Jakub Bernat, Slawomir Jan Stepien, Artur Stranz and Paulina Superczynska
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…
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.
Details
Keywords
Jakub Bernat, Slawomir Jan Stepien, Artur Stranz and Paulina Superczynska
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…
Abstract
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.
Details
Keywords
Sławomir Stępień and Jakub Bernat
The purpose of this paper is to present a method of modeling the variable reluctance stepper motor using the time‐stepping finite element technique. The proposed model is used to…
Abstract
Purpose
The purpose of this paper is to present a method of modeling the variable reluctance stepper motor using the time‐stepping finite element technique. The proposed model is used to minimize the step response overshoots considering the stator and rotor tooth geometry.
Design/methodology/approach
A strongly coupled field‐circuit model considering magnetic nonlinearity of the stepper motor is presented. As the main contribution, the Nelder‐Mead method of the motor geometry optimization that minimize the step response overshoots and positioning error is proposed.
Findings
The proposed method can be applied to obtain the optimal tooth/pole geometry of the stepper motor which is efficient to perform the possibly accurate positioning.
Originality/value
The paper examines the application of the presented optimization method to minimize the positioning error of the four‐phased variable reluctance stepper motor.
Details
Keywords
Slawomir Stepien and Jakub Bernat
The purpose of this paper is to present a method of modeling the variable reluctance stepper motor using the time‐stepping finite element technique. The proposed model is used to…
Abstract
Purpose
The purpose of this paper is to present a method of modeling the variable reluctance stepper motor using the time‐stepping finite element technique. The proposed model is used to obtain the optimal control law for the input circuit solving the linear‐quadratic problem.
Design/methodology/approach
A strongly coupled field‐circuit model of the stepper motor is presented. Also, the method of the optimal control that minimizes the power loss in the motor windings is proposed.
Findings
The proposed optimal control method can be applied to the electrical machines connected to the electronic converters. Calculated control signals may be used to obtain the optimal waveforms of the input voltages at each phase of the analyzed machine.
Originality/value
The paper examines the application of the presented control method to minimize the power loss in the stator windings of the four‐phased variable reluctance stepper motor.