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A New Nonlinear PID Controller and its Parameter Design
Abstract:A new nonlinear PID controller and its stability analysis are presented in this paper. A nonlinear function is deduced from the similarities between the control effort and the electric-field effect of a capacitor. The conventional linear PID controller can be modified into a nonlinear one by this function. To analyze the stability of the nonlinear PID controlled system, an idea of energy equivalence is adapted to avoid the conservativeness which is usually arisen from some traditional theorems and Criterions. The energy equivalence is naturally related with the conceptions of Passivity and T-Passivity. As a result, an engineering guideline for the parameter design of the nonlinear PID controller is obtained. An inverted pendulum system is tested to verify the nonlinear PID control scheme.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1060836Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF
 J.Q. Han, "Auto disturbances rejection control technique," Frontier Science, 2007, 1(1): 24 - 31(in Chinese).
 M. Margaliot, G. Langholz, "Hyperbolic optimal control and fuzzy control," IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans, 1999, 29(1): 1 - 10.
 A. Brian, A.W. Bruce, "Nonlinear PID control with partial state knowledge: Damping without derivatives," The International Journal of Robotics Research, 2000, 19(8): 715 - 731.
 Z.Q. Sun, "Intelligence control theory and technique," Beijing: Tsinghua University Press, 1997(in Chinese).
 W.B. Gao, "Introduction to Nonlinear Control Systems," Beijing: Science Press, 1988(in Chinese).
 G. Calcev, G. Campion, "T-passivity and related concepts," European Control Conference. Belgium: Brussels, 1997, paper WE-E-D1.
 D. Aeyels, "A new asymptotic stability criterion for nonlinear time-variant differential equations," IEEE Transactions on automatic control. 1998, 43(7): 968-971.
 J.C. Willems, "Dissipative dynamical systems-Part I: general theory," Arch. Rational Mechanics and Analysis. 1972, 45: 321-351.
 I.B. Christopher, I. Alberto, "Passivity,feedback equivalence, and the global stabilization of minimum phase nonlinear system," IEEE Transactions on automatic control. 1991, 36(11):1228-1240.