Multi-objective optimization of PI controller for BLDC motor speed control and energy saving in Electric Vehicles: a constrained swarm-based approach

Proportional Integral Derivative (PID) controllers are widely employed in industrial applications due to their effectiveness, simplicity, and versatility. Within the automotive sector, one notable application of the Proportional Integral (PI) controller is in the realm of electric motors, particularly the Brushless Direct Current (BLDC) motors powering Electric Vehicles (EVs). The precision of speed control over BLDC motors, renowned for their efficiency and reliability, is paramount for optimizing vehicle performance and ensuring energy efficiency. PIDs must be tuned each time they are used in an application to optimize performance. A well-known empirical hit and trial tuning strategy is the Ziegler–Nichols method, which results in sub-optimal performance in the presence of locally optimal solutions of large-dimensional search spaces. Existing Artificial Intelligence methods tailored for PID controller tuning often focus on singular optimization aspects, neglecting potential performance gains achievable through multi-objective considerations. Furthermore, prevalent swarm-based PID optimization methods typically initialize the population randomly without imposing any bounds on input parameters, thus rendering them susceptible to inconsistent, unreliable, sub-optimal solutions in unconstrained search environments. In our research endeavors, we mathematically model the multi-objective optimization of BLDC motor speed control, energy usage, and efficiency using constrained Differential Evolution and Particle Swarm Optimized PID controllers. The Ziegler–Nichols tuning method is used to ascertain the initial PI parameters and define bounds within the input space. Our methodology addresses a critical gap by integrating real-time road gradient data into the EV control system, enhancing precision and minimizing energy consumption, especially during challenging road conditions. The proposed approach significantly improves motor speed control and energy efficiency in EVs. With our proposed swam-based optimization over 30 iterations, MSE decreased by approximately 95.4% (from 3.8834 to 0.1809), while energy consumption reduced by about 3.1% (from 1.015 kWh to 0.984 kWh). These results highlight the effectiveness of our method in enhancing both speed control precision and energy efficiency. In addition, code related data is available at Github.