Estimating models of inverse systems

Abstract

Abstract-This paper considers the problem of how to estimate a model of the inverse of a system. The use of inverse systems can be found in many applications, such as feedforward control and power amplifier predistortion. The inverse model is here estimated with the purpose of using it in cascade with the system itself, as an inverter. A good inverse model in this setting would be one that, when used in series with the original system, reconstructs the original input. The goal here is to select suitable inputs, experimental conditions and loss functions to obtain a good input estimate. Both linear and nonlinear systems will be discussed.For nonlinear systems, one way to obtain a linearizing prefilter is by Hirschorn's algorithm. It is here shown how to extend this to the postdistortion case, and some formulations of how the pre-or postinverter could be estimated are also presented.

Iterative motion feedforward tuning: A data-driven approach based on instrumental variable identification

“…The proposed approach is closely related to Söderström and Stoica (1983), Gilson and Van den Hof (2005), Jung and Enqvist (2013) and Karimi, Butcher, and Longchamp (2008), and extends this work to iterative tuning of feedforward controllers. Furthermore, the motivation for the proposed approach is similar to the approach in Kim and Zou (2013), i.e., combine the advantages of model-based feedforward and ILC without the need for an approximate model of the system.…”

Identification of systems with unknown inputs using indirect input measurements

“…Estimating the model (20) is thus in some sense the inverse problem to estimating the one in (21). Which formulation that is preferable depends on the application, for instance, in estimation of inverse models it might be beneficial to directly estimate the inverse rather than to first estimate a model and then inverting it, see Jung and Enqvist (2013). ◻…”

Fast Adaptive Digital Pre-Distortion Scheme for Application in Cellular Base Station Power Amplifiers

“…There are different methods for estimating a system's inverse. These include inversion by feedback, analytic inversion, and inversion by system simulation [35]. Inversion by feedback requires that a model that characterises the PA is selected.…”