Control of a nonlinear flexure-jointed X-Y positioning stage using LTV-FIR command prefiltering for finite-time error cancellation

This paper presents a new command input prefilter that achieves exact residual vibration cancellation for a single degree-of-freedom oscillator with linear time-varying (LTV) dynamics. The prefilter has a time-varying finite impulse response (FIR) function that is constructed using a time-warping technique and can be convolved with any command input signal to achieve finite settling time. Numerical results confirm that a discrete-time implementation of the prefilter can suppress vibration more effectively than robust linear time-invariant prefilter designs. The LTV-FIR prefilter was applied to a flexure-based X-Y micro-positioning platform having nonlinear dynamics and cross-coupling between motion axes. A configuration-dependent LTV model was constructed by using polynomial interpolation of a set of experimentally identified LTI models. Prefiltering was applied separately to X and Y axis command variables and a cross-coupling compensation technique used to minimize dynamic interaction between the motion axes. The LTV-FIR prefilter is shown to be effective for settling-time reduction in point-to-point motions (reduced from >6 to ≈0.4 seconds). Moreover, improved motion performance could be achieved over a large operating space without the use of high-gain feedback control, which is inappropriate in this case due to noise excitation and the risk of instability.