Abstract
A control law for retarded time-delay systems is considered, concerning infinite closed-loop spectrum assignment. An algebraic method for spectrum assignment is presented with a unique optimization algorithm for minimization of spectral abscissa and effective shaping of the chains of infinitely many closed-loop poles. Uncertainty of plant delays of a certain structure is considered in a sense of a robust simultaneous stabilization. Robust performance is achieved using mixed sensitivity design, which is incorporated into the addressed control law.
Highlights
Time-delay systems are an important and well established topic in modern control theory [1,2,3]
An algebraic method for spectrum assignment is presented with a unique optimization algorithm for minimization of spectral abscissa and effective shaping of the chains of infinitely many closed-loop poles
Infinite dimensional spectrum of such systems might cause difficulties in appropriate spectrum assignment using standard control laws, which means that stabilization cannot be always achieved
Summary
Time-delay systems are an important and well established topic in modern control theory [1,2,3]. The remaining controller parameters are used to shift the chains of infinitely many system poles as far to the left of the dominant poles as possible Another pole-placement-based technique has been introduced in [14] for retarded systems and in [15] for neutral systems. Elimination of any part of the spectrum is not admissible and we tackle the problem of infinite closed-loop spectrum assignment, which is indispensable especially in the case of uncertain delays. We present an algebraic method for infinite closed-loop spectrum assignment, which reduces the number of parameters in the search routine for the appropriate stabile closed-loop spectrum. It is shown that mixed sensitivity design might be incorporated into the addressed control law regarding uncertain time delays to obtain an optimal controller. We demonstrate our results on an example and give final remarks in conclusions
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