Linear quadratic-based optimal current control of BLDC motor minimizing control error and considering accurate finite element model

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.

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.

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.

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