LQ Optimal Prefiltering for Fast Tracking and Robust Vibration Suppression

Reference tracking and vibration suppression are typical goals in motion control systems. Standard feedforward methods to achieve these goals are inversion-based feedforward control and input shaping. The former achieves perfect tracking but lacks robustness to uncertainties in the system dynamics while the latter may account for robustness at the expense of reduced tracking performance. In this work, a continuous time finite-impulse-response (FIR) prefilter design for linear systems is proposed which allows to trade off tracking performance against robustness. The approach is based on a finite time linear quadratic (LQ) optimal control formulation of the filtering task. Robustness is taken into account by penalizing large magnitudes of the trajectory sensitivity. Tracking delay can be reduced by adjusting the filter length which is a free design parameter. With the proposed prefiltering scheme fast and robust tracking can be achieved. An important application is simultaneous tracking and vibration suppression for motion systems with uncertain elasticity parameters which is used as a simulation example.