A New PID Controller with Lyapunov Stability for Regulation Servo Systems
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, the stability of second order uncertain systems with regulation of PID type controllers is analyzed by using Lyapunov second method for the first time in the time domain. The property of the stability of PIDregulation servo systems is revealed in sense of Lyapunov, i.e., bounded stability due to the disturbances and uncertainties. By means of the results of this stability analysis, the maximum norm bound of the error from the output without variation of the uncertainties and disturbances is determined as a function of the gains of the PID control,which make it enable to analyze the effect resulted from the variations of the disturbances and uncertainties using this norm bound for given PID gains. Using the relationship of the error from the output without variation of the uncertainties and disturbances and the PID gain with maximum bounds of the disturbances and uncertainties, the robust gain design rule is suggested so that the error from the output without the variation of the disturbances and uncertainties can be guaranteed by the prescribed specifications as the advantages of this study. The usefulness of the proposed algorithm is verified through an illustrative example.
Abstract
In this paper, the stability of second order uncertain systems with regulation of PID type controllers is analyzed by using Lyapunov second method for the first time in the time domain. The property of the stability of PIDregulation servo systems is revealed in sense of Lyapunov, i.e., bounded stability due to the disturbances and uncertainties. By means of the results of this stability analysis, the maximum norm bound of the error from the output without variation of the uncertainties and disturbances is determined as a function of the gains of the PID control,which make it enable to analyze the effect resulted from the variations of the disturbances and uncertainties using this norm bound for given PID gains. Using the relationship of the error from the output without variation of the uncertainties and disturbances and the PID gain with maximum bounds of the disturbances and uncertainties, the robust gain design rule is suggested so that the error from the output without the variation of the disturbances and uncertainties can be guaranteed by the prescribed specifications as the advantages of this study. The usefulness of the proposed algorithm is verified through an illustrative example.
참고문헌 (17)
- K. J. Astrom, "Automatic tuning of PID controllers" (1988), Instrument society of America
- J. G. Ziegler, "Optimum settings for automatic controllers", Trans. ASME, 64, pp.759~768 (1942)
- R.E. Kalman, "Control system analysis and design via the second method of Lyapunov", Trans. ASME, 82(3), pp.371~393 (1960)
- K. J. Chien, "On self tuning regulators", Trans ASME, 74, pp.175~ (1952)
- S. Fukuta, "On the determination of the optimal feedack gains for multivariable linear systems incorporating integral action", Int. J. Control, 31(6), pp.1027~1040 (1980)
- S. Marsili-Libelli, "Optimal design of PID controller", Int. J. Control, 33(4), pp.601~616 (1981)
- T. Hagglund, "Automatic tuning PID controller based on dominant pole design", Proceedings of the IFAC Conference on Adaptive Controle of Chemical Processes (1985)
- I. H. Suh, "A design and experiment of speed controller with PI-plus bang-bang action for a DC Servomotor with transistorized PWM drives", IEEE Tran. Ind. Electronics, IE-31(4), pp.338~345 (1984)
- N. J. Krikelis, "Design of tracking systems subject to actuator saturation and integral wind-up", Int. J. Control, 39(4), pp.667~682 (1984)
- Youbin Peng, "Anti-Winuo, Bumpless, and Conditioned Transfer Techniques for PID Controllers", IEEE Control Systems, pp.48~57 (1996)
- K. J. Astrom, "Automatic tuning of simple regulators with specfications on phase and amplitude margins", Automatica, 20, pp.645~651 (1984)
- W. K. Ho, "Tuning of PID controllers based on Gain and Phase Margin Specifications", Automatica, 31, pp.497~502 (1995)
- K. J. Astrom, "Toward intelligent PID control", Automatica, 28(1), pp.1~9 (1992)
- Y. Nishikawa, "A method for auto-tuning of PID control parameters", Automatica, 20(3), pp.321~332 (1984)
- R. Ortega, "PID self-tunners: Some Theoretical and practical aspects", IEEE Tran. on Ind. Electronics, IE-31(4), pp.332~337 (1984)
- C. L. Nachtigal, "Adaptive controller performance evaluation: Foxboro EXACT and ASEA Novatune", Proceedings ACC-86, pp.1428~1433 (1986)
- Z. Y. Zhao, "Fuzzy gain scheduling of PID controllers", IEEE Trans. Systems, Man & Cybernetics, 23, pp.1392~1398 (1993)