Multi-objective metaheuristic optimization of PI controller gains for BLDC motor control in electric vehicle applications

Hani Albalawi; Hani Albalawi

doi:10.3934/math.2026990

AIMS Mathematics

2026, Volume 11, Issue 8: 24552-24581. doi: 10.3934/math.2026990

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Multi-objective metaheuristic optimization of PI controller gains for BLDC motor control in electric vehicle applications

Hani Albalawi ^{1,2
,
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1.
Zero Emission Technologies Innovation Center, University of Tabuk, Tabuk, 47913, Saudi Arabia
2.
Department of Electrical Engineering, Faculty of Engineering, University of Tabuk, Tabuk, 47913, Saudi Arabia

Received: 02 May 2026 Revised: 14 July 2026 Accepted: 30 July 2026 Published: 11 August 2026
MSC : 90C59, 90C30, 34A08, 68T20

Brushless DC (BLDC) motors are widely employed in electric vehicle (EV) propulsion systems because of their high efficiency, compact structure, and favorable dynamic performance. However, achieving accurate and energy-efficient speed regulation remains challenging when the drive operates under time-varying load torque caused by road gradient and operating-resistance variation. In this paper, I present a multi-objective optimization framework for tuning the proportional-integral (PI) controller gains of a BLDC motor drive for EV applications, with the dual objective of improving speed-tracking performance and reducing energy consumption. To balance computational efficiency and practical relevance, a two-stage evaluation strategy was adopted in which Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) were first used to optimize the controller gains over a short 0.4 s simulation horizon, after which the resulting gains were validated over a 120 s drive cycle under inclination-equivalent loading conditions. During the optimization stage, the Ziegler- Nichols (ZN) controller produced a Root Mean Square Error (RMSE) of 0.29420 and an energy consumption of 61.5263 J, whereas PSO reduced these values to 0.12971 and 60.727 J, and GA achieved 0.13052 and 60.729 J, respectively. These results corresponded to RMSE improvements of 55.912% and 55.636%, together with energy reductions of 1.2991% and 1.2958% for PSO and GA, respectively, relative to the ZN baseline. Over 10 independent runs, PSO and GA yielded mean fitness values of 0.65933 and 0.66100, with corresponding standard deviations of 0.00092 and 0.00118, respectively. Under the 120 s full-cycle validation, all three controllers exhibited near-ideal performance in the no-load case, whereas under the varying-load case, the optimization-based controllers outperformed the baseline controller, with PSO achieving the lowest overall loaded-case fitness value. The results demonstrated that metaheuristic multi-objective tuning provides an effective and practical framework for improving BLDC motor control in EV drive systems, yielding major gains in tracking performance together with modest but consistent energy savings.
- BLDC motor,
- electric vehicle,
- PI control,
- Particle Swarm Optimization,
- Genetic Algorithm,
- multi-objective optimization,
- energy efficiency
Citation: Hani Albalawi. Multi-objective metaheuristic optimization of PI controller gains for BLDC motor control in electric vehicle applications[J]. AIMS Mathematics, 2026, 11(8): 24552-24581. doi: 10.3934/math.2026990

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Abstract

Brushless DC (BLDC) motors are widely employed in electric vehicle (EV) propulsion systems because of their high efficiency, compact structure, and favorable dynamic performance. However, achieving accurate and energy-efficient speed regulation remains challenging when the drive operates under time-varying load torque caused by road gradient and operating-resistance variation. In this paper, I present a multi-objective optimization framework for tuning the proportional-integral (PI) controller gains of a BLDC motor drive for EV applications, with the dual objective of improving speed-tracking performance and reducing energy consumption. To balance computational efficiency and practical relevance, a two-stage evaluation strategy was adopted in which Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) were first used to optimize the controller gains over a short 0.4 s simulation horizon, after which the resulting gains were validated over a 120 s drive cycle under inclination-equivalent loading conditions. During the optimization stage, the Ziegler- Nichols (ZN) controller produced a Root Mean Square Error (RMSE) of 0.29420 and an energy consumption of 61.5263 J, whereas PSO reduced these values to 0.12971 and 60.727 J, and GA achieved 0.13052 and 60.729 J, respectively. These results corresponded to RMSE improvements of 55.912% and 55.636%, together with energy reductions of 1.2991% and 1.2958% for PSO and GA, respectively, relative to the ZN baseline. Over 10 independent runs, PSO and GA yielded mean fitness values of 0.65933 and 0.66100, with corresponding standard deviations of 0.00092 and 0.00118, respectively. Under the 120 s full-cycle validation, all three controllers exhibited near-ideal performance in the no-load case, whereas under the varying-load case, the optimization-based controllers outperformed the baseline controller, with PSO achieving the lowest overall loaded-case fitness value. The results demonstrated that metaheuristic multi-objective tuning provides an effective and practical framework for improving BLDC motor control in EV drive systems, yielding major gains in tracking performance together with modest but consistent energy savings.

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