"Iterative Learning Control": From Academia to Industry

"Iterative Learning Control": From Academia to Industry YangQuan Chen Department of Electrical and ComputerEngineering Utah State University A Seminar at The University of Windsor June 14, 2001

Outline • What is Iterative Learning Control (ILC) • Historical Comments • From “Analysis” to “Design” • Industrial Application I (ABB robots) • Industrial Application II (Seagate HDD) • To Probe Further and My Recent Results • Concluding Remarks

Intuitions What can we human beings get from doing the same thing over and over? Yes, “skill". When a machine is operated to perform the same task repeatedly, can it do the job better and better? This is "iterative learning control (ILC)".

Control Design Problem

Step 1: Robot at rest, waiting for workpiece. Step 2: Workpiece moved into position. Step 3: Robot moves to desired location and executes its task. Step 4: Robot returns to rest and waits for next workpiece. Systems that Execute the Same Trajectory Over and Over

Errors Are Repeated WhenTrajectories are Repeated • A typical joint angle trajectory for the example might look like this: • Each time the system is operated it will see the same overshoot, settling • time and steady-state error. They did NOT make use the repetitiveness! • Iterative learning control attempts to improve the transient response by • adjusting the input to the plant during future system operation based on • the errors observed during past operation.

Memory based • Iterative Learning Control Scheme is memory-based. System Memory Memory Memory Learning Controller

ILC vs. FBC • A typical ILC algorithm has the form : Whereas a feedback control (FBC) has the form : • The subscript kindicates the trial or the repetition number. • The subscript tindicates the time. • All signals shown are assumed to be defined on a finite interval t ,and t [0, is the input applied to the system during the k -th trial. is the output of the system during the k-th trial. is the desired output of the system. , is the error observed between the actual output and the desired output during the k-th trial.

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... t-1 t-1 t-1 t t t t+1 t+1 t+1 t-1 t-1 t-1 t-1 t-1 t-1 t-1 t-1 t-1 t t t t t t t t t t+1 t+1 t+1 t+1 t+1 t+1 t+1 t+1 t+1 Trial (k-1) Trial k Trial (k+1) Error Input (a) ILC: Error Input (b) Conventional feedback:

Feedback-Feedforward Configuration

Arimoto’s 6 Postulations on ILC • P1.Every cycle (pass, trial, batch, iteration, repetition) ends in a fixed time of duration T>0. • P2.A desired output yd(t) is given a priori over [0,T]. • P3.Repetition of the initial setting is satisfied. • P4.Invariance of the system dynamics is ensured throughout these repeated iterations. • P5.Output can be measured and the tracking error can be utilized in the construction of the next input. • P6.The system dynamics are invertible, that is, for a given desired output yd(t)with a piecewise continuous derivative, there exists a unique input ud(t) that drives the system to produce yd(t)

ILC historical review (1) • Historical Roots of ILC go back about 25 years. • Idea of a “multipass” system studied by Owens and Rogers in mid- to late-1970's, with several resulting monographs. • Learning control concept introduced (in Japanese) by Uchiyama in 1978. • Pioneering work of Arimoto, et al. 1984-present. • Related research in repetitive and periodic control. • 1993 Springer monograph had about 90 ILC references. (Kevin L. Moore)

ILC historical review (2) • 1997 Asian Control Conference had 30 papers on ILC (out of 600 papers presented at the meeting) and the first panel session on this topic. • 1998 survey paper has about 250 ILC references. • Web-based online, searchable bibliographic database maintained by Yangquan Chen has about 500 references (see http://cicserver.ee.nus.edu.sg/~ilc). • ILC Workshop and Roundtable and three devoted sessions at 1998 CDC. • Edited book by Bien and Xu resulting from 1997 ASCC • Springer-Verlag monograph by Chen and Wen, 1999.

ILC historical review (3) • 4 invited sessions at 2000 ASCC (Shanghai) with an Invited Panel Discussion on ILC. • 3 invited sessions at ICARCV 2000 (Singapore), • The 2nd Int. Conference on nD Systems. (Poland) • Tutorial at ICARCV 2000 and first IEEE CDC Tutorial Workshop 2000, Sydney. • Special Issues in Int. J. of Control (2000), Asian J. of Control (2001) and J. of Intelligent Automation and Soft Computing (2001). • Industrial use, e.g., Seagate and ABB (Sweden)

ILC historical review (4) • Murray Garden (1967). Learning control of actuators in control systems. United States Patent 3,555,252. • Chen, YangQuan and Kevin L. Moore. “Comments on US Patent 3555252: LEARNING CONTROL OF ACTUATORS IN CONTROL SYSTEMS.” ILC Invited Sessions. In Proc. of the ICARCV'2000 (The Sixth International Conference on Control, Automation, Robotics and Vision).(archeological contribution!)

Past efforts • Past work in the field demonstrated the usefulness and applicability of the concept of ILC: • Linear systems. • Classes of nonlinear systems. • Applications to robotic systems.

Current efforts • Present status of the field reflects the continuing efforts of researchers to: • Develop design tools. • Extend earlier results to broader classes of systems. • Realize a wider range of applications. • Understand and interpret ILC in terms of other control paradigms and in the larger context of learning in general.

A Partial Classification of ILC Research • Systems: • Open-loop vs. closed-loop. • Discrete-time vs. continuous-time. • Linear vs. nonlinear. • Time-invariant or time-varying. • Relative degree 1 vs. higher relative degree. • Same initial state vs. variable initial state. • Presence of disturbances. • Update algorithm: • Linear ILC vs. nonlinear ILC.

A Partial Classification of ILC Research • First-order ILC vs. higher-order. • Current cycle vs. past cycle. • Fixed ILC or adaptive ILC. • Time-domain vs. frequency analysis. • Analysis vs. design. • Assumptions on plant knowledge. • Applications: • Robotics. • Chemical processing. • Mechatronic systems (HDD, CD/DVD).

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... t-1 t-1 t-1 t-1 t-1 t-1 t-1 t-1 t-1 t-1 t-1 t-1 t t t t t t t t t t t t t+1 t+1 t+1 t+1 t+1 t+1 t+1 t+1 t+1 t+1 t+1 t+1 Trial (k-1) Trial k Trial (k+1) Error Input (a) ILC with Current Cycle Feedback Error Input (b) Higher-Order ILC

ILC Panel Discussion at ASCC’2000 General Trend: from “Analysis” to “Design” • Analysis: • Attack the Arimoto’s classical 6 Postulates for ILC. • Structurally known uncertain nonlinear systems. System class… Combined Feedforward-Feedback analysis! • Add practical constraints in analysis: changing delay, anti-windup • Spatial ILC (state-dependent repetitiveness), distributed parameter system, redundancy in control authorities... • Design: • How to explicitly use the available (assumed) prior knowledge? • Systematic design method - e.g. via noncausal filtering, Local Symmetrical Integration (LSI) etc. • Supervisory Iterative Learning Control (e.g. planning while tracking via ILC)

ILC Design: as easy as PID? • Yamamoto, S. and Hashimoto, I. (1991). Recent status and future needs: The view from Japanese industry. In Arkun and Ray, editors, Proceedings of the fourth International Conference on Chemical Process Control, Texas. Chemical Process Control -CPCIV. • Survey by Japan Electric Measuring Instrument Manufacturer's Association, more than 90% of the control loops were of the PID type. • Bialkowski, W. L. (1993). Dreams versus reality: A view from both sides of the gap. Pulp and Paper Canada, 94(11). • A typical paper mill in Canada has more than 2000 control loops and that 97% use PI control.

Tuning knobs of ILC • Only two tuning knobs: • learning gain • bandwidth of the learning filter • an example: my ASCC’2000 paper • Chen, YangQuan and Kevin L. Moore, ``Improved Path Following for an Omni-Directional Vehicle Via Practical Iterative Learning Control Using Local Symmetrical Double-Integration,'' Asian Control Conference 2000, July 5-7, 2000, Shanghai, China. pp. 1878-1883. • Note: Full version of this paper will appear in the Special Issue of ILC in Asian Journal of Control, 2001

LSI2-ILC Scheme LSI2 -ILC Block Diagram: Overall control signal: LSI2 -ILC Speical Case TL2 =0: LSI2 LSI2 -ILC Speical Case TL =0: ILC feedforward updating law: In the sequel, TL1=TL2 =TL

LSI2-ILC: Analysis & Design • Discrete-time form: • Frequency domain: a

LSI2-ILC: Design Procedures • Convergence Condition: • Design of TL: • Design of For given TL , the optimal choice of

Performance Limit & Rule Based Learning • Performance limit and heuristics • Best achievable convergence rate: • Heuristics for better ILC performance: (Rule Based Learning) 1. re-evaluate TL at the end of every iteration. 2. start ILC with a smaller and increase when the tracking error keeps decreasing and decrease while the tracking error keeps increasing. 3. use a cautious (larger) TL at the beginning of ILC iteration and then decrease TL when the ILC scheme converges to a stage with little improvement. ...

USU-ODV Simulation for LSI2-ILC • USU ODV • Three parts to the control problem: • Outer-Loop Control: Compute the center-of-gravity motion required to follow the desired path. • Wheel Coordination: Determine appropriate commands for each individual wheel to produce the desired overall vehicle motion. • Smart Drive Control: Generate input signals for the actuators in each wheel (steering motor, speed motor). 6 smart wheels

USU-ODV Simulation for LSI2-ILC • PI-control and LSI2-ILC

Standard deviation of tracking errors observations: It. 0 0.18520.14360.1057 1 0.10860.05730.0810 2 0.08780.05080.0629 3 0.07680.03780.0535 4 0.06790.03230.0471 5 0.05960.03140.0438 1. Simple ILC scheme 2. Simple design steps 3. Stable monotone convergence 4. Less modeling efforts 5. Add-on to existing controller 6. Effective in ODV path-following 7. Rule-based ILC possible 8. Practically applicable.

ABB Robotics • Swiss - Swedish company (part of the ABB Group) • Production and most of the R&D in Västerås, Sweden • 600 employees (at ABB Robotics) • Produces ~ 10,000 robots/year • Installed a total of 90,000 robots in the world • Leading producer of industrial robots

Motivation for ILC in ABB robots • Highly repetitive dynamics • In production (laser cutting) the same procedure is repeated by the robot many times • Easy to implement in an already existing control structure • Can easily co-exist with other improvements of the control system

Previous solution in ABB robots • Traditional feedback and feedforward control • Model based feedforward control (non adaptive but user configurable) • Resulting absolute accuracy (approx) 0.5 - 5 mm

Laser measurement device ILC implementation for ABB Laser Cutting Robots 1. Measure the position 2. Compensate in cartesian coordinates 3. Run the program again

After using ILC (in laser cutting) • After the second ILC: Path Errors: 0.10mm • NOTE: previous error range = 0.5 to 5 mm • Tuned in approximately one minute • Minor improvements after 2 iterations • Improvements in the example • No ILC • ILC 1st Iteration 50% • ILC 2nd Iteration 61%

Typical Hard Disk Drive

"Iterative Learning Control": From Academia to Industry