LMI based robust state feedback control of negative-imaginary systems

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The importance of robust feedback control for uncertain negative imaginary system lies in its practical relevance and engineering applications, for example, lightly damped flexible structures with collocated position sensors and force actuators. This article investigates an LMI based robust static state internally stabilizing feedback controller of the negative imaginary system in presence of strictly negative imaginary uncertainties. The paper first presents some basic theory of negative imaginary systems and then, a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems. The paper provides a systematic controller synthesis procedure based on negative imaginary lemma to achieve robustness in the feedback control of negative imaginary systems. To show the effectiveness of controller synthesis method, one design example is considered and a static state-feedback controller is constructed to force the plant to be stable. The simulation results of this article demonstrate the usefulness of the design method and we believe that feedback control of the negative imaginary system can benefit control engineering practitioners in a number of ways.

Original languageEnglish
Pages (from-to)347-356
Number of pages10
JournalInternational Journal of Dynamics and Control
Volume5
Issue number2
DOIs
Publication statusPublished - 01-06-2017

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State Feedback Control
State feedback
Feedback control
Controllers
Feedback Control
Feedback
Controller
Flexible structures
Robust control
Actuators
Synthesis
Flexible Structure
Positive Feedback
Sensors
Engineering Application
Robust Control
State Feedback
Interconnection
Damped
Design Method

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Mechanical Engineering
  • Control and Optimization
  • Modelling and Simulation

Cite this

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abstract = "The importance of robust feedback control for uncertain negative imaginary system lies in its practical relevance and engineering applications, for example, lightly damped flexible structures with collocated position sensors and force actuators. This article investigates an LMI based robust static state internally stabilizing feedback controller of the negative imaginary system in presence of strictly negative imaginary uncertainties. The paper first presents some basic theory of negative imaginary systems and then, a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems. The paper provides a systematic controller synthesis procedure based on negative imaginary lemma to achieve robustness in the feedback control of negative imaginary systems. To show the effectiveness of controller synthesis method, one design example is considered and a static state-feedback controller is constructed to force the plant to be stable. The simulation results of this article demonstrate the usefulness of the design method and we believe that feedback control of the negative imaginary system can benefit control engineering practitioners in a number of ways.",
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LMI based robust state feedback control of negative-imaginary systems. / Choudhary, Santosh Kumar.

In: International Journal of Dynamics and Control, Vol. 5, No. 2, 01.06.2017, p. 347-356.

Research output: Contribution to journalArticle

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