Robust Mixed H2-H∞ Control Synthesis for Dual-Stage Hard Disk Drives Using Convex Optimization

Abstract

This paper presents a convex optimization-based control synthesis method for a dual-stage hard disk drive system that is robust to model uncertainty. A mixed H2-H∞ approach is used that minimizes the steady-state variance of the piezoelectric (PZT) micro-actuator stroke through the H2 norm, while constraining the closed-loop sensitivity through the H∞ norm. Robustness of the closed-loop sensitivity to model uncertainty is ensured through the use of a time-domain integral quadratic constraint (IQC) quantification of the voice coil motor (VCM) plant model uncertainty and a circle criterion-based matrix inequality condition. The synthesis method is derived in discrete time and involves iteratively solving semidefinite programs with linear matrix inequality (LMI) constraints. Numerical simulations demonstrate the benefits of the proposed synthesis method over other approaches in the literature that do not explicitly consider robustness to model uncertainty or the minimization of PZT micro-actuator stroke.