An analysis and design framework for robust control of a multi-axis active vibration isolation system with unknown payload

Abstract

This paper presents a framework for model-based analysis of robust stability and performance for a multi-axis active vibration isolation system with constant but unknown payload and subject to modelling errors associated with structural flexibility. The theoretical treatment involves a linear time-invariant system subject to real parameter uncertainty associated with the unknown payload. A set of performance indices are formulated based on generalized $\mathcal{H}2$ ( $\mathcal{H}g$ ) and $\mathcal{H}\infty$ measures. A method for stability/performance verification is then developed using a parameter-dependent Lyapunov function that incorporates the kinetic energy of the uncertain payload mass. This allows nonconservative bounds on the performance indices to be established via numerical solution of a corresponding set of matrix inequalities. The approach is especially suitable, and computationally efficient, for multi-degree-of-freedom systems as the overall (symmetric positive-definite) properties of the system mass matrix are accounted for without involving information for each scalar parameter. The associated LMIs can therefore be solved in polynomial time with respect to the number of unknown parameters. Numerical examples for the case of sky-hook damping control and multi-objective $\mathcal{H}g/\mathcal{H}\infty$ control are provided that demonstrate the effectiveness of the method as a tool for model-based controller evaluation and multi-objective optimization.