SDRE-based high performance feedback control for nonlinear mechatronic systems

Abstract

Purpose The purpose of the paper is to present modeling and control of a nonlinear mechatronic system. To solve the control problem, the modified state-dependent Riccati equation (SDRE) method is applied. The control problem is designed and analyzed using the nonlinear feedback gain strategy for the infinite time horizon problem. Design/methodology/approach As a new contribution, this paper deals with state-dependent parametrization as an effective modeling of the mechatronic system and shows how to modify the classical form of the SDRE method to reduce computational effort during feedback gain computation. The numerical example compares described methods and confirms usefulness of the proposed technique. Findings The proposed control technique can ensure optimal dynamic response, reducing computational effort during control law computation. The effectiveness of the proposed control strategy is verified via numerical simulation. Originality/value The authors introduced an innovative approach to the well-known SDRE control methodology and settled their research in the newest literature coverage for this issue.

Numerical Solution of SDRE Control Problem – Comparison of the Selected Methods

“…Currently, this method is very well-konwn and commonly used among others in the field of satellite and control [11], integrated guidance and control design [13], autopilot design [4], robotics [10], magnetic systems including levitation [6], and flight control [16]. The method based on SDRE design runs in two main steps: the first is related to the computation of the state department coefficient matrices (using algebraic manipulations is possible to derive the SDC model) [17] and the second deals with solution of an algebraic matrix Riccati equation.…”

“…The solution of an algebraic matrix Riccati equation (ARE) [2] is used to obtain a control law. The algebraic Riccati equation (ARE) using the SDC matrices is then solved on a regular basis to give the suboptimum control law [17]. The remaining steps involve matrix inversion and multiplication.…”

“…The method based on continuous solving of the SDRE equation is time-consuming. Therefore, from the very beginning of this equation, new methods of faster solving the Riccati equation had been invastigated [17].…”

“…An algebraic Riccati (ARE) using the SDC matrices is then solved on-line to give the suboptimal control law. The SDC form has the structure [2,8,17,15]:…”