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

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.