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

This paper addresses 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. As a side effect of the inverse shaper, the closed loop dynamics become infinite dimensional and, therefore, the design of the controller requires a targeted approach. We present a two-stage method, which firstly makes the closed-loop system asymptotically stable by minimizing the spectral abscissa and, secondly, computes a controller that minimizes the H-infinity norm of the weighted closed-loop transfer functions. Hereto, we employ recent control design algorithms for delay systems, supporting a description by delay differential algebraic equations (DDAEs). The latter are very flexible in modelling interconnected systems, particularly the interconnection of system, controllers, shaper and weights. The overall approach is illustrated by simulations of a two-degree of freedom mechanical model.status: submitte