The suspension system is classified into three types passive suspension, semi-active, and active suspension. The term a quarter car model originated in the early part of the 20th century. It is considered the best way for studying the effectiveness of vehicle stability. This paper presents the modelling and control of a nonlinear active suspension system for a quarter car, the mathematical model represents a spring-mass (Quarter of the chassis) and unsprung mass (the wheel), with two degrees of freedom (2-DOF) system characterized by a pair of the differential equations. The objective of this work is to determine control strategy to deliver better performance with respect sprung displacement; sprung mass velocity; suspension deflection; peak overshoot; setting time. The active control of the suspension system is achieved using fractional-order PID (FOPID) tuned by particle swarm optimization algorithms (PSO algorithms) because the ordinary FOPID did not give good results, and linear quadratic regulator (LQR) control actions. The results are developed and simulated in MATLAB/Simulink. It is observed that the LQR controller gives better ride comfort by reducing the RMS error and the vibration of various types of road conditions as compared to an intelligent FOPID controller.

In this chapter, the authors used a comparative study between passive and active suspension of quarter car models with deference intelligent controllers. This study aims to obtain an active suspension that adapts to all types of roads, especially rough and slippery ones, and absorbs shocks resulting from road vibrations, which gives more comfort to passengers and the driver. The results have proven that FOPID gave better results than PID in all types of road testing. The concerns related to the proposed chapter are that the car makers have a fear of the Fractional-Order controller FOPID to the difficulty of achieving it in the industrial field because of the difficulty of its mathematical equations and its high cost.

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