Model predictive tracking control of uncertain moving structures with nonaffine saturated actuation: Rotating control force

Abstract

This article presents a novel scheme for model-based control of multi-input–multi-output (MIMO) systems considering input nonaffinity, nonlinear dynamical effects, and bounded modeling uncertainty. Commonly, model-based control of a nonaffine system is conducted based on an equivalent pseudo-affine expression. However, validity of this approximation necessitates boundedness of inputs and states. Furthermore, existence of truncation errors is inevitable when obtaining the pseudo-affine model. Therefore, robustness to bounded uncertainty should be ensured even in cases where the original system is deterministic. To address the expressed issues, in this study the boundedness assumptions are incorporated in a constrained robust model predictive control (MPC) algorithm. The corresponding MPC scheme is based on construction of cost according to predicted sliding functions over a finite prediction horizon. It should be noted that for the considered class of uncertain nonlinear nonaffine system, obtaining the perquisite robust stability and feasibility conditions is non-trivial. To attain the aforementioned qualities, it is proposed that sliding functions can be expressed as the sum of input-based terms (using pseudo-affine approximation of input gains based on Taylor expansion) and dynamical variation terms. Subsequently, robust stability is ensured by constructing a Lyapunov-based terminal cost. Constraints satisfaction conditions are determined based on calculation of the corresponding feasible region. Numerical simulations for a nonlinear nonaffine mechanical system indicate efficiency of the presented control model. Comparisons with other applicable schemes highlight significant features of the presented algorithm and the attained improvements regarding stability and control feasibility are discussed.