A New Nonlinear PID Controller and its Parameter Design
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.
[1] J.Q. Han, "Auto disturbances rejection control technique," Frontier
Science, 2007, 1(1): 24 - 31(in Chinese).
[2] 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.
[3] 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.
[4] Z.Q. Sun, "Intelligence control theory and technique," Beijing: Tsinghua
University Press, 1997(in Chinese).
[5] W.B. Gao, "Introduction to Nonlinear Control Systems," Beijing: Science
Press, 1988(in Chinese).
[6] G. Calcev, G. Campion, "T-passivity and related concepts," European
Control Conference. Belgium: Brussels, 1997, paper WE-E-D1.
[7] D. Aeyels, "A new asymptotic stability criterion for nonlinear
time-variant differential equations," IEEE Transactions on automatic
control. 1998, 43(7): 968-971.
[8] J.C. Willems, "Dissipative dynamical systems-Part I: general theory,"
Arch. Rational Mechanics and Analysis. 1972, 45: 321-351.
[9] 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.
[1] J.Q. Han, "Auto disturbances rejection control technique," Frontier
Science, 2007, 1(1): 24 - 31(in Chinese).
[2] 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.
[3] 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.
[4] Z.Q. Sun, "Intelligence control theory and technique," Beijing: Tsinghua
University Press, 1997(in Chinese).
[5] W.B. Gao, "Introduction to Nonlinear Control Systems," Beijing: Science
Press, 1988(in Chinese).
[6] G. Calcev, G. Campion, "T-passivity and related concepts," European
Control Conference. Belgium: Brussels, 1997, paper WE-E-D1.
[7] D. Aeyels, "A new asymptotic stability criterion for nonlinear
time-variant differential equations," IEEE Transactions on automatic
control. 1998, 43(7): 968-971.
[8] J.C. Willems, "Dissipative dynamical systems-Part I: general theory,"
Arch. Rational Mechanics and Analysis. 1972, 45: 321-351.
[9] 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.
@article{"International Journal of Information, Control and Computer Sciences:54417", author = "Yongping Ren and Zongli Li and Fan Zhang", title = "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.", keywords = "Nonlinear PID controller, stability, gain equivalence,dissipative, T-Passivity.", volume = "4", number = "12", pages = "1887-6", }