### Speed control of MT2240A DC motor with observer-based linear quadratic regulator

#### Abstract

The design of Direct Current (DC) motor speed control, which is preferred due to its high torque in industrial applications, is a challenging task. The Linear Quadratic Regulator (LQR) controller ensures the well-controlled behavior of the system by minimizing the error in speed control. This can only be achieved if the rank of the controllability matrix is maximum. The rank value of the MT2240A DC motor used in the study is calculated as one. In this study, the LQR controller enriched with an observed-based design was used to overcome this problem. In the experiments, the transient and steady-state behavior metrics of the speed control were compared in the simulation environment of the plant controlled by the Proportional Integral Derivative (PID) controller, and the closed-loop response of the plant to determine the efficiency of the presented design. It was observed that the LQR controller has an optimum response with more effective transient and steady-state responses compared to the PID controller. This result enabled the LQR controller design, which was inadequate in terms of controllability, and the results is proved that the observation-based LQR controller dynamically responded better.

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Ö. Cihan, M. Javadzadehkalkhoran, A. Kutlar, “Improvement of the electronic control unit for ignition and injection in a Wankel engine,” Gümüşhane University Journal of Science and Technology, 10(3), pp. 742-751, 2020.

M. Park, Y. Kang, “Experimental verification of a drift controller for autonomous vehicle tracking: A circular trajectory using LQR method,” International Journal of Control Automation and Systems, 19(1), pp. 404-416, 2021.

A. K. Mishra, S. R. Das, P. K. Ray, R. K. Mallick, A. Mohanty, D. K. Mishra, “PSO-GWO optimized fractional order PID based hybrid shunt active power filter for power quality improvements,” IEEE Access, vol.8, pp. 74497-74512, 2021.

B. Jakovljević, P. Lino, G. Maione, “Control of double-loop permanent magnet synchronous motor drives by optimized fractional and distributed-order PID controllers,” European Journal of Control, vol. 58, pp. 232-244, 2021.

M. A. Ebrahim, M. N. Ahmed, H. S. Ramadan, M. Becherif, J. Zhao, “Optimal metaheuristic-based sliding mode control of VSC-HVDC transmission systems,” Mathematics and Computers in Simulation, vol. 179, pp. 178-193, 2021.

Y. Shin, R. Smith, S. Hwang, "Development of a model predictive control system using an artificial neural network: A case study with a distillation column," Journal of Cleaner Production, vol. 277, pp. 124124, 2020.

D. A. Souza, V. A. de Mesquita, L.L. Reis, W. A. Silva, J. G. Batista, “Optimal lqi and PID synthesis for speed control of switched reluctance motor using metaheuristic techniques," International Journal of Control, Automation and Systems, 19(1), pp. 221-229, 2021.

K. M. Haneesh, T. Raghunathan, “Robust Control of DFIG Based Wind Energy System Using an H∞ Controller,” Journal of Electrical Engineering & Technology, 16(3), pp. 1693-1707, 2021.

M. A. L. Beteto, E. Assunção, M. C. M. Teixeira, E. R. P. D. Silva, L. F. S. Buzachero, R. da Ponte Caun, “Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach,” International Journal of Systems Science, 52(12), pp. 2518-2537, 2021.

S. Zimmermann, R. Poranne, R., S. Coros, “Dynamic manipulation of deformable objects with implicit integration,” IEEE Robotics and Automation Letters, 6(2), pp. 4209-4216, 2021.

S. Mukherjee, H. Bai, H., A. Chakrabortty, “Reduced-dimensional reinforcement learning control using singular perturbation approximations,” Automatica, vol. 126, pp. 109451, 2021.

S. K. Pandey, B. Singh, “PV–BES Microgrid System with LQR-Tuned CC–CVF-Based Control Algorithm.,” Journal of the Institution of Engineers (India): Series B, 102(3), pp. 585-593, 2021.

P. Yu, K.Z. Liu, X. Liu, X. Li, M. Wu, M., J. She, “Analysis of equivalent‐input‐disturbance‐based control systems and a coordinated design algorithm for uncertain systems,” International Journal of Robust and Nonlinear Control, vol. 31, pp. 1755–1773, 2021.

T. H. Lee, W. Liang, C. W. de Silva, K. K. Tan, “Advanced Disturbance Observer-Based Failure Detection for Force Sensor,” Springer Force and Position Control of Mechatronic Systems, pp. 179-198, 2021.

T. Wang, H. Wang, H. Hu, C. Wang, “LQR optimized BP neural network PI controller for speed control of brushless DC motor,” Advances in Mechanical Engineering, 12(10), pp.1687814020968980, 2020.

F. Ahmad, P. Kumar, A. Bhandari, P. P. Patil, “Simulation of the quadcopter dynamics with LQR based control,” Materials Today: Proceedings, vol. 24, pp. 326-332, 2020.

H. Maghfiroh, M. Gunawan, M. Anwar, “Optimal energy control of DC-drive conveyor using LQR method,” AIP Conference Proceedings, 2217(1), pp. 030145, 2020.

S. Masroor, C. Peng, A. A. Ali, M. Aamir, "Network-Based Speed Synchronization Control in the Brush DC Motors Via LQR and Multi-agent Consensus Scheme,” Wireless Personal Communications, 106(4), pp. 1701-1718, 2019.

J. Bharti, G. Phadke, D. Patil, “Optimization of DC Motor Speed Control Using LQR Technique,” International Conference on Data Science, Machine learning & Applications, 29-30 May 2019, Hyderabad, India, pp. 1492-1499, 2020.

M. Sharma, “A review on DC motor speed control using artificial neural network,” International Journal of Engineering, Science and Mathematics, 7(8), pp. 27-33, 2018.

M. A. Aravind, N. S. Dinesh, K. Rajanna, “Application of EMPC for precise position control of DC-motor system with Backlash,” Control Engineering Practice, vol. 100, pp. 104422, 2020.

H. Patel, H. Chandwani, “Simulation and experimental verification of modified sinusoidal pulse width modulation technique for torque ripple attenuation in Brushless DC motor drive,” Engineering Science and Technology, an International Journal, 24(3), pp. 671-681, 2021.

R. Isermann, J. Schaffnit, S. Sinsel, “Hardware-in-the-loop simulation for the design and testing of engine-control systems,” Control Engineering Practice, 7(5), pp. 643-653, 1999.

A. A. Hagras, “Nonlinear adaptive extended state space predictive control of permanent magnet synchronous motor,” International Transactions on Electrical Energy Systems, 29(1), pp. e2677, 2019.

B. H. Nguyen, M. P. Cu, M. T. Nguyen, M. S. Tran, H. C. Tran, “LQR and fuzzy control for reaction wheel inverted pendulum model,” Robotica & Management, 24(1), pp. 19-23, 2019.

S. Masroor, C. Peng, Z. A. Ali, "Event-triggered multi-agent consensus of DC motors to regulate speed by LQR scheme," Mathematical and Computational Applications, 22(1), pp. 14, 2017.

A. Owczarkowski, D. Horla, J. Zietkiewicz, “Introduction of feedback linearization to robust LQR and LQI control–analysis of results from an unmanned bicycle robot with reaction wheel,” Asian Journal of Control, 21(2), pp. 1028-1040, 2019.

S. S. Sankeshwari, R. H. Chille, “Performance Analysis of Disturbance Estimation Techniques for Robust Position Control of DC Motor,” International Journal of Control, Automation, and Systems, 18(2), pp. 486-494, 2020.

N. Kumar, J. Ohri, “Novel m-PSO optimized LQR control design for Flexible Link Manipulator: An experimental validation. Majlesi,” Journal of Electrical Engineering, 14(2), pp. 81-92, 2020.

P. C. Eze, “An Enhanced PID Control Technique for Mobile Satellite Dish Antenna Network within Nigeria. Journal of Electrical Engineering, Electronics,” Control and Computer Science, 6(3), pp. 25-30, 2020.

S.O. Madbouly, A. M. Sharaf, “A novel regulation inter-coupled control scheme for a doubly-fed wind induction system,” Turkish Journal of Electromechanics and Energy, 1(2), pp. 8-16, 2016.

I. A. Aden, H. Kahveci, M. E. Şahin, “Single input, multiple output DC-DC buck converter for electric vehicles,” Turkish Journal of Electromechanics & Energy, 2(2), pp. 7-13, 2017.

A. Boztaş, O. Demirbaş, & M. E. Şahin, “Investigation of vertical axis wind turbines and the design of their components,” Turkish Journal of Electromechanics and Energy, 6(2), pp. 64-72, 2021.

K. J. Åström, T. Hägglund, K. J. Astrom, “Advanced PID control,” Research Triangle Park: ISA-The Instrumentation, Systems, and Automation Society, vol. 461, 2006.

URN: https://sloi.org/urn:sl:tjoee71205

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