Robust controller synthesis for systems with input nonlinearities

A trade-off between gain variation and parametric uncertainty

Wassim M. Haddad, Vikram Kapila

Research output: Contribution to journalArticle

Abstract

A feedback control-system design problem involving input nonlinearities and structured plant parameter uncertainities is considered. Multivariable absolute stability theory is merged with the guaranteed cost control approach to robust stability and performance to obtain a theory of full- and reduced-order robust control design that accounts for input time-varying sector bounded nonlinearities. The principal result is a sufficient condition for characterizing dynamic controllers of a fixed dimension which are guaranteed to provide robust stability for plant parametric variations and absolute stabilization for input nonlinearities. The proposed framework provides a systematic design trade-off between classical robustness guarantees (i.e., gain and phase margins) versus parametric robustness. Furthermore, the framework is directly applicable to uncertain systems with saturating controls and provides fixed-order dynamic output feedback controllers with guaranteed domains of attraction.

Original languageEnglish (US)
Pages (from-to)567-583
Number of pages17
JournalInternational Journal of Robust and Nonlinear Control
Volume8
Issue number7
StatePublished - 1998

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Control nonlinearities
Parametric Uncertainty
Trade-offs
Nonlinearity
Robust Stability
Synthesis
Controller
Controllers
Uncertain systems
Robust control
Robustness
Feedback control
Guaranteed Cost Control
Dynamic Output Feedback
Absolute Stability
Control System Design
Robust Performance
Stabilization
Robust Design
Systems analysis

Keywords

  • Absolute stabilization
  • Domains of attraction
  • Reduced-order controllers
  • Robust stability and performance
  • Saturation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

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abstract = "A feedback control-system design problem involving input nonlinearities and structured plant parameter uncertainities is considered. Multivariable absolute stability theory is merged with the guaranteed cost control approach to robust stability and performance to obtain a theory of full- and reduced-order robust control design that accounts for input time-varying sector bounded nonlinearities. The principal result is a sufficient condition for characterizing dynamic controllers of a fixed dimension which are guaranteed to provide robust stability for plant parametric variations and absolute stabilization for input nonlinearities. The proposed framework provides a systematic design trade-off between classical robustness guarantees (i.e., gain and phase margins) versus parametric robustness. Furthermore, the framework is directly applicable to uncertain systems with saturating controls and provides fixed-order dynamic output feedback controllers with guaranteed domains of attraction.",
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