# Performance Investigation of Active, Semi-Active and Passive Suspension Using Quarter Car Model
## 1 Introduction
It was seen that the proposed active suspension significantly improved passenger ride comfort over a traditional passive suspension. In [15], a PIDcontrolled active suspension for a quarter car model was designed in MATLAB/Simulink in order to improve suspension performance over a traditional passive system. The PID controller was tuned using the Ziegler and Nichols method, and response plots of sprung mass displacement and acceleration, suspension working space, and tyre deflection were analysed. It was concluded that the active suspension had better performance capabilities than the passive suspension in terms of ride comfort and road-holding ability [15]. The suspension systems were tested under two different road profiles (step input and random road input), but only the peak amplitudes of the response plots were compared. Moreover, other researchers, such as [PERSON] et al. [16], [PERSON] et al. [17], and [PERSON] et al. [18], have utilised controlled suspension systems, namely semi-active suspension systems, as an optimisation technique to improve the suspension performance of in-wheel motor electric vehicles, solving one of their main drawbacks. As seen, there is a wide range of research that quantifies the performance improvement when using controlled suspensions systems. However, in all the studies highlighted [5; 9; 10; 11; 12; 13; 14; 15], researchers chose to focus the optimisation and comparison effort on either semi-active or active suspensions but never both systems at the same time in a single testing environment. Furthermore, previous work on the topic of controlled suspensions lacked comprehensiveness in terms of using multiple road profile inputs, a detailed performance criteria, and a range of response plots for analyses. This is an important area of further research in order to quantify and observe the trends of both the semi-active and active suspensions, which can then influence the choice of a controlled suspension system suitable for particular applications. As such, the aim of this study is to investigate controlled suspension systems by modelling and tuning both a semi-active and fully active suspension, using a PID controller, in order to achieve optimised comfort and handling. The performances of the controlled suspension systems are then compared to a traditional passive setup. The current study uses a linear two-degree-of-freedom lumped element quarter car model, with vertical motion only. PID control was employed in both the semi-active and fully active suspension systems due to its wide industry usage as well as simplicity. Furthermore, simulated testing of the suspension systems was carried out in MATLAB/Simulink for three common road profiles/conditions a vehicle might undergo in a real-world scenario. Moreover, the sprung mass acceleration as well as sprung mass displacement \(w\) used as indicators of ride comfort based on [2; 4; 19], whilst tyre deflection was used as a measure of road-holding ability (vehicle handling) based on [4; 20]. Suspension working space was also analysed as it formed an important consideration when compromising between ride comfort and handling, based on [21].