Optimal Robust Design of a Complex Fractional-Order PID Controller for Automotive Cruise Control Applications

Abstract

Automobile Cruise Control (ACC) systems regulate vehicle speed at a predefined setpoint, thereby reducing driver workload, enhancing driving comfort, and improving fuel efficiency. This paper presents a control-oriented investigation of ACC speed regulation using integer-order (IO) and non-integer-order (NIO) controllers, including proportional integral derivative (PID), tilt integral derivative (TID), fractional-order PID (FOPID), fractional-order TID (FOTID), and complex fractional-order PID (COPID) controllers. The analysis, design, and tuning of the seven-parameter COPID controller constitute the primary contribution of this work. A time-domain-based parameter estimation framework is developed to ensure satisfactory control performance. Controller parameters are optimized using four population-based metaheuristic algorithms: Artificial Rabbits Optimization (ARO), Arithmetic Optimization Algorithm (AOA), Supply-Demand Optimization (SDO), and Biogeography-Based Optimization (BBO). Error-based and performance-based objective functions are incorporated for comprehensive tuning of IO and NIO controllers. The effectiveness, robustness, and consistency of the optimization techniques are systematically evaluated through statistical analysis. Simulation results demonstrate that the BBO-optimized, ZLG-tuned COPID controller consistently outperforms the other controllers, achieving reduced rise time (TR), settling time (TS), and percentage overshoot (MP). Robustness analysis under parameter variations and external disturbances further confirms superior disturbance rejection and stable performance, establishing COPID as a reliable and efficient control strategy for ACC systems.