Comparison of the stability boundary and the frequency response stability condition in learning and repetitive control

• Autorzy: Szathys Songschon , Richard W. Longman
• Języki publikacji: EN

Abstrakty

EN

In iterative learning control (ILC) and in repetitive control (RC) one is interested in convergence to zero tracking error as the repetitions of the command or the periods in the command progress. A condition based on steady state frequency response modeling is often used, but it does not represent the true stability boundary for convergence. In this paper we show how this useful condition differs from the true stability boundary in ILC and RC, and show that in applications of RC the distinction between these conditions is of no practical significance. In ILC satisfying this frequency condition is important for good learning transients, even though the true stability boundary is very different.

Słowa kluczowe

EN

iterative learning control; monotonic convergence; stability; repetitive control

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2003
• Tom: 13
• Numer: 2
• Strony: 169-177

Daty

wydano

2003

otrzymano

2002-10-27

Twórcy

autor

Szathys Songschon

• King Mongkut's University of Technology Thonburi, Bangkok 10140, Thailand

autor

Richard W. Longman

• Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA

Bibliografia

• Arimoto S., Kawamura S. and Miyazaki F. (1984): Bettering operation of robots by learning. — J. Robot. Syst., Vol. 1, No. 2, pp. 123–140.
• Casalino G. and Bartolini G. (1984): A learning procedure for the control of movements of robotic manipulators. — Proc. IASTED Symp. Robotics and Automation, Amsterdam, The Netherlands, pp. 108–111.
• Craig J.J. (1984): Adaptive control of manipulators through repeated trials. — Proc. 1984 Amer. Contr. Conf., San Diego, CA, pp. 1566–1573.
• De Luca A., Paesano G. and Ulivi G. (1992): A frequencydomain approach to learning control: Implementation for a robot manipulator. — IEEE Trans. Ind. Electron., Vol. 39, No. 1, pp. 1–10.
• Edwards J.B. (1974): Stability problems in the control of multipass processes. — Proc. IEE, Vol. 121, No. 11, pp. 1425– 1432.
• Edwards J.B. and Owens D.H. (1982): Analysis and Control of Multipass Processes. — New York: Wiley.
• Elci H., Longman R.W., Phan M., Juang J.-N. and Ugoletti R. (1994): Discrete frequency based learning control for precision motion control. — Proc. 1994 IEEE Int. Conf. Systems, Man, and Cybernetics, San Antonio, Texas, pp. 2767–2773.
• Hara S. and Yamamoto Y. (1985a): Synthesis of repetitive control systems and its applications. — Proc. 24th IEEE Conf. Decision and Control, Fort Lauderdale, Florida, pp. 326– 327.
• Hara S., Omata T. and Nakano M. (1985b): Stability of repetitive control systems. — Proc. 24th IEEE Conf. Decision and Control, Fort Lauderdale, Florida, pp. 1387–1392.
• Huang Y.-C. and Longman R.W. (1996): The source of the often observed property of initial convergence followed by divergence in learning and repetitive control. — Adv. Astron. Sci., Vol. 90, pp. 555–572.
• Inoue T., Nakano M. and Iwai S. (1981): High accuracy control of a proton synchrotron magnet power supply. — Proc. 8th World Congress of IFAC, Kyoto, Japan, XX, pp. 216–221.
• Longman R.W. (2000): Iterative learning control and repetitive control for engineering practice. — Int. J. Contr., Special Issue on Iterative Learning Control, Vol. 73, No. 10, pp. 930–954.
• Middleton R.H., Goodwin G.C. and Longman R.W. (1989): A method for improving the dynamic accuracy of a robot performing a repetitive task. — Int. J. Robot. Res., Vol. 8, No. 5, pp. 67–74.
• Nakano M. and Hara S. (1986): Microprocessor-based repetitive control. — Microprocessor-Based Contr. Syst., pp. 279– 296.
• Omata T., Nakano M. and Inoue T. (1984): Applications of repetitive control method to multivariable systems. — Trans. SICE, Vol. 20, No. 9, pp. 795–800.
• Owens D.H. (1977): Stability of multipass processes. — Proc. IEE, Vol. 124, No. 11, pp. 1079–1082.
• Phan M. and Longman R.W. (1988): A mathematical theory of learning control for linear discrete multivariable systems. — Proc. AIAA/AAS Astrodyn. Conf., Minneapolis, Minnesota, pp. 740–746.
• Pierre D.A. (1989): Reformulated Nyquist criterion for discretetime systems. — IEEE Trans. Education, Vol. 32, No. 1, pp. 59–61.
• Tomizuka M., Tsao T.-C. and Chew K.-K. (1989): Analysis and synthesis of discrete time repetitive controllers. — J. Dyn. Syst. Meas. Contr., Vol. 111, No. 3, pp. 353–358.
• Uchiyama M. (1978): Formulation of high-speed motion pattern of a mechanical arm by trial. — Trans. Soc. Instrum. Contr. Eng., Vol. 14, No. 6, pp. 706–712, (in Japanese).