Settle time performance comparisons of stable approximate model inversion techniques

Abstract

We compare the achievable settle time for small rest-to-rest maneuvers using two stable approximate model inversion output tracking methods: the zero phase error tracking controller (ZPETC) and noncausal series approximation. The plant dynamics of interest are known, discrete-time, single-input single-output (SISO), linear time-invariant (LTI), and nonminimum phase (NMP), with a single left-half-plane zero outside the unit circle. The approximate inversion methods are evaluated over a range of NMP zero locations and aggressive seek durations. Using a plant inverse (PI) architecture, we find that the ZPETC algorithm provides better settle performance for particular plants with a NMP zero near the unit circle. Conversely, the noncausal series approximation method achieves faster settle times when these plants' NMP zero is far from the unit circle. With a closed-loop inverse (CLI) architecture, both the series approximation and ZPETC algorithms yield faster settle times than either algorithm in PI, regardless of NMP zero location