# Performance Investigation of Active, Semi-Active and Passive Suspension Using Quarter Car Model
## 1 Introduction  
An ideal vehicle suspension system should facilitate two main functions, namely ride quality and vehicle handling. Ride quality refers to the comfort perceived by passengers, which is achieved by the isolation of the vehicle body from external disturbances such as road irregularities. Vehicle handling can be represented by road holding, i.e., the ability of the suspension to control the motion of unsprung masses to maintain firm contact with the road [1]. The passive suspension is the traditional arrangement used in most production vehicles--it consists of a spring and damper of fixed spring constant and damping coefficient, respectively [2]. The popularity of the passive suspension lies in its simplistic design, reliability, and no external power requirements. However, the use of a constant damping coefficient limits the optimisation of a passive suspension to achieve simultaneous improvement in comfort and handling [3]. As comfort (body isolation) is improved via adjustment of the damping coefficient, axle response and road-to-wheel contact (vehicle handling) can become worse [4]. Therefore, a trade-off in comfort or handling has to be made when choosing a single damping coefficient value for the passive suspension system. Therefore, the design and tuning of a passive suspension involves finding the best single compromise between the conflicting goals of comfort and handling [2]. As such, the optimal solution is a suspension system that can adjust its parameters to suit the variations in operating conditions, i.e., an adjustable suspension is required to facilitate the various road disturbances encountered, whereby an ideal unique response is required for each different disturbance. The solution is realised in terms of the semi-active and fully active suspension systems [5]. A semi-active suspension is similar to the passive design since there is a fixed spring constant; however, an electronically controlled variable damper is used to adjust the damping coefficient in a closed-loop feedback configuration [2]. Using an appropriate control strategy, the semi-active suspension can reduce the compromise found in the passive suspension, resulting in optimised comfort and handling regardless of the road surface [6]. Active suspension systems provide an additional force (energy) input to the traditional passive system by means of an actuator which is usually installed in parallel with the spring and damper. The supply of force is regulated by a suitable control strategy that uses information from vehicle sensors [7]. Generally, the fully active suspension design can give the best performance over a wide range of road conditions out of all three suspension types, but it is also the most complex, is costly, and has a high energy demand [5]. It follows that semi-active suspensions have been commercially favoured by automotive OEMs since the 1990s due to their ability to offer the best compromise of performance (comfort and handling) and cost (in terms of power consumption, weight, and power requirements) as compared to the active suspension. The MagneRide suspension is one such semi-active setup that has been used commercially by OEMs such as Cadillac and Land Rover since the 2000s [8]. The research on controlled suspension systems is both vast and extensive, with numerous studies using experimental or simulation methods to investigate and improve the performance and control of both semi-active and full active suspension systems. Using MATLAB/Simulink, [PERSON] and [PERSON] [9] modelled and observed the performance of semi-active and passive suspension systems controlled using P, PD, PI, and PID controllers, all of which were tuned using the trial and error method. The sprung mass displacement response was analysed for each road profile and used as an indicator of comfort and handling. The PID-controlled semi-active suspension offered the best comfort and handling performance when tested for three different road profiles. [PERSON] et al.