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Feedback Controls and Optimal Gain Design of Delayed Periodic Linear Systems

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA

J. Q. Sun

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA

In this paper we present an application of a semi-discretization method to the stability analysis of PID feedback controls of linear systems with time delay. The method develops a mapping of the system response in a finite-dimensional state space. Minimization of the largest absolute value of the eigenvalues of the mapping leads to optimal control gains. Numerical examples of both time-invariant and periodic linear systems are presented to demonstrate the method. The tracking control problem of linear systems with time delay is also discussed. We have found that the semi-discretization method provides accurate stability boundaries and performance contours in the parametric space of control gains, and offers an alternative to the classic design approaches of feedback controls.

Key Words: Semi-discretization • delayed feedback control • optimal feedback gains • root locus • time-delayed linear systems • Mathieu equation

Journal of Vibration and Control, Vol. 11, No. 2, 277-294 (2005)
DOI: 10.1177/107754605040947


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