LPV model identification for motion control systems

Abstract

Motion systems for optical and manufacturing applications have demanding performance requirement in terms of speed and precision. Linear system description alone is often inadequate to meet the design and performance assessment requirements. Linear parameter varying (LPV) formulation is a promising approach to address system nonlinearity by using a family of linear time invariant (LTI) systems parameterized by the operating point. It is attractive as many aspects of the linear system theory, such as systems identification, parameter estimation, and feedback control, are still applicable, at least locally around each operating point. This paper addresses the issue of constructing a multi-input/multi-output (MIMO) LPV characterization based on local data around multiple operating points. The goal is to capture the large motion behavior by suitably interpolating the local LTI models. The identification of the LPV model parameters is posed as a nonlinear least square problem. An efficient iterative relaxation algorithm consisting of alternating least square problems is proposed for the solution. The proposed approach is applied to the simulation and experiment of a two-degree-of-freedom fast steering mirror (FSM). The LPV response matches well with the nonlinear system response for both small and large motion ranges, demonstrating the efficacy of the approach.