Model Inversion Architectures for Settle Time Applications with Uncertainty

We compare two common model inversion architectures, plant inverse (PI) and closed-loop inverse (CLI), by evaluating their ability to achieve settle time performance improvements. The plant models of interest are discrete-time, single-input single-output (SISO), linear time-invariant (LTI), nonminimum phase (NMP), and uncertain. We use a simple algebraic analysis to show that PI and CLI yield the same desired to actual output dynamics if the plant is minimum phase. Using a stable inverse approximation when the plant is certain but NMP, the same algebraic analysis shows that CLI achieves superior settle time performance relative to PI when the settle boundaries are tight. Simulation and experimental data are used to derive conclusions when the plant is NMP and uncertain. We show that CLI has superior performance over PI for our plant dynamics of interest when low frequency parametric uncertainty is present. For higher frequency unstructured uncertainty, the distinction between the two inversion architectures is negligible