Convolution-Based Input Shaping for Finite-Time Settling in Non-LTI Systems: An LTV Approach

This paper gives the formulation of a parameter-dependent input shaping filter suitable for residual vibration reduction in motion control of non-LTI systems. The method is based on the assumption that the vibratory dynamics can be represented by a second order linear ODE with time-varying coefficients that can be estimated during motion. The control implementation involves a time-varying filter function that is convolved with the system command/actuation signal in real-time. Discrete-time implementation and performance aspects are studied by numerical simulation. Numerical results for a benchmark mechanical system are presented that reveal limitations due to non-linear dynamics impacting on the accuracy of the LTV assumption. Results from implementation on a flexure-jointed X-Y motion stage mechanism are shown that confirm the applicability and effectiveness of the method in achieving reduced vibration and settling time for step-wise motion tasks.