Slawomir Jan Stepien, Paulina Superczynska, Damian Dobrowolski and Jerzy Dobrowolski
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…
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.
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
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.