive, paving the way for identifying and learning of modelsand controllers from experimental data. Several ongoing developments are outlined that constitute part of an overallframework for control, identification, and learning of complex motion systems. In turn, this may pave the way fornew mechatronic design principles, leading to fast lightweight machines where spatio-temporal flexible mechanics areexplicitly 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 (1).Also, in semiconductor assembly processes, including wirebonders and die bonders, see Fig. 1(c), products have to bepositioned with varying trajectories, up to 72000 productsper hour (2). Furthermore, for printing systems, ranging fromdesktop printers to industrial printers and 3D printing, seeFig. 1(d), printing accuracy and speed are essential. In scien-tific instruments, such as atomic force microscopes (AFMs)and scanning electron microscopes (SEM), the sample needsto be accurately positioned (3) (4), whereas in computed tomog-raphy CT scanners the detector is positioned for medical imag-ing, see Fig. 1(e). The accuracy and speed of these posi-tioning systems hinges on the motion control design (5) (6) (7)

and determines the capabilities and market position of themanufacturing 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 stiff and highlyreproducible. In conjunction with moderate performance re-quirements, the control bandwidth is well-below the resonancefrequencies of the flexible mechanics, as is also schemati-cally shown in Fig. 2(a). As a result, the system can oftenbe completely decoupled (8) in the frequency range relevantfor control. Consequently, the control design is divided into

a) Correspondence to: [email protected]∗ Eindhoven University of Technology, Department of Mechanical

Engineering, Eindhoven, The Netherlands.

well-manageable single-input single-output (SISO) controlloops, for which standard guidelines exist for their manualtuning by control engineers for both feedback and feedfor-ward, see (7) (9) (10) (11) and Sec. 2.2. In addition, SISO learningcontrol approaches that are suitable for motion control arewell-developed, see (12) (13).

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 effective, hasto increase, leading to flexible dynamics in the cross-overregion, see Fig. 2(b) and also (14) (15) (16). On the other hand, therequirement for rigid-body behavior puts high requirementson the mechatronic system design, e.g., in terms of exotic andstiff materials and hence cost.

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 outlined (Sec. 4), reveal-ing the need for system identification techniques. Next, feed-forward and learning control are addressed (Sec. 5). Hence,this paper addresses both feedback, identification, feedfor-ward, and learning, extending the earlier papers (17) (18) (19). Fi-nally, an outlook on ongoing and related developments inprovided (Sec. 6).

2. Traditional motion control

2.1 Motion systems Mechatronic positioning sys-tems consist of mechanics, actuators, and sensors (9) (20). Theactuators typically generate forces and are considered as inputto the system. The sensors typically measure position and areconsidered as output of the system.

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

Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems (Tom Oomen)

(a) Experimental wafer stage. (b) Prototype reticle stage. (c) Wire bonder.

(d) Industrial flatbed printer.

JOURNAL OF LATEX CLASS FILES, VOL. 13, NO. 9, SEPTEMBER 2014 8

Fig. 5: Philips Allura Centron interventional X-ray system.

θ2

z

y

θ2

z

y

θ1 θ1

Fig. 6: Schematic representation of geometrical effect ofscheduling variable θ2.

in the sense of a single degree of freedom of the system. Asimplified model with input u = [u1, u2]T and output y =[ya,1, ye,2]T = [x, θ2]T is used for the simulations.

Numerical experiments are performed using a multisineexcitation signal with a period length of 10 seconds lead-ing to a spectral distance of 0.1 Hz. The experiments haveidentical excitation frequencies and a flat spectrum. Eachperiod is repeated 6 times leading to a measurement timeof 60 seconds for each of the frozen scheduling parametersets. Over the full scheduling domain, 25 frozen positions aredefined, leading to a total measurement time of 25 minutes.An additive measurement noise is included such that the SNRfor the acceleration and encoder measurement are 30dB and20dB respectively. The simulated measurements, obtained ina closed-loop situation as in Sec. III-C, are processed usingthe standard approach as in Sec. III-A and using the proposednD-LPM approach as presented in Sec. III-B, where for thesingle scheduling parameter the Taylor series expansion as in(42) is used.

The resulting plant estimations are shown in Fig. 8 forthe LPM and the 2D-LPM where the parameters indicatedin Table I are used. It is observed by comparing 7a to 7e, 7b

TABLE I: Local estimation parameters

Tuning parameters Qg Qt Qz n piLPM 3 2 − 8 −2D-LPM 3 2 1 8 2

to 7f, etc., that the plant estimations from the proposed 2Dapproach appear less noisy and take the underlying dynamicalbehavior into account better compared to the LPM. Lookingat the diagonal terms of the systems dynamics, i.e., G11 andG22, the overall behavior over the entire frequency-schedulingdomain appear smoother using the 2D approach. Looking atG21, the systems dynamics remain relatively noisy using bothapproaches, however, the anti-resonance using the 2D-LPMapproach is more clearly than using the LPM. The effectsof measurement noise on the estimations has been reducedsignificantly.

To enable a quantitative comparison, the estimation errorand variance are evaluated. Since an estimation error is onlyavailable when the true system is known, the simulation modelis exploited for this analysis. For each frozen scheduling pa-rameter set, the LTI plant is determined. In Fig. 8, a qualitativemeasure for the performance of the two methods is shown fora single scheduling parameter. The absolute estimation error,defined by,

e[i,j] =∣∣∣G[i,j] −G[i,j]

x

∣∣∣ , (44)

with the superscript [i, j] the elements of the transfer functionmatrix, G the true system, Gx represents any estimated system,with G2DLPM the plant dynamics obtained using the 2D-LPM approach and GLPM the plant dynamics from the LPMapproach per LTI. The total variance follows from (33) aftermapping to the plant using (36). Note that the estimation erroris not a general quality measure, since for physical systems, thetrue system dynamics underlying the identification experimentare unknown.

Besides comparing the LPM for each LTI position indepen-dently and the 2D-LPM, an additional comparison is shownin Fig. 8b, where a moving average filter is used over thescheduling parameter on the results of the LPM. The movingaverage filter is calculated using,

Gs(ΩαP ,θβ) =1

3

1∑

m=−1

GLPM (ΩαP ,θβ +m), (45)

where Gs is the smoothened plant. Although this filter doesnot relate the dynamics in the obtained FRM to the measureddata, it does provide a comparison between a simple additionalstep on the LPM and the proposed 2D-LPM.

Figure 8b shows that the estimation errors from the LPMare larger than the proposed 2D-LPM and the result afteradditional smoothening. Comparing the latter two methodsit can be seen that, in general, the 2D-LPM has the lowestestimation error. Additional to the improved estimation errors,the estimated variances are significantly lower using the 2D-LPM approach, which leads to the conclusion that, for thissimulation example, the nD-LPM approach enables an accu-rate and efficient estimation of the plant dynamics withoutintroducing additional estimation errors.

VI. EXPERIMENTAL RESULTS

The proposed approach is applied to the experimental medi-cal X-ray system in Fig. 5. Similar experiments are performedas described in Sec. V. However, due to the presence of

(e) CT scanner.

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

Controlbandwidth

Flexibledynamics

Frequency

Loop-gain

(a) Traditional loop-gain.

Frequency

Loop-gain

Controlbandwidth

Flexibledynamics

(b) Envisaged loop-gain in next-generation systems.

Fig. 2. Envisaged developments in motion systems. In traditional motion systems, the control bandwidth, i.e., thefrequency where the loop-gain crosses 0 dB takes place in the rigid-body region. In next-generation systems, flexi-ble dynamics are foreseen to occur within the control bandwidth. Indeed, on the one hand, increasing performancerequirements necessitate a larger bandwidth. On the other hand, lightweight constructions lead to the occurrence offlexible dynamics at lower frequencies.

In the frequency range that is relevant for control, the dy-namical behavior is mainly determined by the mechanics. Inparticular, the mechanics can typically be described as (21) (22) (23)

Gm =

nRB∑i=1

cibTi

s2︸︷︷︸rigid−body modes

+

ns∑i=Nrb+1

cibTi

s2 + 2ζiωis + ω2i︸︷︷︸

flexible modes

, · · · · (1)

where nRB is the number of rigid-body modes, the vectorsci ∈ R

ny , bi ∈ Rnu are associated with the mode shapes, and

ζi, ωi ∈ R+. Here, ns ∈ N may be very large and even in-finite (24). 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 (10) (25), (1) can directly be extended.

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

∑nRBi=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., (8). Such frequency response data is inexpen-sive, fast, and accurate to obtain. The importance of suchfrequency response data is further clarified in Sec. 4.8.

2.2 Traditional control architecture The motioncontrol architecture in Fig. 3 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 vector of error signals tobe minimized, f is a feedforward signal, K is the feedbackcontroller, and v represents disturbances. It is remarked thatthese are tacitly used for both continuous and discrete timesystems. Indeed, for manual tuning often the continuous timedomain is used as in (1) - (2). For automated algorithms, as

2 IEEJ Trans. XX, Vol.137, No.xx, 2017


K G

−

r

f

e

v

y

Fig. 3. Traditional motion control architecture.

developed in Sec. 4 and Sec. 5, the discrete time domain ismore natural. These domains can be directly linked, see (26) (27).

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 effectively compensate for reference-induced error signals.In particular, f should be selected such that r − G f is min-imized, possibly taking into account the weighting inducedby the closed-loop system. In the low-frequency range, thesystem is decoupled and Gflex can be ignored in (2), in whichcase f = G−1r = s2r, which is the Laplace transformation ofthe acceleration profile. Note that in (2), the mass of the rigid-body mode is normalized to unity. In practice, the feedforwardsignal is selected as f = ms2r, which is tuned in the time do-main by decorrelating the measured error signal in (3) andthe acceleration profile, details of which can be found in (28).Furthermore, the compliance of the higher-order modes Gflexcan be addressed in a snap term. Also, nonlinear effects suchas friction can be effectively compensated. All these terms canbe directly tuned manually in a straightforward manner (28).

2.2.2 Traditional feedback design For an appropri-ately designed feedforward signal, δ = r −G f is small. In thiscase, the feedback controller has to minimize S (δ − v), whereS is subject to a number of constraints and limitations (29),and hence cannot be made zero in general. The main idea isthat rigid-body decoupling of G enables the shaping of thediagonal elements of S through a decentralized feedback con-troller (30, Sec. 10.6). As a result, each diagonal element of K 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 the flexi-ble modes in Gflex that hamper stability and/or performance.

2.2.3 Traditional learning control The feedforwardcontroller in Sec. 2.2.1 performs well for a range of referencesr: the corresponding command signal f is automatically up-dated for each task, which possibly has a varying reference r.In the case where the setpoint r does not vary, see, e.g., (2) foran application example, the feedforward f may be obtained orimproved using learning techniques. For SISO systems, theseare fairly well-developed, see, e.g., (12) (13) for an approach thatrelates 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(ωi), for frequencies ωi;• decouple the plant to obtain an FRF of G;• design K 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.

Sensor

Fig. 4. 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.

3. Precision motion control developments

3.1 Future mechatronic designs A radically newlightweight 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.

( 2 ) Increased accuracy is enabled by contactless motion,e.g., through magnetic levitation (31), since this avoids frictionand enhances reproducibility. In addition, in certain appli-cations, including EUV lithography (32) (33), motion has to beperformed in vacuum. Contactless motion is then essential toavoid 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 highstiffness 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. 4,as well as an increased susceptibility to disturbances (9, 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.

3.2 Challenges for advanced motion control of 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. 4. A key challenge liesin inferring the unmeasured performance variables. Similarly,in printing applications, both in 2D and 3D additive manufac-turing, performance is desired where material is deposited onthe substrate, while the sensor is mounted on the motor, withflexible dynamics in between, see Fig. 5.



Fig. 5. Schematic illustration of a printing system wherethe performance variables are not directly measured. Inparticular, the sensor is mounted on the motor, while thebelt deformation causes a deposition error.

( 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 providestiffness and damping to the mechanical deformations. Suchan oversensed and/or overactuated situation is in sharp con-trast to 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. 4, the spatio-temporal deforma-tions are observed differently if the sensor is attached to thefixed world. In the sense of the model in (1), this implies thatthe ci, bi vectors depend on the actual position of the system,and (1) may be viewed as a local linearization of the overallnonlinear system. Similarly, in certain systems, includinggantry stage designs, mass distributions change due to mo-tion, leading to additional position-dependent behavior. A keychallenge lies in handling the position dependence of futuresystems.

( 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-turing machines and scientific instruments involve multiplecontrolled subsystems, e.g., in the schematic illustration ofa wafer scanner in Fig. 4, 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 aerror budgets. As a result, performance limitations (29) in eachsubsystem will negatively impact the overall performance. Ajoint design enables that individual subsystems will be able tocompensate each other’s limitations. A main challenge lies inan increase of the complexity of the control 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 lithogra-

Fig. 6. Example of flexible tasks in 2D and 3D printing.

K

P

w z

yu

Fig. 7. Generalized plant setup, where P(G). Note thatK can be equal as in Fig. 3, but can also be extended togenerate the signal f in Fig. 3.

phy, have to be attenuated. These increase proportionally tomass reduction (9, Sec. 9.5.2) and must be explicitly compensated.

( 7 ) Versatile 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 compensatefor surface roughness (9, Sec. 9.4.1), ( c ) die bonders and wire bon-ders perform pick-and-place tasks based on actual productlocations (2), and ( d ) 2D printing tasks involve varying refer-ences and media width (34). As a result, the positioning systemsin such machines have to perform a class of tasks, see Fig. 6.

3.3 A generalized plant approach A generalizedplant framework allows for a systematic way to address thefuture challenges in advanced motion control. In particular,the envisaged developments on future mechatronic systemdesign, as described in Sec. 3.1, lead to challenges for motioncontrol design, as are identified in Sec. 3.2.

The generalized plant is depicted in Fig. 7. The general-ized plant is by no means new, and is at the basis of commonoptimization-based control algorithms (30). However, the gen-eralized plant allows a systematic and unified framework inwhich the challenges in Sec. 3.2 can be cast and conceptuallyaddressed. In contrast, the traditional architecture in Fig. 3,which directly fits in the setup of Fig. 7, does not allow toaddress these challenges, even at a conceptual level.

In Fig. 7, z are the performance variables, addressing Chal-lenge 1, which arises in addition to the already present mea-sured variables y. Indeed, y and u are the measured variablesand manipulated variables, respectively, the dimensions ofwhich will drastically increase in view of Challenge 2. Thevariable w contains the exogenous inputs, typically includingboth reference signals and disturbances (Challenge 6), i.e.,r and d in Fig. 3. Now, these variables may all be position-dependent (Challenge 3), and in addition, the variable r mayvary for each task (Challenge 7). Furthermore, if multiplesystems are addressed simultaneously, either due to their in-teraction, or their interaction due to a shared, overall machinecontrol goal (Challenge 4), then this substantially increasesthe signal dimensions. Similarly, a joint thermal-mechanicalcontrol design (Challenge 5) involves signals and systems inboth the thermal domain and the positioning domain.

The generalized plant approach in Fig. 7 directly reveals theadditional complexity arising from the challenges outlined inSec. 3.2. Here P(G) denotes the generalized plant, which con-



tains the input-output plant G as well as the interconnectionstructure, e.g., Fig. 3. 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. Indeed, the generalizedplant is a conceptual framework to pose the overall problem,the actual design of motion controllers requires substantiallymore steps. Importantly, the controller K in Fig. 7 can beeither a feedback controller, a feedforward controller, or both.Due to the fundamentally different objectives of these con-trollers, these are investigated sequentially in the forthcomingsections.

4. Feedback and identification for controlFeedback control, i.e., K in Fig. 3, is essential to deal with

uncertainty in the system dynamics G and disturbances v.Indeed, the main goal of feedback is to render the systeminsensitive to such uncertainties. Note that the commonly im-posed requirement of stability is only a direct consequence ofthe presence of uncertainties. In this section, feedback controldesign is investigated in view of the challenges 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 (30). 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) = ‖Fl(P(G),K)‖ · · · · · · · · · · · · · · · · · · · · · · · · (4)

is posed, where the goal is to compute

Kopt = arg minK

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

Here, ‖.‖ denotes a suitable norm, e.g., H2 or H∞, and 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.Indeed, P(G) is the generalized plant depicted in Fig. 7 that en-compasses most controller architectures, see (30, Sec. 3.8) for details.Next, note that Fl(G,K) is typically a closed-loop transferfunction matrix, e.g., the general four-block problem

Fl(G,K) = W[

GI

](I + KG)−1

[K I

]V, · · · · · (7)

where W and V are user-chosen weighting filters of suitabledimensions. For instance, if W =

[I 0

], V =

[0 I

]T,

then (7) reduces to

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

It is emphasized that Go in (5) denotes the true system, e.g.,one of the systems depicted in Fig. 1. Note that Go is unknownand will be represented by a model G, as is elaborated next.

10 -3 10 -2 10 -1 100 101 102 103-150

-100

-50

0

50

100

150

|.|[dB]

10 -3 10 -2 10 -1 100 101 102 103

f [Hz]

-180

-90

0

90

180

6(.)[]

Fig. 8. Example 1: true system Go in (9) (solid blue),model G1 in (10) (dashed red), model G2 in (11) (dash–dotted green).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1t

0

0.02

0.04

0.06

0.08

0.1

y

Step open-loop

Fig. 9. Example 1: open-loop response to the input fin (12). True system Go in (9) (solid blue). The modelG1 in (10) (dashed red) closely matches the true output.However, model G2 in (11) (dash-dotted green) shows astrong deviation compared to the true response.

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 sucha model, see (35) (36) (37) for an overview. Indeed, the machine isoften already built, enabling direct 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 (38); andiii) identification experiments are based on finite time dis-turbed observations, leading to uncertainties on estimatedparameters, e.g., ζi and ωi 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 · (2π100)s + (2π100)2 · · · · · (9)



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1t

-3

-2

-1

0

1

2

3y

Step closed-loop

Fig. 10. Example 1: closed-loop response to the inputf in (12) with optimal controller K = 105. True systemGo in (9) (solid blue). The model G2 in (11) (dash-dot-ted green) now closely matches the true output. In con-trast, the model G1 in (10) (dashed red), which accuratelypredicted the open-loop response, performs poorly whenpredicting the closed-loop response.

and the modelsG1 =

1s2 −

1s2 + 2 · 0.1 · (2π100)s + (2π100)2 · · · · (10)

andG2 = 1

s2+2·1s·(2π0.2)+(2π0.2)2 + 1s2+2·0.1·(2π100)s+(2π100)2 , (11)

see Fig. 8 for a Bode plot.Next, an input

f (t) =

1 0 ≤ t ≤ 0.10 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. 3. Inaddition, r and v are zero in Fig. 3. The responses are depictedin Fig. 9. It is observed that G1 matches the true responseaccurately, while G2 shows a very different response. In par-ticular, Go and G1 show an unbounded response due to therigid-body behavior, while G2 shows a bounded response. TheBode plots in Fig. 8 support this observation, since the modelG2 does not have a −40dB/dec slope at low frequencies. Thekey point is that most system identification techniques delivera model that compares to G1, which is of course desired if thegoal is to simulate Go in open-loop as in Fig. 9.

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. 3, then the results in Fig. 10 are ob-tained. The difference of these closed-loop results are strikingcompared to Fig. 9: 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. 9, is verysuitable for predicting the closed-loop response.

The main conclusion from Example 1 is that the quality ofmodels should be evaluated in view of their subsequent goal.The main goal of the models here is to deliver a controllerthat performs well on the true system in closed-loop. In thissection, the identification of models in view of feedback con-trol is investigated, the feedforward and ILC case is furtherelaborated on in Sec. 5.1.5.

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), which is bounded by

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 relatedto 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(G)) involves a norm. Hence, by rewriting andapplying the triangle inequality for a certain K,

J(Go,K)= J(G,K) + J(Go,K) − J(G,K) · · · · · · · · · (15)≤ J(G,K) + ‖Fl(P(Go),K) − Fl(P(G),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) isdirectly obtained as the (weighted) closed-loop system withKexp implemented.

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

GCR = arg minG‖Fl(P(Go),Kexp)−Fl(P(G),Kexp)‖.(17)

Essentially, in (17) a control-relevant model GCR is identifiedthat aims at representing closed-loop behavior. The minimiza-tion in (17) can be directly performed using the algorithm in,e.g., (39). Note that (17) depends on the controller K. If K ischosen equal to Kopt, then typically the best result is obtained.Since Kopt is unknown, the result will depend on the qualityof Kexp. To mitigate this dependence, the controller synthesis(13) and control-relevant identification (17) can be solved al-ternately, aiming to minimize the upper bound (16). Such aniterative procedure is at the basis of many approaches, includ-ing (40) (41) (42) (43) (44) (45). Unfortunately, such an iterative approachdoes not necessarily work, since the triangle inequality in (16)only holds valid for a fixed K, and does not allow for itera-tive 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 (30), the true system behavior isrepresented by a model set G such that

Go ∈ G. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (18)



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

G =G∣∣∣G = Fu(H,∆u),∆u ∈ ∆u

, · · · · · · · · · · · · · · · (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, see (30, (8.23)) for details. Note that G is recoveredif the uncertainty is zero, so that G = Fu(H, 0).

It remains to specify ∆u in more detail. In view of theconsidered motion control objectives, anH∞ norm, i.e.,

‖H‖∞ = supωσ(H( jω)), · · · · · · · · · · · · · · · · · · · · · · · · · (21)

with σ denoting maximum singular value, is selected for thefollowing reasons.( 1 ) H∞-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., (46).

( 2 ) The H∞ norm provides a suitable means to quantifyperformance objectives for motion systems in (4). In par-ticular, theH∞ norm allows a loopshaping-based design,see (47) (48) for a general perspective and (7) (49) (50) (51) (52) for amotion control perspective. In addition, controller syn-thesis is typically most straightforward if a single normis used for representing uncertainty and specifying theperformance objectives.

Hence,

∆u =∆u ∈ H∞

∣∣∣ ‖∆u‖∞ ≤ γ, · · · · · · · · · · · · · · · · · · (22)

where γ ∈ R+. Associated with G is the worst-case criterion

JWC(G,K) = supG∈G

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

Hence, by minimizing the worst-case performance

KRP = arg minK

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

the controller KRP achieves robust performance in the sensethat using (18), it leads to the tight 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 thecontrol-relevant identification problem of a nominal model Gin 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 K

as in (24), it is minimized for the entire set G, leading to therobust-control-relevant identification criterion

GRCR = minG

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

subject to (18).

Combining the arguments implies that

J(Go,KRP) ≤ JWC(GRCR,KRP) ≤ JWC(GRCR,Kexp),(27)

hence guaranteed performance enhancement is achieved. Al-though this also depends on Kexp, it can be iterated, leading tomonotonous performance enhancement (53), which is in sharpcontrast to the suggested iterative procedure in Sec. 4.3.

The key question is how to actually determine the modelset (26). The approach pursued here is to continue along thepath in Sec. 4.3, i.e., to determine a control-relevant modelas in (17). A second step aims at extending the model GCRwith ∆u such that (26) is actually addressed. Many techniqueshave been developed for selecting the structure of uncertainty,e.g., (54, Table 9.1), as well as quantifying its size (55) (56). 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 =

G∣∣∣G = G2 + ∆u, ‖∆u‖∞ ≤ γ

. · · · · · · · · · (28)

Then, since G2 ∈ H∞ and by (28), G ⊂ H∞. However,since Go < H∞, (18) cannot be satisfied. The main reasonis that Go contains a rigid-body mode, which is neitherincluded in G2, nor in anH∞-norm-bounded perturbation∆u. This is confirmed by Fig. 8, where G2 has a boundedmagnitude, yet Go → ∞ for ω→ 0. Hence, no bounded∆u can capture the model mismatch using the structure(28).

( 2 ) Suppose that the previous issue 1 is appropriately dealtwith, and a certain bound γ guarantees that (18) is sat-isfied, the next question is how this actually minimizesJWC(G,Kexp) over G in (26). Indeed, often G satisfies(18), yet contains an element or a subset that is not sta-bilized by Kexp, in which case (26) is unbounded, see,e.g., (17, Table 1).

( 3 ) Suppose that issue 1 and 2 are addressed, the final ques-tion is how JWC(G,Kexp) in (26) can be actually mini-mized.

These three issues 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., (51) (57),due to inappropriately dealing with Issues 1 - 3, above.

The main trick to address Issues 1 and 2 has a very longhistory in control and is known as the dual form of the Youlaparameterization. The Youla parameterization (58) parameter-izes all controllers that stabilize a certain system. The dualform, as is considered here, see also (53) (59) (60) (61) (62), 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,



100 101 102 103−220

−200

−180

−160

−140

−120

−100

−80

−60

outputyx

i n p u t u x

100 101 102 103−220

−200

−180

−160

−140

−120

−100

−80

−60i n p u t u y

100 101 102 103−220

−200

−180

−160

−140

−120

−100

−80

−60

f [Hz ]

outputyy

100 101 102 103−220

−200

−180

−160

−140

−120

−100

−80

−60

f [Hz ]

|Pi,j|[d

B]

Fig. 11. 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 (17).

• Go is stabilized by Kexp, hence (18) is satisfied for a suffi-ciently large γ,

• 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 (63), this freedom isexploited through a new coprime factorization, which directlyconnects the size of uncertainty γ in (22) and the control-relevant identification criterion (17). The underlying theoryclosely connects to recent developments in, e.g., (64). A keyconsequence of this approach is that it provides an automaticscaling of the uncertainty, both in input/output directions andfrequency. In turn, this enables the use of unstructured uncer-tainty in (22), which has important consequences for solving(24), e.g., using D − K iterations (65).

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 theH∞ 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 γ using any model uncertainty quantificationprocedure that delivers the minimal γ such that (18) issatisfied, e.g., (66) (67) (68).

( 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 next.

101

102

103

−200

−150

−100

101

102

103

−200

−150

−100

101

102

103

−200

−150

−100

101

102

103

−200

−150

−100

101

102

103

−200

−150

−100

101

102

103

−200

−150

−100

101

102

103

−200

−150

−100

101

102

103

−200

−150

−100

101

102

103

−200

−150

−100

Frequency (Hz)

Magnitude(dB)

Fig. 12. Sec. 4.7.2: Overactuation of a prototype waferstage (69). The original model G has torsion mode with aresonance frequency of 143 Hz (dashed red). After closingthe torsion loop, this resonance shifts to 193 Hz, where theequivalent plant model is shown (solid red). The identifiedfrequency response function with the torsion loop closed(dotted blue) confirms the result.

4.7.1 Case 1: multivariable modeling for robust con-trol. To show that the approach in Sec. 4.6 can deal withmultivariable 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 (30, Sec. 2.4.5) of 90 Hzwith PID characteristics.

The identification results are depicted in Fig. 11. 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 (17) for details. Thiserror can be further reduced by repeating the design cycle inSec. 4.6, as well as an error-based redesign (26).

4.7.2 Case 2: overactuation. The closed-loop band-width is often limited by resonance phenomena (69), even ifmultivariable loopshaping techniques (52) are used that addressthe input/output directionality of Gflex in (2). In view of theideas in Sec. 3.2, additional actuators and sensors can be ex-ploited. From a practical perspective, these can be employedto add active damping and stiffness. This technique has beensuccessfully applied to a prototype wafer stage, where in theresult of Fig. 12 a single actuator and sensor pair address thetorsion mode, leading to a 35% bandwidth increase comparedto the traditional input-output situation. These techniques arebeing extended to the 14 input-14 output prototype reticlestage in Fig. 1(b), which can potentially achieve a significantaccuracy and throughput enhancement by lightweight stagedesign, see Sec. 3.1. Finally, it is emphasized that the useof overactuation and oversensing has important benefits com-pared to traditional notch filters, as mentioned in Sec. 2.2.4.In particular, notch filters essentially render the vibrationalmodes unobservable, and only focus on local performance.In contrast, the proposed approach using overactuation andoversensing typically improves global performance (23).



xy

z

xy

Fig. 13. 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 (73) .

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. 3, see (25)

for details and an experimental example.4.7.4 Case 4: position-dependent control. Motion

systems perform motions by definition. Hence, it can be ex-pected that the system in Fig. 4 is position dependent, sincethe sensor observes the mode-shapes differently for changingpositions. As a result, the position-dependence of the observa-tion enables casting the system into the framework of linearparameter-varying (LPV) systems (70) (71), for which reliablesynthesis techniques are available. However, the identificationof such systems from data is challenging (72). Recently, a newapproach has been developed (73) to model position-dependentsystems for LPV control, which consists of two steps.( 1 ) Identify the system at a large number of frozen positions

nθ, which are considered as ny ·nθ auxiliary outputs. Iden-tify the high-dimensional nu input ny · nθ 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 promising, see Fig. 13.4.7.5 Case 5: systems of systems. The overall con-

trol of the wafer stage in Fig. 4 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 frameworkof Fig. 7 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 (74) for recent results in this direction, as well asreferences therein.

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. 7, and the approach inSec. 4.6 has recently been applied to a thermal control sys-tem with thermal actuators and sensors (75). 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) (66) (76), compensation through disturbance observers (77),and disturbance-based control (26) (78).

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 tra-ditional approach in Sec. 2.2.2. Although the theory is laidout, the algorithms still require significant user interaction.Also, numerical aspects are highly challenging (79) (80) (81) (82), es-pecially for the complex systems envisaged in Sec. 3.2.

Taking into account the current level of maturity of the toolsdescribed in this section and based on significant experiencewith multivariable motion systems, the following procedureenables a systematic design of motion controllers.

Procedure 1 Advanced motion control design procedure.1. Interaction analysis. Decoupled?

• yes: independent SISO design (Sec. 2.2.2). No: next step2. Static decoupling (Equation (2)). Decoupled?

• yes: independent SISO design (Sec. 2.2.2). No: next step3. Decentralized MIMO design: loop closing procedures (83, Sec. 1.3.3)

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

Not successful? Next step4. Optimal & robust control (Sec. 4.6)

• centralized controller with typically best performance• requires parametric model

Procedure 1 has proven to perfectly balance effort vs. con-trol requirements (83). Indeed, the effort in terms of user inter-vention and modeling are only increased if necessitated by thecontrol requirements. Interestingly, the first three steps are allbased on FRF data, whereas the last step, i.e., the procedureof Sec. 4.6 involves the use of a parametric model.

Note that all four steps in Procedure 1 are based on FRFdata. Indeed, Step 4 in Procedure 1 involves the identificationproblem Sec. 4.3, which is again based on FRFs. This has ledto a renewed interest in identifying FRFs of complex mecha-tronic systems, where traditionally noise excitation has beenused (7) (51). These have been extended towards periodic exci-tation for motion systems (17), and more recently substantialadvancements have been made using local parametric mod-eling techniques (84), including extensions to linear parameter-varying (LPV) systems (85) and multivariable systems (86).

5. Feedforward and learning

Feedforward and learning control are essential for highperformance 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 and repetitive control Iterative learn-ing control (ILC) (13) is particularly promising for positioningsystems that perform repeating tasks. Typically, the feedfor-ward signal f in Fig. 3 is updated based on past experimentsor 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 (87). For SISO systems, a well-developed de-sign framework is available (12), yet in view of the challenges inSec. 3.2, ILC algorithms of the form (29) are not directly appli-



printheadpaper

y

motor

u

rollers

worm drive

z

scanner

encoder

Fig. 14. Schematic side-view illustration of the posi-tioning drive in a printer system for inferential ILC inSec. 5.1.1. The paper position z is controlled using the mo-tor. The feedback uses real-time encoder measurements y.The performance z is measured line-by-line using the scan-ner, which is used for iterative learning control purposes.

ii

“commandsignals1Dof2DofCombined˙temp” — 2014/9/4 — 10:48 — page 1 — #1 ii

ii

ii

0 0.5 1 1.5 2−200

−100

0

100

200Parallel 1-DOF

u∞,f∞,uC ∞

Time [s]

(a)

0 0.5 1 1.5 2

u∞,η∞·2·105

Time [s]

Serial 2-DOF

(b)

Fig. 15. Signals after convergence of inferential ILC inSec. 5.1.1. In traditional motion control architectures(Fig. 3), the ILC command signal f (red dashed) cancelsthe feedback controller output (blue dashed, also Ke inFig. 3), leading to an internally unstable system (the over-all input u (black solid) remains bounded). An adaptedcontroller architecture leads to closed-loop stability in a2D systems setting, see (91), leading to both a bounded ILCcommand signal f (black solid) and bounded feedbackcontroller output (red-dashed).

cable. The challenges in Sec. 3.2 are now briefly investigatedin the context of ILC, see (19) for a more detailed overview.Repetitive control (88) (89) is a control strategy that is similar toILC, yet does not reset the system after each repetition. Thementioned challenges are focussed on ILC, yet also apply torepetitive control situations.

5.1.1 Inferential ILC for unmeasurable feedback sig-nals. Often, the performance variables are not directly ac-cessible to the feedback controller, but they can be measuredafter a task is completed. For instance, in printing invisiblemarkers can be used (90, Sec. 5.3). This idea is illustrated in Fig. 14.When ILC is applied to the z measurement, whereas feedbackis applied to y, it is generally impossible to track a referencefor both, i.e., to ensure that both r− y and r− z are small. Thiscan lead to severe consequences when attempting to do so,e.g., using integral action in conjunction with ILC, as is illus-trated in Fig. 15. To systematically address these aspects, a2D systems approach, see (87), is used in the context of inferen-tial ILC framework developed in (91), which also encompassesrelated inferential ILC approaches, including (92).

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 effectiveup to the Nyquist frequency, imposing model quality require-ments over the entire frequency range, which is in sharp con-

0 2 4 6 8 10 12

Trial j [-]

10-5

100

||ej|| 2

Fig. 16. Multivariable ILC in Sec. 5.1.2. Independentlydesigned ILC loops (, ×) converge when implemented in-dependently. However, when implemented simultaneously(), the multivariable ILC does not converge.

0 2 4 6 8 10 12

Trial j [-]

10-2

10-1

100

||ej|| 2

Fig. 17. Multivariable ILC in Sec. 5.1.2. MultivariableILC designs (93): decentralized with robustness for interac-tion (×), centralized based onH∞ preview control (), andcentralized based on MIMO ZPETC () lead to convergentILC algorithms. In contrast, a decentralized design thatignores interaction () leads to a divergent error norm.

trast to the results in Fig. 11. In (93), the ILC analogue ofProcedure 1, which aims at advanced motion feedback controldesign, is developed. Indeed, as is shown in Fig. 16, a decen-tralized ILC that ignores interaction may lead to an unstableILC algorithm in the iteration domain when both loops areclosed simultaneously. In Fig. 17, several solutions are shownthat lead to a stable ILC iteration. Here, the decentralizeddesign requires the least modeling effort, i.e., only the diago-nal terms need to be modeled parametrically. A centralizeddesign typically improves the performance, yet requires a fullmultivariable parametric model. Hence, the procedure in (93)

appropriately balances the required modeling effort and theperformance requirements. As an additional aspect in dealingwith multivariable systems, the potential of additional inputsfor ILC is established in (94).

5.1.3 ILC for position-dependent systems. SinceILC is effective over a much larger frequency range com-pared to feedback, the effect of position-dependent dynamicsis amplified. In particular, when applying ILC to the position-dependent printer in Fig. 1(d), linearized models either lead toa divergent scheme or slow convergence, see Fig. 18. An LTVapproach, see (95), can effectively deal with position-dependentbehavior. Initial results towards an LPV approach are reportedin (96), whereas an LPTV approach is pursued in (97).

5.1.4 Systems of systems. The design procedure in(93) can directly be applied to such systems, whereas a system-atic ILC add-on as in Sec. 4.7.5 is developed in (98).

5.1.5 Flexible tasks. One of the largest drawbacks oftraditional ILC is that it requires the reference r in Fig. 3 tobe fixed. This is in sharp contrast to traditional feedforwardcontrol as is outlined in Sec. 2.2.1. The main goal of recentresearch, including (90) (99) (100) (101) has been to combine the per-formance advantages of learning control with the extrapolationcapabilities of the feedforward structures in Sec. 2.2.1.

As an application example, the wire bonder in Fig. 1(c) has



0 0.5 1 1.5 2 2.5 30

1

2

3

time [s]

r y[m

]/r x

[m]

Fig. 9. Reference trajectory ry ( ) introducesposition-dependent dynamics due to the moving carriage mass.Reference rx ( ) is a forward-backward movement. Rotation ϕ issuppressed, i.e., rϕ = 0.

0 1 2 3 4 5 6 7 8 910−10

1010

1030

trial j [#]

J

Fig. 10. Performance criterion for simulations on an LTV systemwith ILC based on: LTV model, wf = 10−10 ( ); LTI model aty = 1.6 m, wf = 10−10 ( ); LTI model at y = 6 m, wf = 10−10

( ); and LTI model at y = 6 m, wf = 102 ( ). The LTI modelat y = 6 m requires additional robustness (larger wf ) to converge.

obtained. If a poor LTI model is chosen, for example aty = 6 m, there is no convergence ( ). Convergence canbe guaranteed by introducing robustness through increas-ing wf [43]. Indeed, for wf = 102 there is convergence( ), but at the cost of performance. Note that y = 6 mis not feasible for the current system, but might becomeso for larger printing systems. The result stresses the needfor identification of accurate position-dependent modelswhich is part of future research.

The simulation example shows the benefit of ILC basedon an LTV model when the system to control is LTV.For accurate LTI models, high performance is still achiev-able but at the cost of slower convergence, whereas forinaccurate LTI models performance needs to be sacrificedto guarantee convergence. Importantly, resource-efficientILC in Algorithm 8 can directly be applied to LTV models,while preserving computational cost O(N).

6. Experimental implementation

In this section, the resource-efficient ILC approach isapplied to the industrial flatbed printer in an experimentwith task length N = 100000 which forms contribution IV.

−120−80−40

|Pxx|[dB]

−180−90

0

90

180

6P

xx[]

−120−80−40

|Pϕx|[dB]

10−2 100 102−180−90

0

90

180

Frequency [Hz]

6P

ϕx[]

|Pxϕ|[dB]

6P

xϕ[]

|Pϕϕ|[dB]

10−2 100 102

Frequency [Hz]

6P

ϕϕ[]

Fig. 11. Bode diagram of the system P for the 2× 2 Arizonagantry based on an averaged frequency response measurement.

6.1. System modeling

The previous section shows the importance of an accu-rate system model to obtain both fast convergence andhigh performance in the error norm. However, the accu-racy of the derived position-dependent model based on firstprinciples is limited and identification of accurate position-dependent models is part of ongoing research. Still, for theconsidered range of operation, the simulation study in Sec-tion 5 reveals that an LTI model is sufficiently accurate toguarantee convergence, albeit at a lower rate compared tothe LTV model, see Fig. 10. This validates the use of LTImodels in the present experimental study. For the exper-iments in this paper, ILC is based on an LTI model de-rived from an averaged frequency response measurement,see Fig. 11 for the Bode diagram of the model P . Forfeedback, the feedback controller in Fig. 7 is used.

6.2. Experiment design

Contrary to the simulation case study in Section 5,where ILC was applied to a multi-input, single outputsystem, in the experiments ILC is applied to multi-input,multi-output system. During printing the gantry positionis typically fixed while the carriage with the print headsmoves over the gantry. In between the printing, the gantryperforms a stepping motion in x-direction in order to coverthe next part of the medium. Without controlling the car-riage, this results in the reference trajectories as shown inFig. 12, with task length N = 100000. The small rotationin ϕ during printing can be used for correcting misalign-ments.

11

Fig. 18. Position-dependent ILC in Sec. 5.1.3. ApplyingILC to the position-dependent printer in Fig. 1(d). First,a linearized model at an edge position is used. This LTImodel leads to a divergent iteration when applied to theposition-dependent system (∗). Inclusion of a Q-filter forrobustness leads to convergence, yet limited performanceenhancement (×). Linearization of the model at a differentlocation leads to a convergent ILC (+) without the needfor a Q-filter, hence leading to improved performance. AnLTV design (95) leads to superior performance: it achieveshigh performance and fast convergence.

0 0.01 0.02−3.5

−1.5

0.5x 10

−3

r [m

]

time [s]

Fig. 19. Varying references in ILC, see Sec. 5.1.5, asoccurring in the wire bonder of Fig. 1(c). Due to varyingproduct locations, the end-position varies.

varying references for every product due to position variabil-ity. As a result, the end-position of the point-to-point motionvaries, see Fig. 19. ILC is highly susceptible to such changes,see Fig. 20, since a reference change at iteration 10 leads to alarge performance degradation. Note that the reference is keptconstant from iteration 0-9 for illustration purposes only. Formore details on the wire bonder application, see (2). For a suc-cessful applications on the printer system of Fig. 1(d), see (34).For an application to the wafer stage of Fig. 1(a), see (102).

The theoretical framework is further extended towards inputshaping (103) and rational feedforward structures in (104) (105) (106),which have as key advantage that these can exactly compensatenon-minimum phase dynamics, see (107) for a detailed exposi-tion, and also (95) (108) (109) for further details and applications.

Finally, a strongly related approach that further connectsto system identification in Sec. 4.3 is developed in (28) (110) (111).In particular, this approach essentially constitutes a frame-work for identification of models for feedforward, where theanswer lies in identifying the inverse system directly usinginstrumental variable system identification (112). For a detailedcomparison to ILC-based approaches, see (102). Notice that inILC, the identification criterion for the model, which is neededto construct the learning filter, is slightly different and shouldbe chosen such that the model error is less than 100 % in therelevant frequency range of interest, see (93) for details in thisdirection.

0 2 4 6 8 10 12 14 16 1810

−6

10−5

10−4

10−3

Task [−]

||e||2[m

]

Fig. 20. Varying references in ILC, see Sec. 5.1.5, asoccurring in the wire bonder of Fig. 1(c). In iteration 0−9,the blue reference of Fig. 19 is used, while from itera-tion 10 at further, the green dashed reference of Fig. 19is used. Clearly, standard ILC (red) is highly sensitiveto reference changes, whereas the proposed ILC with ba-sis function in (2) (green) enables high performance forversatile references.

6. OutlookAdvanced motion control is a highly challenging and im-

portant area. Several issues arising from ongoing develop-ments in applications have been identified, along with severalsolution strategies that are being developed. Many relatedchallenges, e.g., for specific application areas, have not beenaddressed in the present paper, including (4) (113) (114) (115) (116). Inaddition, numerical aspects are highly challenging for com-plex systems, in control (117), system identification (79) (80) (81) (82),and learning (95). In addition, resource-efficient approaches forILC based on sparse optimization are investigated in (118). Fur-thermore, nonlinear control techniques have been investigatedin, e.g., (119) (120) (121). Digital implementation aspects are inves-tigated in (116) (122) (123). Finally, data-driven techniques to avoidmodeling altogether are being investigated in, e.g., (121) (124) (125)

for feedback control and (126) (127) for ILC.In the near future, developments in advanced motion control

may enable a paradigm shift in mechatronic system design. In-deed, a very lightweight design is foreseen, see Fig. 4, wherestiffness is obtained through active control. Indeed, basedon measured sensor information, the controller predicts thespatio-temporal behavior (either locally at the performancelocation or globally, and determines a suitable force profilefor accurately positioning the stage and its internal flexibledynamics, see Fig. 21 for details. In addition, thermal be-havior will be actively controlled. These future systems mayachieve unprecedented accuracy, speed, and cost, and willcommunicate with other subsystems to increase overall sys-tem performance.

AcknowledgementI 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, for the jointresearch that led to the results in this paper.

References

( 1 ) V. M. Martinez and T. F. Edgar. Control of lithography in semiconductormanufacturing. IEEE Control Systems Magazine, 26(6):46–55, 2006.

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

( 3 ) D. Abramovitch, S. Andersson, L. Pao, and G. Schitter. A tutorial on the me-chanics, dynamics, and control of atomic force microscopes. In Proceedings



Fig. 21. Control of future lightweight stages as in Fig. 4.Based on measured sensor information, the controller pre-dicts the spatio-temporal behavior (either locally at theperformance location or globally), and determines a suit-able force profile for accurately positioning the stage andits internal flexible dynamics.

of the 2007 American Control Conference, pages 3488–3502, New York, NewYork, United States, 2007.

( 4 ) 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 Proceedings of the 2016 AmericanControl Conference, pages 3069–3076, Boston, Massachusetts, United States,2016.

( 5 ) K. Ohnishi, M. Shibata, and T. Murakami. Motion control for advancedmechatronics. IEEE Transactions on Mechatronics, 1(1):56–67, 1996.

( 6 ) H. S. Lee and M. Tomizuka. Robust motion controller design for high-accuracy positioning systems. IEEE Transactions on Industrial Electronics,43(1):48–55, 1996.

( 7 ) M. Steinbuch and M. L. Norg. Advanced motion control: An industrialperspective. European Journal of Control, 4(4):278–293, 1998.

( 8 ) J. Stoev, J. Ertveldt, T. Oomen, and J. Schoukens. Tensor methods for MIMOdecoupling and control design using frequency response functions. Mecha-tronics, 45:71–81, 2017.

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

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

(11 ) H. Butler. Position control in lithographic equipment an enabler for current-day chip manufacturing. IEEE Control Systems Magazine, 31(5):28–47, 2011.

(12 ) M. Steinbuch and R. v. d. Molengraft. Iterative learning control of industrialmotion systems. In 1st IFAC Symposium on Mechatronic Systems, pages967–972, Darmstadt, Germany, 2000.

(13 ) 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 Control Systems Magazine, 26(3):96–114, 2006.

(14 ) G. J. Balas and J. C. Doyle. Control of lightly damped, flexible modes in thecontroller crossover region. Journal of Guidance, Control, and Dynamics,17(2):370–377, 1994.

(15 ) D. Hyland, J. Junkins, and R. Longman. Active control technology for largespace structures. Journal of Guidance, Control, and Dynamics, 16(5):801–821,1993.

(16 ) I. R. Petersen and A. Lanzon. Feedback control of negative-imaginary systems.IEEE Control Systems Magazine, 30(5):54–72, 2010.

(17 ) 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 Transactions on Control SystemsTechnology, 22(1):102–118, 2014.

(18 ) T. Oomen. Advanced motion control for next-generation precision mechatron-ics: Challenges for control, identification, and learning. In IEEJ InternationalWorkshop on Sensing, Actuation, Motion Control, and Optimization (SAM-CON), pages 1–12, Nagaoka, Japan, 2017.

(19 ) L. Blanken, R. de Rozario, J. van Zundert, S. Koekebakker, M. Steinbuch, andT. Oomen. Advanced feedforward and learning control for mechatronic sys-tems. In Proceedings of the 3rd DSPE Conference on Precision Mechatronics,pages 79–86, Sint-Michielsgestel, The Netherlands, 2016.

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

(21 ) W. K. Gawronski. Advanced Structural Dynamics and Active Control ofStructures. Springer, New York, New York, United States, 2004.

(22 ) A. Preumont. Vibration Control of Active Structures: An Introduction, vol-ume 96 of Solid Mechanics and Its Applications. Kluwer Academic Publishers,New York, New York, United States, second edition, 2004.

(23 ) S. Moheimani, D. Halim, and A. J. Fleming. Spatial Control of Vibration:Theory and Experiments. World Scientific, Singapore, 2003.

(24 ) P. C. Hughes. Space structure vibration modes: How many exist? Which onesare important? IEEE Control Systems Magazine, 7(1):22–28, 1987.

(25 ) T. Oomen, E. Grassens, and F. Hendriks. Inferential motion control: An iden-tification and robust control framework for unmeasured performance variables.IEEE Transactions on Control Systems Technology, 23(4):1602–1610, 2015.

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

(27 ) T. Oomen. Controlling aliased dynamics in motion systems? An identifi-cation for sampled-data control approach. International Journal of Control,87(7):1406–1422, 2014.

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

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

(30 ) S. Skogestad and I. Postlethwaite. Multivariable Feedback Control: Analysisand Design. John Wiley & Sons, West Sussex, United Kingdom, secondedition, 2005.

(31 ) J. C. Compter. Electro-dynamic planar motor. Precision Engineering,28(2):171–180, 2004.

(32 ) G. D. Hutcheson. The first nanochips. Scientific American, pages 48–55, April2004.

(33 ) B. Arnold. Shrinking possibilities. IEEE Spectrum, 46(4):26–28, 50–56, 2009.(34 ) J. Bolder, J. van Zundert, S. Koekebakker, and T. Oomen. Enhancing flatbed

printer accuracy and throughput: Optimal rational feedforward controller tun-ing via iterative learning control. IEEE Transactions on Industrial Electronics,64(5):4207–4216, 2017.

(35 ) L. Ljung. System Identification: Theory for the User. Prentice Hall, UpperSaddle River, New Jersey, United States, second edition, 1999.

(36 ) R. Pintelon and J. Schoukens. System Identification: A Frequency DomainApproach. IEEE Press, New York, New York, United States, second edition,2012.

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

(38 ) R. S. Smith. Closed-loop identification of flexible structures: An experimentalexample. Journal of Guidance, Control, and Dynamics, 21(3):435–440, 1998.

(39 ) T. Oomen and M. Steinbuch. Identification for robust control of complexsystems: Algorithm and motion application. In M. Lovera, editor, Control-oriented modelling and identification: theory and applications. IET, 2015.

(40 ) R. J. P. Schrama. Accurate identification for control: The necessity of aniterative scheme. IEEE Transactions on Automatic Control, 37(7):991–994,1992.

(41 ) 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,Massachusetts, United States, 1993.

(42 ) R. A. de Callafon and P. M. J. Van den Hof. Filtering and parametrizationissues in feedback relevant identification based on fractional model repre-sentations. In Proceedings of the 3rd European Control Conference, pages441–446, Rome, Italy, 1995.

(43 ) P. M. J. Van den Hof and R. J. P. Schrama. Identification and control - closed-loop issues. Automatica, 31(12):1751–1770, 1995.

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

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

(46 ) 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.

(47 ) D. C. McFarlane and K. Glover. Robust Controller Design Using NormalizedCoprime Factor Plant Descriptions, volume 138 of Lecture Notes in Controland Information Sciences. Springer-Verlag, Berlin, Germany, 1990.

(48 ) J. C. Doyle and G. Stein. Multivariable feedback design: Concepts for a clas-sical/modern synthesis. IEEE Transactions on Automatic Control, 26(1):4–16,1981.

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

(50 ) U. Schonhoff and R. Nordmann. AH∞-weighting scheme for PID-like mo-tion control. In Proceedings of the 2002 Conference on Control Applications,pages 192–197, Glasgow, Scotland, 2002.



(51 ) M. van de Wal, G. van Baars, F. Sperling, and O. Bosgra. MultivariableH∞/µ feedback control design for high-precision wafer stage motion. ControlEngineering Practice, 10(7):739–755, 2002.

(52 ) F. Boeren, R. van Herpen, T. Oomen, M. van de Wal, and M. Steinbuch.Non-diagonal H∞ weighting function design: Exploiting spatial-temporaldeformations for precision motion control. Control Engineering Practice,35:35–42, 2015.

(53 ) R. A. de Callafon and P. M. J. Van den Hof. Suboptimal feedback control by ascheme of iterative identification and control design. Mathematical Modellingof Systems, 3(1):77–101, 1997.

(54 ) K. Zhou, J. C. Doyle, and K. Glover. Robust and Optimal Control. PrenticeHall, Upper Saddle River, New Jersey, United States, 1996.

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

(56 ) J. Chen and G. Gu. Control-Oriented System Identification: AnH∞ Approach.John Wiley & Sons, New York, New York, United States, 2000.

(57 ) R. A. de Callafon and P. M. J. Van den Hof. Multivariable feedback relevantsystem identification of a wafer stepper system. IEEE Transactions on ControlSystems Technology, 9(2):381–390, 2001.

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

(59 ) C. C. H. Ma. Comments on “A necessary and sufficient condition for stabilityof a perturbed system”. IEEE Transactions on Automatic Control, 33(8):796–797, 1988.

(60 ) F. Hansen, G. Franklin, and R. Kosut. Closed-loop identification via thefractional representation: Experiment design. In Proceedings of the 8th Amer-ican Control Conference, pages 1422–1427, Pittsburgh, Pennsylvania, UnitedStates, 1989.

(61 ) H. Niemann. Dual Youla parameterisation. IEE Proceedings Control Theory& Applications, 150(5):493–497, 2003.

(62 ) 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.

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

(64 ) A. Lanzon and G. Papageorgiou. Distance measures for uncertain linear sys-tems: A general theory. IEEE Transactions on Automatic Control, 54(7):1532–1547, 2009.

(65 ) A. Packard and J. Doyle. The complex structured singular value. Automatica,29(1):71–109, 1993.

(66 ) T. Oomen, R. van der Maas, C. R. Rojas, and H. Hjalmarsson. Iterativedata-driven H∞ norm estimation of multivariable systems with applicationto robust active vibration isolation. IEEE Transactions on Control SystemsTechnology, 22(6):2247–2260, 2014.

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

(68 ) T. Oomen and O. Bosgra. Well-posed model uncertainty estimation by designof validation experiments. In 15th IFAC Symposium on System Identification,pages 1199–1204, Saint-Malo, France, 2009.

(69 ) 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. Mechatronics, 24(6):619–631, 2014.

(70 ) M. Groot Wassink, M. van de Wal, C. Scherer, and O. Bosgra. LPV control fora wafer stage: Beyond the theoretical solution. Control Engineering Practice,13:231–245, 2003.

(71 ) J. De Caigny, J. F. Camino, and J. Swevers. Interpolation-based modelingof MIMO LPV systems. IEEE Transactions on Control Systems Technology,19(1):46–63, 2011.

(72 ) 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.

(73 ) 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 IFAC 2017 Triennial World Congress,pages 15140–15145, Toulouse, France, 2017.

(74 ) E. Evers, M. van de Wal, and T. Oomen. Synchronizing decentralized controlloops for overall performance enhancement: A Youla framework applied to awafer scanner. In IFAC 2017 Triennial World Congress, pages 11332–11337,Toulouse, France, 2017.

(75 ) 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.

(76 ) M. Boerlage, B. de Jager, and M. Steinbuch. Control relevant blind iden-tification of disturbances with application to a multivariable active vibra-tion isolation platform. IEEE Transactions on Control Systems Technology,

18(2):393–404, 2010.(77 ) R. Voorhoeve, N. Dirkx, T. Melief, W. Aangenent, and T. Oomen. Estimating

structural 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.

(78 ) J. van Zundert and T. Oomen. On optimal feedforward and ILC: The roleof feedback for optimal performance and inferential control. In IFAC 2017Triennial World Congress, pages 6267–6272, Toulouse, France, 2017.

(79 ) A. Bultheel, M. van Barel, Y. Rolain, and R. Pintelon. Numerically robusttransfer function modeling from noisy frequency domain data. IEEE Transac-tions on Automatic Control, 50(11):1835–1839, 2005.

(80 ) 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.

(81 ) R. van Herpen, O. Bosgra, and T. Oomen. Bi-orthonormal polynomial basisfunction framework with applications in system identification. IEEE Transac-tions on Automatic Control, 61(11):3285–3300, 2016.

(82 ) R. Voorhoeve, A. van Rietschoten, E. Geerardyn, and T. Oomen. Identificationof high-tech motion systems: An active vibration isolation benchmark. In17th IFAC Symposium on System Identification, pages 1250–1255, Beijing,China, 2015.

(83 ) 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.

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

(85 ) R. van der Maas, A. van der Maas, R. Voorhoeve, and T. Oomen. Accurate FRFidentification of LPV systems: nD-LPM with application to a medical X-raysystem. IEEE Transactions on Control Systems Technology, 25(4):1724–1735,2017.

(86 ) R. Voorhoeve, A. van der Maas, and T. Oomen. Non-parametric identificationof multivariable systems: A local rational modeling approach with appli-cation to a vibration isolation benchmark. Mechanical Systems and SignalProcessing, To Appear.

(87 ) E. Rogers, K. Galkowski, and D. H. Owens. Control Systems Theory andApplications for Linear Repetitive Processes. Number 349 in Lecture Notesin Control and Information Sciences. Springer, Berlin, Germany, 2007.

(88 ) R. W. Longman. Iterative learning control and repetitive control for engineer-ing practice. International Journal of Control, 73(10):930–954, 2000.

(89 ) G. Pipeleers, B. Demeulenaere, and J. Swevers. Optimal Linear ControllerDesign for Periodic Inputs, volume 394 of Lecture Notes in Control andInformation Sciences. Springer, London, United Kingdom, 2009.

(90 ) 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.

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

(92 ) J. Wallen Axehill, I. Dressler, S. Gunnarsson, and A. Robertsson. Estimation-based ILC applied to a parallel kinematic robot. Control Engineering Practice,33:1–9, 2014.

(93 ) L. Blanken, S. Koekebakker, and T. Oomen. Design and modeling aspects inmultivariable iterative learning control. In Proceedings of the 55th Conferenceon Decision and Control, pages 5502–5507, Las Vegas, Nevada, United States,2016.

(94 ) J. van Zundert and T. Oomen. On inversion-based approaches for feedforwardand ILC. Mechatronics, To appear.

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

(96 ) R. de Rozario, T. Oomen, and M. Steinbuch. ILC and feedforward controlfor LPV systems: with application to a position-dependent motion system.In Proceedings of the 2017 American Control Conference, pages 3518–3523,Seattle, Washington, United States, 2017.

(97 ) J. van Zundert and T. Oomen. An approach to stable inversion of lptv systemswith application to a position-dependent motion system. In Proceedings of the2017 American Control Conference, pages 4890–4895, Seattle, Washington,United States.

(98 ) S. Mishra, W. Yeh, and M. Tomizuka. Iterative learning control design for syn-chronization of wafer and reticle stages. In Proceedings of the 2008 AmericanControl Conference, pages 3908–3913, Seattle, Washington, United States,2008.

(99 ) J. van de Wijdeven and O. Bosgra. Using basis functions in iterative learn-ing control: Analysis and design theory. International Journal of Control,



83(4):661–675, 2010.(100) M. Heertjes, D. Hennekens, and M. Steinbuch. MIMO feed-forward design

in wafer scanners using a gradient approximation-based algorithm. ControlEngineering Practice, 18(5):495–506, 2010.

(101) D. J. Hoelzle, A. G. Alleyne, and A. J. Wagoner Johnson. Basis task approachto iterative learning control with applications to micro-robotic deposition.IEEE Transactions on Control Systems Technology, 19(5):1138–1148, 2011.

(102) 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 Transactions on Mechatronics, 22(2):826–837, 2017.

(103) 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.

(104) J. Bolder and T. Oomen. Rational basis functions in iterative learning control- with experimental verification on a motion system. IEEE Transactions onControl Systems Technology, 23(2):722–729, 2015.

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

(106) L. Blanken, G. Isil, S. Koekebakker, and T. Oomen. Flexible ILC: Towardsa convex approach for non-causal rational basis functions. In IFAC 2017Triennial World Congress, pages 12613–12618, Toulouse, France, 2017.

(107) J. van Zundert and T. Oomen. Inverting nonminimum-phase systems fromthe perspectives of feedforward and ILC. In IFAC 2017 Triennial WorldCongress, pages 12607–12612, Toulouse, France, 2017.

(108) S. Devasia, D. Chen, and B. Paden. Nonlinear inversion-based output tracking.IEEE Transactions on Automatic Control, 41(7):930–942, 1996.

(109) 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.

(110) F. Boeren, D. Bruijnen, and T. Oomen. Enhancing feedforward controllertuning via instrumental variables: With application to nanopositioning. Inter-national Journal of Control, 90(4):746–764, 2017.

(111) F. Boeren, L. Blanken, D. Bruijnen, and T. Oomen. Optimal estimation ofrational feedforward controllers: An instrumental variable approach and non-causal implementation on a wafer stage. Asian Journal of Control, 20(1):1–18,2018.

(112) T. Soderstrom and P. G. Stoica. Instrumental Variable Methods for Sys-tem Identification, volume 57 of Lecture Notes in Control and InformationSciences. Springer-Verlag, Berlin, Germany, 1983.

(113) S. Devasia, E. Eleftheriou, and S. Moheimani. A survey of control issuesin nanopositioning. IEEE Transactions on Control Systems Technology,15(5):802–823, 2007.

(114) S. Moheimani and E. Eleftheriou. Dynamics and control of micro- andnanoscale systems. IEEE Control Systems Magazine, 33(6):42–45, 2013.

(115) G. Cherubini, C. C. Chung, W. C. Messner, and S. Moheimani. Introductionto the special section on advanced servo control for emerging data storagesystems. IEEE Transactions on Control Systems Technology, 20(2):292–295,2012.

(116) D. Y. Abramovitch. Trying to keep it real: 25 years of trying to get the stuff

I learned in grad school to work on mechatronic systems. In Proceedings ofthe 2015 Multi-conference on Systems and Control, pages 223–250, Syndey,Australia, 2015.

(117) S. Van Huffel, V. Sima, A. Varga, S. Hammarling, and F. Delebecque. High-performance numerical software for control. IEEE Control Systems Magazine,24(1):60–76, 2004.

(118) T. Oomen and C. R. Rojas. Sparse iterative learning control with application toa wafer stage: Achieving performance, resource efficiency, and task flexibility.Mechatronics, 47:134–137, 2017.

(119) S. Galeani, S. Tarbouriech, M. Turner, and L. Zaccarian. A tutorial on modernanti-windup design. European Journal of Control, 15(3-4):418–440, 2009.

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

(121) M. Steinbuch, J. van Helvoort, W. Aangenent, B. de Jager, and R. van deMolengraft. Data-based control of motion systems. In Proceedings of the2005 American Control Conference, pages 529–534, Toronto, Canada, 2005.

(122) J. van Zundert, T. Oomen, D. Goswami, and W. Heemels. On the potentialof lifted domain feedforward controllers with a periodic sampling sequence.In Proceedings of the 2016 American Control Conference, pages 4227–4232,Boston, Massachusetts, United States, 2016.

(123) H. Fujimoto, Y. Hori, and A. Kawamura. Perfect tracking control basedon multirate feedforward control with generalized sampling periods. IEEETransactions on Industrial Electronics, 48(3):636–644, 2001.

(124) S. Formentin, K. van Heusden, and A. Karimi. A comparison of model-basedand data-driven controller tuning. International Journal of Adaptive Control

and Signal Processing, 28(10):882–897, 2014.(125) M. Heertjes, B. van der Velden, and T. Oomen. Constrained iterative feedback

tuning for robust control of a wafer stage system. IEEE Transactions onControl Systems Technology, 24(1):56–66, 2016.

(126) P. Janssens, G. Pipeleers, and J. Swevers. A data-driven constrained norm-optimal iterative learning control framework for LTI systems. IEEE Transac-tions on Control Systems Technology, 21(2):546–551, 2013.

(127) J. Bolder, S. Kleinendorst, and T. Oomen. Data-driven multivariable ILC:Enhanced performance by eliminating L and Q filters. International Journalof Robust and Nonlinear Control, To appear.

Tom Oomen (Non-member) He received the M.Sc. degree (cumlaude) and Ph.D. degree from the Eindhoven Uni-versity of Technology, Eindhoven, The Netherlands.He held visiting positions at KTH, Stockholm, Swe-den, and at The University of Newcastle, Australia.Presently, he is an assistant professor with the Depart-ment of Mechanical Engineering at the EindhovenUniversity of Technology. He is a recipient of theCorus Young Talent Graduation Award, the 2015IEEE Transactions on Control Systems Technology

Outstanding Paper Award, and the 2017 IFAC Mechatronics Best PaperAward. He is Associate Editor on the IEEE Conference Editorial Board,IFAC Mechatronics, and the IEEE Control Systems Letters (L-CSS). His re-search interests are in the field of system identification, robust control, andlearning control, with applications in mechatronic systems.


Documents

Advanced Motion Control for Precision Mechatronics: … Motion Control for Precision Mechatronics: Control, Identiﬁcation, and Learning of Complex Systems (Tom Oomen) (a) Experimental