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 (T_R), settling time (T_S), and percentage overshoot (M_P). 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.