Robust control design issues for input-shaped discrete systems

Input shaping techniques reduce the residual vibration of undermapped systems by convolving the command input with a sequence of impulses. The exact cancellation of residual vibration depends on the amplitudes and instances of the utilized impulses. Subsequently, the characteristics of the impulse train are related to the damping factors and natural frequencies of the systems poles. Despite the advantages offered by these open-loop robust input-shaped filters (simplicity, ease of implementation, saturation avoidance, etc.), the need for a closed-loop framework to handle these input-shaped systems deserves attention. In this work, the dynamics of the input-shaped continuous system are given by a controller that is designed to correspond to a state-feedback scheme which assures the asymptotic stability of the system while minimizing the cost function. Riccati-based as well as LMI-based approaches relying on recent theoretical advancements of time-delayed systems have been used to synthesize the controller. The design of the robust controller of the input-shaped system amounts to the synthesis of a controller for the nominal system that can withstand an additive perturbation. Simulation studies on a prototype system of a single flexible link manipulator are offered to highlight the efficacy of the suggested scheme.