Robust Stability and Nonlinear Loop-Shaping Design for Hybrid Integrator-Gain-Based Control Systems

In this paper, the use of quasi-linear tools for the closed-loop design and analysis of Hybrid Integrator-Gain Systems (HIGS) is considered. A nonlinear motion control design procedure is proposed in which quasi-linear loop-shaping methods, based on describing functions, are combined with rigorous conditions for closed-loop stability. The latter are established by means of multiple piecewise quadratic Lyapunov functions. Admissible functions are found by solving a set of numerically tractable linear matrix inequalities (LMIs). The potential of the robust design method is illustrated by simulation results of a two-mass-spring-damper system.