Infinite-time linear–quadratic optimal control of the BLDC motor exploiting a nonlinear finite element model

Abstract

Purpose

This paper aims to present a nonlinear finite element model (FEM) of the Brushless DC (BLDC) motor and the application of the optimal linear–quadratic control-based method to determine the excitation voltage and current waveform considering the minimization of the energy injected to the input circuit and energy lost. The control problem is designed and analyzed using the feedback gain strategy for the infinite time horizon problem.

Design/methodology/approach

The method exploits the distributed parameters, nonlinear FEM of the device. First, dynamic equations of the BLDC motor are transformed into a suitable form that makes an ARE (algebraic Riccati equation)-based control technique applicable. Moreover, in the controller design, a Bryson scaling method is used to obtain desirable properties of the closed-loop system. The numerical techniques for solving ARE with the gradient damping factor are proposed and described. Results for applied control strategy are obtained by simulations and compared with measurement.

Findings

The proposed control technique can ensure optimal dynamic response, small steady-state error and energy saving. The effectiveness of the proposed control strategy is verified via numerical simulation and experiment.

Originality/value

The authors introduced an innovative approach to the well-known control methodology and settled their research in the newest literature coverage for this issue.

Citation

Bernat, J., Stepien, S.J., Stranz, A. and Superczynska, P. (2017), "Infinite-time linear–quadratic optimal control of the BLDC motor exploiting a nonlinear finite element model", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 36 No. 3, pp. 633-648. https://doi.org/10.1108/COMPEL-09-2016-0419