Multi-objective genetic algorithm fractional-order PID controller for semi-active magnetorheologically damped seat suspension

Recently, fractional-order proportional–integral–derivative (FOPID) controllers are demonstrated as a general form of the classical proportional–integral–derivative (PID) using fractional calculus. In FOPID controller, the orders of the derivative and integral portions are not integers which offer more flexibility in succeeding control objectives. This paper proposes a multi-objective genetic algorithm (MOGA) to optimize the FOPID controller gains to enhance the ride comfort of heavy vehicles. The usage of magnetorheological (MR) damper in seat suspension system provides considerable benefits in this area. The proposed semi-active control algorithm consists of a system controller that determines the desired damping force using a FOPID controller tuned using a MOGA, and a continuous state damper controller that calculates the input voltage to the damper coil. A mathematical model of a six degrees–of–freedom seat suspension system incorporating human body model using an MR damper is derived and simulated using Matlab/Simulink software. The proposed semi–active MR seat suspension is compared to the classical PID, optimum PID tuned using genetic algorithm (GA) and passive seat suspension systems for predetermined chassis displacement. System performance criteria are examined in both time and frequency domains, in order to verify the success of the proposed FOPID algorithm. The simulation results prove that the proposed FOPID controller of MR seat suspension offers a superior performance of the ride comfort over the integer controllers.