Brief paper: PID controller synthesis for a class of unstable MIMO plants with I/O delays

Authors:
A. N. Gündeş;H. Özbay;A. B. Özgüler
Affiliations:
Department of Electrical and Computer Engineering, University of California, Davis, CA 95616, USA;Department of Electrical and Electronics Engineering, Bilkent University, Ankara 06800, Turkey;Department of Electrical and Electronics Engineering, Bilkent University, Ankara 06800, Turkey
Venue:
Automatica (Journal of IFAC)
Year:
2007

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Abstract

Conditions are presented for closed-loop stabilizability of linear time-invariant (LTI) multi-input, multi-output (MIMO) plants with I/O delays (time delays in the input and/or output channels) using PID (Proportional+Integral+Derivative) controllers. We show that systems with at most two unstable poles can be stabilized by PID controllers provided a small gain condition is satisfied. For systems with only one unstable pole, this condition is equivalent to having sufficiently small delay-unstable pole product. Our method of synthesis of such controllers identify some free parameters that can be used to satisfy further design criteria than stability.