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

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 (LTI) system subject to real parameter uncertainty
associated with the unknown payload. A set of performance indices are
formulated based on generalized H2 (Hg) and H∞ 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 multiobjective
Hg/H∞ control are provided that demonstrate the effectiveness of
the method as a tool for model-based controller evaluation and multiobjective
optimization.