# Performance Investigation of Active, Semi-Active and Passive Suspension Using Quarter Car Model
## 1 Introduction
[5] investigated the performance of semi-active suspensions by performing a simulated comparison between a quarter car PID-controlled semi-active suspension and a standard passive suspension, modelled in MATLAB/Simulink. The trial-and-error method was used for tuning the PID controller, and response plots for sprung mass displacement and suspension working space were obtained for three different road profiles and were used as indicators of ride comfort and stability. Based on results obtained in [5], it was concluded that the addition of an active damping element can greatly enhance ride comfort and vehicle stability, especially over rough and uneven road surfaces. [PERSON] et al. [10] investigated the performance of different control strategies used in a semi-active suspension system (PID, fuzzy logic, and fuzzy-hybrid) in order to improve ride comfort and handling. The semi-active suspension was implemented with a controllable MR damper, and it was found that a semi-active suspension can effectively improve ride comfort and vehicle handling whereby the fuzzy and fuzzy-hybrid controllers' performances were noticeably better than that of the PID controller. [PERSON] and [PERSON] [11] compared the performance of semi-active and passive quarter car suspension systems by simulating the response of the systems to different vehicle velocities of a half sine wave bump and for different road profiles, using MATLAB/Simulink. It was found that changing the vehicle velocity for the half-sine wave bump input affected the peak amplitude and settling time of the response plots for both the semi-active and passive suspensions. Furthermore, for the other road profiles, improved performance was noted using the PID-controlled semi-active suspension as opposed to the passive suspension. However, the response plots used in the study were only based on the sprung mass displacement, and little detail was provided on the PID gain values used as well as the tuning process. Nevertheless, [PERSON] and [PERSON] [11] reached similar conclusions to the other researchers by stating that the use of a semi-active suspension can significantly improve ride comfort and road holding for different road profiles and vehicle velocities compared to a passive setup. In [12], MATLAB/Simulink was used to investigate active quarter car suspensions controlled with P, PI, PID, Genetic Algorithm (GA)-PID, and Auto-tuned PID controllers. The root curve seat method was used for the tuning of P, PI, and PID controllers. It was found that the PID controller produced a better performance than the P and PI variations, similar to the findings in [8]. Further investigation showed that increased performance was achieved with the Auto-tuned and GA-PID controller. However, in [12], only one road profile and response plot (suspension working space) was used in analysing the behaviour of the suspension systems. [PERSON] and [PERSON] [13] modelled and compared a passive suspension system to an active suspension system using a modified PID controller in MATLAB/Simulink. The modified PID controller had the proportional and derivative terms in the feedback path, while the integral term was left in the forward path. The controller was tuned using the trial and error method, and a range of response plots (sprung mass displacement, acceleration, velocity, suspension working space) was used to evaluate vehicle handling and ride comfort. Based on the results obtained in [13], the proposed modified PID controller offered significant improvements over both the conventional PID controller and the passive suspension system, which, in turn, reflected improvements in car stability and comfort of passengers. However, only a single road profile was used in simulation testing. [PERSON] et al. [14] proposed an (ARC)-based H-infinity controller for an active suspension in order to improve ride comfort and to reduce vibrations. A full car model was used, and the active suspension was modelled with electrohydraulic actuators to represent the non-linear characteristics.