Robust Input Shaping Design for Uncertain Second-order Dynamics Systems

Abstract

Models of dynamics systems with resonance modes might include uncertainty on the exact numerical value of the damping and natural frequency. These models are referred to as parametric uncertainty models. Input shaping (IS) design is often computed for a nominal model, rejecting any possible variations in the parameters. Input shaping that is robust for a parametric uncertainty on the resonance mode over a range is required. The process defined in this paper considers the problem of robust input shaping, where a single input signal is designed for a range of uncertainty in the parameters of a dynamic model. Robust input shaping is achieved by considering the extreme cases in the parameter variations, and designing a robust input signal for which constraints on both input and output signals are satisfied. The approach is tested on a second order model with 10% variation in the natural frequency and 10% variation on the damping, which illustrates the ability to design a robust input signal.