Active control of vibration in a flexible structure with uncertain parameters via sliding mode and H/μ techniques

M. C. Pai, Alok Sinha

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper presents a new approach for the robust control of vibration in flexible structures with uncertain parameters. The algorithm is based on sliding mode control and H / μ techniques. First, the sliding mode control algorithm is developed using state feedback and the chattering behavior is eliminated using boundary layers around sliding hyperplanes. The LQ control method and H control method for designing sliding hyperplanes are presented. The switching control is chosen to satisfy the so-called reaching condition. Then, the small gain theorem / μ analysis is applied to analyze the asymptotic behavior of the closed-loop system with parametric uncertainties inside boundary layers. Using a flexible tetrahedral truss structure, numerical examples are presented to verify the theoretical analysis. Results from H full state feedback control method, sliding mode with H full state feedback control method, LQ control method and sliding mode with LQ control method are presented and compared.

Original languageEnglish (US)
Pages (from-to)1-7
Number of pages7
JournalAmerican Society of Mechanical Engineers, Design Engineering Division (Publication) DE
Volume97
StatePublished - Dec 1 1998

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Flexible structures
State feedback
Sliding mode control
Feedback control
Boundary layers
Robust control
Closed loop systems

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

Cite this

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abstract = "This paper presents a new approach for the robust control of vibration in flexible structures with uncertain parameters. The algorithm is based on sliding mode control and H∞ / μ techniques. First, the sliding mode control algorithm is developed using state feedback and the chattering behavior is eliminated using boundary layers around sliding hyperplanes. The LQ control method and H∞ control method for designing sliding hyperplanes are presented. The switching control is chosen to satisfy the so-called reaching condition. Then, the small gain theorem / μ analysis is applied to analyze the asymptotic behavior of the closed-loop system with parametric uncertainties inside boundary layers. Using a flexible tetrahedral truss structure, numerical examples are presented to verify the theoretical analysis. Results from H∞ full state feedback control method, sliding mode with H∞ full state feedback control method, LQ control method and sliding mode with LQ control method are presented and compared.",
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AB - This paper presents a new approach for the robust control of vibration in flexible structures with uncertain parameters. The algorithm is based on sliding mode control and H∞ / μ techniques. First, the sliding mode control algorithm is developed using state feedback and the chattering behavior is eliminated using boundary layers around sliding hyperplanes. The LQ control method and H∞ control method for designing sliding hyperplanes are presented. The switching control is chosen to satisfy the so-called reaching condition. Then, the small gain theorem / μ analysis is applied to analyze the asymptotic behavior of the closed-loop system with parametric uncertainties inside boundary layers. Using a flexible tetrahedral truss structure, numerical examples are presented to verify the theoretical analysis. Results from H∞ full state feedback control method, sliding mode with H∞ full state feedback control method, LQ control method and sliding mode with LQ control method are presented and compared.

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