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

Date
2007-01
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Source Title
Automatica
Print ISSN
0005-1098
Electronic ISSN
1873-2836
Publisher
Elsevier BV
Volume
43
Issue
1
Pages
135 - 142
Language
English
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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.

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