Mixed-sensitivity design of a dynamic controller for systems pre-compensated by input shapers

Abstract

We employ recent control design algorithms for delay systems to address the mixed sensitivity design of a dynamic controller for multiple degree of freedom systems interconnected with an inverse signal shaper. A delay based inverse shaper is included within a feedback loop in order to eliminate oscillatory modes due to an attached flexible substructure, which has been shown to be advantageous to inducing directly the filtering property by an appropriate controller design. Due to the presence of the inverse shaper, the closed loop dynamics become infinite dimensional. Furthermore we design fixed-order controllers, aiming at an easy implementation. As a consequence of these two features standard techniques from H-infinity control can no longer be used. We present a two-stage method, which firstly makes the closed-loop system asymptotically stable and, secondly, computes a low-order controller that minimizes the H-infinity norm of the weighted closed-loop transfer functions. The approach is grounded in recent methods for fixed-order H-infinity control of delay systems, and the delay-differential algebraic equations (DDAE) modelling and control framework.