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1 ITERATIVE LEARNING CONTROL OF INDUSTRIAL MOTION SYSTEMS Maarten Steinbuch and René van de Molengraft Eindhoven University of Technology, Faculty of Mechanical Engineering, Systems and Control Group, P.O. Box 513, 56 MB Eindhoven, The Netherlands, phone/fax: / Abstract: Repetitive and iterative learning control are control strategies for systems that perform repetitive tasks or on which periodic disturbances act. In the field of motion systems this occurs if disturbances are position dependent or if dynamics are excited in a similar way during each point to point motion. For this class of systems design procedures for feedback controllers are recapitulated and feedforward strategies are explained. Iterative learning control in particular is a powerful concept, and design rules can be used to reduce the error far above the feedback bandwidth for repeatedly operated machines. Experiments illustrate the value of these design rules. Copyright cfl2 IFAC Keywords: Learning control,repetitive control, motion control, disturbance rejection, tracking, mechatronics. 1. INTRODUCTION Control systems subjected to periodic disturbances may well benefit from the use of repetitive control. Repetitive controllers employ the internal model principle and consist of a periodic signal generator, enabling perfect (asymptotic) rejection of the periodic disturbances. In case of tracking systems where the task (setpoint) is known to be a predetermined (repeatedly supplied) trajectory, repetitive control is used in a semi openloop (feedforward) fashion known as (iterative) learning control. Equivalent schemes are being used in process industry and are known as `run-torun' control. In cases where periodic measurement noise is significant, repetitive control is applied in the form of digital comb-filters for noise reduction. The papers by Moore et al. (1992) and Tomizuka et al. (1988) cover most of the relevant features of repetitive and iterative learning control. The main focus of this paper is to show how to use iterative learning control (ILC) algorithms for industrial motion systems under repetitive tasks. First, we will present a short review of feedback and feedforward tuning of industrial motion control systems (Section 2). A classification of various methods used for feedforward tuning/design will be discussed in Section 3. In Section 4, Iterative Learning Control will be explained in more detail, including design guidelines. In Section 5, a particular industrial motion system will be introduced. It has the physical structure of an H-drive, with 3 linear motors, and it is being used as component mounter in the semiconductor industry. The use of feedforward schemes, including ILC, is shown using experiments on the H-drive. Finally, the main results will be summarized in Section 6.

2 2. MOTION CONTROL The application field of motion control systems is widely present in industry for motion tasks such as pick-and-place, assembly etc. The underlying disciplines such as mechanics, electronic power supplies and electronics, electric motors, sensor technology and digital control have rapidly developed over the last decade. The field of mechatronic systems has emerged to emphasize the importance of a systems approach for design. In this section we will describe only a small, but basic part of mechatronic (motion) systems, namely the elementary positioning control loop. Consider a typical motion system as it is schematically depicted in Fig. 1. xm x l magnitude [db] phase [deg] frequency [Hz] Fig. 2. Bode diagram of motion system, sensor on motor ( ) or load (- -). feedforward F motor load setpoint - K G position Fig. 1. Motion system. The driving force F is assumed to be generated by a current-controlled motor, such that the input of the system indeed can be seen as force. Either the motor position x m or the load position x l can be measured (in most cases unfortunately not both!). Both masses (or inertias for rotating machines) are assumed to be connected via a mechanical connection with finite stiffness and damping. From the equations of motion, a simple linear dynamic model can be derived. The model has a frequency response function as depicted in Fig. 2, both for the motor position measurement case(f! x m ) and for the load position measurement situation (F! x l ). The frequency responses are elementary for many motion control systems seen in practice, although often more resonances occur at higher frequencies. A block-diagram of the control loop is shown in Fig. 3, where K(s) represents the feedback controller transfer function and G(s) represents the plant transfer function. The use of (acceleration) feedforward is a standard means of obtaining small errors in case of tracking a setpoint signal. In the remainder of this section, first we will focus on feedback loop tuning, and second, we will describe tuning rules for feedforward. Fig. 3. Block-diagram of a motion control system. 2.1 Feedback The (feedback) controller K for the above motion control system consists of the necessary stabilizing PD part, in many cases in the form of a lead/lag filter fi1s+1 fi 2s+1. In most cases integral action is added, as well as a low-pass filter at high frequencies to prevent amplification of noise, and possibly some notches to cope with parasitic dynamics. Rulesof-thumb to tune a motion controller are given in terms of break-points of the various filters. If we denote the bandwidth, defined as the first db crossing of the open-loop frequency response, as! b, then the integral action works up to! b /6, the zero of the lead/lag is at! b /3, the pole is at! b *3 and the low-pass break-point isat! b *1. If stability is endangered by resonances, 2nd order filters (generally called notches if the undamped frequency of the zeros equals that of the poles) are used. Playing with such filters and tuning while inspecting the open-loop frequency response (in Bode, Nyquist or Nichols charts) is what is called (manual) `loopshaping'. The choice of the bandwidth normally depends on various (mixed) performance measures, such as disturbance rejection and settling behaviour under tracking conditions. Moreover, it is a wellknown fact that disturbance dynamics should be accounted for in the controller tuning (and possibly in the controller structure) (Steinbuch and Norg, 1998).

3 position [m] 2.2 Feedforward Once the feedback part K(s) of the controller has been designed and tuned, the feedforward part can be designed; notice that from theory in a modelbased design procedure a simultaneous (2DOF) control design would be done, while in industrial practice the feedback and feedforward designs are separated. For point-to-point motions normally 2nd or 3rd order trajectories are chosen, because with force (i.e. motor current) as input and position as output, the reference trajectory for the output should be at least a twice differentiable signal to prevent unbounded input signals. In Fig. 4 (top) typical position setpoints are shown: 2nd order (dashed) and 3rd order (solid). The corresponding accelerations are shown in Fig. 4 bottom. Motivations for using 3rd order profiles are (i) limited bandwidth of motor current amplifiers, and (ii) prevention of exciting high frequency parasitic dynamics. The price to be payed for such jerk-limited setpoints are higher maximum accelerations (assuming equal set-up time). acceleration [m/s 2 ] time [s] time [s] Fig. 4. Position setpoint signal (top) and acceleration (bottom); 3rd order (solid) and 2nd order (dashed) The actual feedforward path in industrial motion controllers consists normally of acceleration, velocity and coulomb friction feedforward. For systems where inertial forces are the most important, the use of acceleration feedforward determines final tracking performance. The acceleration trajectory as shown in Fig. 4, bottom, is divided by the total process gain (motor/amplifier gain divided by the mass or inertia) to obtain the acceleration (force) feedforward signal. Dependent on viscous and coulomb friction levels, appropriate feedforward signals are added. 3. ADVANCED FEEDFORWARD DESIGN Within industry the use of knowledge of system dynamics does go beyond the simple 1-mass system: the use of `PID+' controllers using notches and other filters to compensate system dynamics is common practice in motion control. With respect to feedforward design the situation is slightly different in that known solutions in literature are not yet widely spread within industry. One could distinguish between two classes of feedforward design: model-based and data-based feedforward design. We will discuss some features of both methodologies. 3.1 Model-based Feedforward design Model-based feedforward design is focused on compensating the dynamics of the system to be controlled. Such dynamics can be rigid body (nonlinear) dynamics, as well as (linear) parasitic dynamics. Based on models the following techniques are known for designing a feedforward (or openloop input) signal, with emphasis on accounting for linear parasitic dynamics, and under the assumption of limitations with respect to maximum velocity, acceleration and jerk. (i) Single mass acceleration feedforward, as described before. Main problem is that settling time may be long if low damped parasitic resonances are excited. (ii) Filtering feedforward and reference signals. In most cases of filtering, low-pass or notch filtering is used to prevent high frequency excitation of parasitic resonances. Drawback is that set-up times can become quite large and robustness for changing dynamics is not trivial. (iii) Input shaping techniques. Here the goal is to shape reference and feedforward signals as with filtering, but this is done in time domain (convolution with series of impulses). Robustness can be accounted for, and set-up times are smaller than with plain filtering, see (Singer, 1999) for an overview of command and input shaping techniques. (iv) Constrained optimization of the input signal (system inversion). This implies minimal set-up times, but computational problems can occur, and robustness is not straightforward. 3.2 Data-based Feedforward design Data-based feedforward tuning uses closed-loop experimental data to adjust feedforward signals. It can be used for compensating plant dynamics, but also for counteracting deterministic disturbances and systematic errors. (i) High gain feedback of integral action. The way this is used in practice is that a very low velocity scanning mode of the motion system is realized.

4 The integral action will attenuate all low frequent (mostly position dependent) disturbances. The output signal of the integral part of the feedback controller is stored and added to the existing feedforward signal. This method is very simple and easy to use. Drawback is that noise contributions are not systematically separated from the deterministic reproducible errors. (ii) Learning control using neural nets. This class of methods exploits repeated operation of the motion system, and stores the information gathered. The motions do not need to be repeatedly the same, but can change from run to run, which is an important benefit. Using a neural network with specific structure feedforward signals can be learnt as a function of time, position or as a function of other signals (`pattern-based learning'). Drawback is that convergence proofs are difficult or even impossible to give. (iii) Iterative Learning Control (ILC). This could be seen as a special form (`repetition-based learning') of the previous method. The method only works for repeatedly applied (equal) motion commands. The error information is stored, filtered and added to the previous feedforward. The basic working principle is also high gain feedback, as with the integral action, but from run to run. If models of the plant are available, stability theory can be applied. Because of this, convergence can be guaranteed which also implies that ILC can be designed to obtain the highest convergence rate 1. Drawback is that the learnt feedforward is only applicable for the specific motion profile applied during learning, although research work is being done to overcome this (Xu and Zhu, 1999). In the next section we will elaborate on ILC. Before we address ILC in more detail, first an illustration will be given of the relevance of databased feedforward tuning. Consider two runs of a motion system in Fig. 5. The figure shows the errors signals of the two runs, as well as the corresponding acceleration profile. The motion is a point-to-point motion, where accuracy is required during the constant velocity phase (from t=.3 until t=.18s). From the figure it can be seen that the two runs show a similar error as function of time. It at least suggests that the reproducible part of the error is relatively large compared to the stochastic part of the error. This motivates further investigation into the possible use of learning type of feedforward tuning for such a system. position error y [nm] y error, September 6 and Oktober time [s] Fig. 5. Reproducible error signal of a scanning motion 4. ITERATIVELEARNING CONTROL 4.1 Working principle Ablock diagram of a feedback controlled system G(s) with ILC added is shown in Fig. 6. The stabilizing feedback controller K(s) is assumed to be given. A run (trial) has a finite duration t 2 [t t e ], and it is assumed that the system is at rest before t and after t e.each run is denoted with an index, so e k (t) (or shortly denoted as e k ) means the error signal e(t) during the k-th run. Iterative learning control works as follows. For a certain setpoint r k (t) and feedforward f k (t) a motion is performed. The resulting error signal e k (t) is stored. In an off-line operation, the error signal is filtered with the filter L(s), called learning filter, and added to the feedforward f k. Then a filter Q(s), called robustness filter, is applied to the sum of the old feedforward and the filtered error. The resulting signal is the new feedforward f k+1 to be used in the next run. setpoint r k + - e k e k K(s) L(s) + + f k+1 Q(s) f k feedforward + + G(s) Fig. 6. Iterative Learning Control block diagram 1 in some sense the method can also be seen as a modelbased design method, see Section 3.2 The design of the learning filter L(s) and of the robustness filter Q(s) determines performance of the ILC algorithm. Most important is to assure convergence of the learning process (Moore et al., 1992).

5 4.2 Convergence For convergence analysis a small-gain type of argument will be used, for which it is assumed that r k =, and all initial conditions are zero. The closed-loop system transfer from feedforward path to the error signal yields: The learning up-date rule is: then eliminate f: or e k = G 1+GK f k (1) f k+1 = Q (f k + Le k ) (2) e k+1 = G 1+GK f k+1 (3) = G 1+GK Q (f k + Le k ) (4) = Q 1+ G 1+GK L e k (5) e k+1 = Q fi fi fi fi Q 1+ G 1+GK L e k (6) which shows the propagation of the error signal from run to run. Convergence will take place if: fi fifi 1 G 1+GK L fi < 1 (7) Apparently, asuitablechoice for L would be L = 1+GK G. However, the process-sensitivity G 1+GK is strictly proper in most cases, and certainly in motion control systems with position as output. This means that it can not be inverted. Moreover, if the transfer function contains non-minimum phase zeros it would imply an unstable inverse. For this reason an approximate inverse is determined: L ß 1+GK G. Hence, the robustness filter Q is required in order to satisfy inequality (7) for all frequencies. ffl use a standard feedforward as initial signal, and perform a point-to-point motion, store the error. Filter this off-line by L(s) and add to the old feedforward. Filter the sum with Q(s)in an anti-causal way to obtain a filtered signal without phase lag, ffl repeat the previous step until the error becomes sufficiently small. Freeze the learnt feedforward. Typically, 3-1 runs are needed to decrease the error with a factor 1-1, depending on the size of the stochastic part of the error relative to its deterministic part. In the next section we will illustrate the power of ILC for an industrial H-drive. 5. APPLICATION TO H-DRIVE The `H-drive' is a XY positioning system with three linear motors. The mechanism is used in Component Mounters as the basic positioning device for pick-and-place operation of components on Printed Circuit Boards. All three linear motor have encoder sensors and are direct drive, electrically commutating motors with current control (Otten et al. 1997). The servo systems are decoupled (single-axis) PID type with low-pass and two notches. Feedforward signals are acceleration, velocity and friction feedforward. The servo's typically have 3 Hz bandwidth and the mechanics show resonances above 15 Hz, see Fig. 8. A form of gain-scheduling assures that gain is not dependent on position; however, resonances are. Typical tracking performance is accelerations up to 8 m=s 2, and errors less than 1 μm. 4.3 Design procedure and guidelines ffl determine a parametric model for the process sensitivity G=(1 + GK). This can be done using standard system identification techniques, for instance using frequency response measurements and fitting in the frequency domain, ffl design the inverse approximation L(s), for instance by using the ZPETC algorithm (Tomizuka et al., 1988), ffl calculate the frequency response of 1 LG=(1 + GK), and design Q as a stable filter such that it equals 1 (Roover and Bosgra, 2), except where 1 LG=(1 + GK) deviates from, Fig. 7. H-drive pick-and-place system

6 Using the model and the controller information, a learning filter L(s) is designed, of which the frequency response is plotted in Fig. 9. The error after learning is plotted in Fig. 1, together with the original error. It can be seen that the improvement is significant. Future work on the H-drive will be focused on the robustness of the ILC scheme for changing operating conditions, and further research for making ILC less sensitive for changes in trajectories. Fig. 1. Error before and after iterative learning control an industrial H-drive system experimentally validates the design procedure. Future work should reveal robustness for modelling errors and changing operating conditions. REFERENCES Fig. 8. Measured and modelled frequency response function of the H drive Moore, K.L., M. Dahley and S.P. Bhattacharyya (1992). Iterative learning control: a survey and new results", Journal of Robotic Systems, vol.9, no.5, pp Otten, G., T.J.A. de Vries, J. van Amerongen, A.M. Rankers and E.W. Gaal (1997). Linear Motor Motion Control Using a Learning Feedforward Controller", IEEE/ASME Trans. Mechatronics, Vol.2, no.3, pp Roover, D. de and O.H. Bosgra (2). Synthesis of Robust Multivariable Iterative Learning Controllers with application to a Wafer Stage", Int. J. of Control,2, 19p. Singer, N., W. Singhose and W. Seering (1999). Comparison of filtering methods for reducing residual vibration", European Journal of Control, pp Fig. 9. Learning filter design for the H-drive 6. CONCLUSIONS In this paper a short review is given of feedback and feedforward tuning for industrial motion control systems. For feedforward tuning Iterative Learning Control provides a powerful method for suppressing systematic errors in motion systems which perform repetitive tasks. The application to Steinbuch, M. and M.L. Norg (1998). Advanced Motion Control: an industrial perspective", European Journal of Control, pp Tomizuka, M., T.C. Tsao and K.K. Chew (1988). Discrete-time domain analysis and synthesis of repetitive controllers", Proc American Control Conference, pp Xu, J. Xu, J.-X. and T. Zhu (1999). Dual-scale direct learning control of trajectory tracking for a class of nonlinear uncertain systems" IEEE Trans. on Automatic Control, vol.44, no.1, pp