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Globally asymptotically stable saturated PID controllers for a double integrator with constant disturbance
Author(s) -
Hu Jinchang,
Zhang Honghua
Publication year - 2012
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.2940
Subject(s) - control theory (sociology) , integrator , pid controller , corollary , bounded function , double integrator , saturation (graph theory) , mathematics , constant (computer programming) , singular perturbation , perturbation (astronomy) , computer science , engineering , control (management) , control engineering , physics , mathematical analysis , bandwidth (computing) , temperature control , computer network , combinatorics , artificial intelligence , quantum mechanics , programming language , pure mathematics
SUMMARY This paper provides a deep insight into the saturated PID control of a double integrator with bounded disturbance. On the basis of the nested saturation functions, a simple PID‐like controller is proposed. The main difficulty in saturation control with bounded disturbances is to prove that the unsaturated regions are invariant. By phase plane and singular perturbation analysis, we prove that the saturation restrictions on the controller can be removed one by one in finite time, and the closed‐loop system can be finally reduced to a nonsaturated PID controlled double integrator. The sufficient conditions for the stability of the closed loop with disturbance are also derived. Finally, numerical simulations are conducted to validate the effectiveness of the proposed control scheme. Copyright © 2012 John Wiley & Sons, Ltd.