# Performance Investigation of Active, Semi-Active and Passive Suspension Using Quarter Car Model
## 4 Results  
As outlined previously, the design goal for the semi-active and fully active suspensions was to minimise sprung mass acceleration, sprung mass displacement, and tyre deflection. In analysing the response plots, parameters such as peak amplitude, settling time, and general shape/behaviour of the trace were taken into consideration. As such, the minimisation goal was achieved by the reduction of peak amplitudes, settling time, and by having a response shape that stayed tight to the equilibrium position. In this regard, the rms value was used to quantify the average magnitude of the response where relevant. Figure 13 compares the sprung mass displacement of the suspension systems for each of the three road profiles. For road profiles 1, 2, and 3, it can be seen that the semi-active and fully active suspensions offered notable reductions of peak amplitudes and faster settling times over the passive suspension system in terms of sprung mass displacement, which would indicate an increased level of ride comfort. More specifically, for road profile 1, there was a 44% and 56% reduction of the passive rms displacement when using the semi-active and fully active suspensions, respectively. In road profile 2, the responses of the semi-active suspension and fully active suspension were near identical and eliminated the overshoot and oscillations seen in the passive suspension response. The variable damping coefficient response in Figure 10 and the actuator force response in Figure 11 show that the semi-active and fully active suspensions reached saturation limits at 2500 Ns/m and 500 N, respectively, in order to reduce the displacement. Ideally, a wider operating limit beyond \(-500\) N \(\leq E_{a}(t)\leq 500\) N for the force actuator could lead to  
Figure 12: Actuator force response of the fully active suspension system for all three (3) road profiles. \begin{table}
\begin{tabular}{c c} \hline
**Controller Gain** & **Tuned Value** \\ \hline \(K_{p}\) & 5 \\ \(K_{i}\) & 0 \\ \(K_{d}\) & 900 \\ \hline \end{tabular}
\end{table} 
Table 3: Tuned PID gain values used in the fully active suspension system. improved performance particularly in an extreme road disturbance; however, this value has to be limited due to safety considerations and also due to power restrictions of a fully active setup. For road profile 3, the semi-active suspension offered the best performance with a 32% reduction in rms displacement compared to the passive suspension, whilst the fully-active suspension offered a 26% reduction in rms displacement. In general, it was observed that, across all road profiles, the fully active suspension produced a less oscillatory response that returned quickly to equilibrium compared to the semi-active suspension. This may be explained by the fact that the fully active suspension introduces an active energy into the system in the form of a force, which stabilises the system response as opposed to the semi-active suspension, which simply adjusts the damping coefficient. This theory is further supported by the variable damping coefficient response and force actuator response seen in Figures 10 and 11, respectively. Figure 14 compares the sprung mass acceleration of the suspension systems for each of the three road profiles. For all road profiles, the semi-active and fully active suspensions displayed similar performances in terms of reduced peak amplitude and slightly faster settling time over the passive suspension system. Whilst similar, the semi-active suspension actually offered a slightly greater performance over the active setup. For example, in road profile 1, the semi-active suspension offered a 39% reduction in rms sprung mass acceleration over the passive setup compared to the 27% reduction of the fully active suspension. In road profiles 2 and 3, the semi-active suspension reduced the rms sprung mass acceleration of the passive setup by 65% and 32%, respectively, whilst the fully active suspension reduced the passive rms sprung mass acceleration by 40% and 26%, respectively.