Tire-Road Separation Time Reduction by an Adaptive Proportional-Integral-Derivative Controller Utilizing Particle Swarm Optimization Algorithm

The article examines quarter-car dynamics with the possible separation of its tire from the road. A set of nondimensionalized differential equations has been proposed to minimize the involved parameters. Time and frequency response investigation of the system has been analyzed insightfully considering tire-road separation. To measure the separation of the tire, a time fraction index is defined, indicating the fraction of separation time in a cycle at steady-state conditions. Minimizing the index is assumed as the objective of the optimized system. An actuator is applied to the vehicle suspension in parallel with the mainspring and damper of the suspension. Particle Swarm Optimization (PSO) is used to properly tune a Proportional-Integral-Derivative (PID) controller for the active suspension system excited by a harmonic excitation. To verify the effectiveness of the control proposed, the controlled result compared with a passive suspension system illustrates the design, achieving a more comfortable ride with a significant decrease of the separation time.