Abstract. An optimal control theory based method is presented aiming at minimizing the energy delivered from source and the power loss in a stepper motor circuit. A linear quadratic current regulator with an infinite time horizon is employed and its appropriateness for this type of a problem explained. With the purpose of improving the accuracy of the control system, the self and mutual inductances of windings are calculated using a finite element model. The numerically computed results are verified experimentally.

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Original scientific paperAn optimal control theory for linear quadratic finite time horizon problem is presented and combined with distributed parameters model of the BLDC (BrushLess Direct-Current) motor. Method appropriateness for minimization of the phase current control error and energy delivered to the drive is proven. The paper focuses on finding the best weighting configuration of the objective function. Presented control strategy is performed and presented employing the numerical computations. Key words: BLDC motor, Numerical analysis, Optimal controlUpravljanje bezkolektorskim DC motorom s distribuiranim parametrima zasnovano na linearnom kvadratičnom regulatoru s konačnim horizontom. U ovom radu je predstavljen problem optimalnog upravljanja modelom bezkolektorskog DC motora s distribuiranim parametrima zasnovan na linearnom kvadratičnom regulatoru na konačnom horizontu. Metoda je prikladna za minimizaciju regulacijske pogreške fazne struje i utrošene energije za pokretanje pogona. Fokus rada je na traženju najboljih koeficijenata funkcije cilja. Predstavljena strategija upravljanja je realizirana i validirana u simulacijama.

Purpose Brushless DC (BLDC) motors are commonly used in the industry. The improvement of power switching electronic elements, especially integrated circuits, has led to the development and improvement of control strategies. The purpose of this paper is to apply the well-known LQR control method for the highly accurate model of the BLDC motor, which is a must for the control system to be optimal and stable. Design/methodology/approach The employed distributed parameter finite element motor model uses a state vector which is dependent not only on time but also on space configuration, thus enabling the end-winding effect, cogging torque or magnetic saturation to be taken into account. The adopted infinite horizon linear quadratic-based controller aims at optimally minimizing current control error considering the energy delivered to the motor. For this reason, the relationship between the quadratic forms of the performance index is investigated and the reference currents’ influence on the results was studied. The presented methodology was confirmed with the numerical analysis of the problem. Findings It was found how the configuration of the optimal control objective function influences the performance and the stability of the drive system subject to energy delivery minimization. An exact configuration was calculated for which the control error was reasonably small. The applicability of the infinite horizon optimal current control for the BLDC drive applications was proved. 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.

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.