Model Inversion Architectures for Settle Time Applications with Uncertainty

Abstract

Abstract-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 discretetime, 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.

Discrete-Time Exact and Approximate Dynamic Inversion for Settle Performance

“…In the presence of these complexities and constraints, we have previously demonstrated the aggressive settle performance capability of dynamic inversion together with reference command generation [Rigney et al, 2006]. In [Rigney et al, 2008], we show inversion-based settle performance compares favorably with minimum energy optimal state transfer techniques [Perez et al, 2003] in our HDD application, while being more amenable to future adaptation.…”

“…Other researchers have investigated the combined use of dynamic inversion and reference trajectory generation to reduce t s [de Gelder et al, 2006], [Piazzi et al, 2000], but the complex off-line optimization procedures are not applicable to on-line implementation on low-cost DSPs. [Rigney et al, 2006] and [Rigney et al, 2008] also discuss the settle performance benefits of the feedforward closedloop inversion (FFCLI) architecture in Fig. 1.…”

Combined Feedforward/Feedback Control of Atomic Force Microscopes

“…This shows the performance sensitivity of the H ∞ controllers to the exact selection of the weighting functions. Similarly, because different modelinversion methods [9], [19], [21], [22], [37], [38], [41] provide varying degrees of dynamic inversion "accuracy" and possible tradeoffs in penalties of noncausal preactuation, exploring different model-inverse methods may lead to better performing F MI controllers. Regardless of the particular method, model-inversion techniques generally yield feedforward F MI controllers of the same order as the plant (7th-order for our plant model).…”

“…• Other feedforward/feedback architectures that have been used in other application areas [21], [22], [37] should be explored for AFMs. In particular, the reference signals Fig.…”

The effect of nonminimum-phase zero locations on the performance of feedforward model-inverse control techniques in discrete-time systems

“…A cousin of the ZPETC is the comparatively named zero-magnitude-error tracking controller (ZMETC) that has appeared in [2], [5], [6], [9] and [14]. Yet another approximation method is the use of the noncausal series expansion discussed in [7], [16] and [17]. Using a zeroth-order series expansion is effectively the same as choosing to ignore the nonminimum-phase zeros (while accounting for the proper DC gain); approximating the inverse of a system in this way offers a more simplistic approach, but may not be as accurate [2], [18].…”