## 4 Numerical Simulation
Figure 5: Bump road profile and head acceleration at different speeds: (**a**) bump road profile at a speed of 10 Km/h; (**b**) head acceleration comparison for 10 km/h bump input; (**c**) bump road profile at a speed of 30 Km/h; (**d**) head acceleration comparison for 30 km/h bump input; (**e**) bump road profile at a speed of 50 Km/h; (**f**) head acceleration comparison for 50 km/h bump input. Table 6 shows the comparison of the performance of passive and semi-active seat suspension for the bump road for the peak-to-peak values of the human body parts, in other words, the head, upper torso, lower torso and things. Table 6 also shows the percentage improvement in the peak-to-peak accelerations owing to a semi-active seat suspension, as compared to the passive system. Overall, it was found that a semi-active seat suspension reduces the acceleration values and, thus, improves the ride comfort. The force generated by the MR damper is shown in Figure 7. It can be noted that the maximum force generated by the MR damper is 500 N, which is under the constraint of the limited seat suspension stroke. This constraint is quite practical to consider in the design, otherwise the suspension might collide with the end's stop [32]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Bump Profile** \\ **Speed** \\ \end{tabular} } & \multirow{2}{*}{**Body Part**} & \multicolumn{2}{c}{**Peak-to-Peak Acceleration (m/s\({}^{2}\))**} & \multirow{2}{*}{**Improvement (\%)**} \\ \cline{3-3} \cline{5-5}  & & **Passive** & & **Semi-Active** \\ \hline \multirow{4}{*}{10 Km/h} & Head & 9.631 & 8.873 & 7.87 \\  & Upper Torso & 9.641 & 8.877 & 7.92 \\  & Lower Torso & 9.969 & 8.926 & 10.46 \\  & Thigh & 10.234 & 9.324 & 8.89 \\ \hline \multirow{4}{*}{30 Km/h} & Head & 15.74 & 14.53 & 7.68 \\  & Upper Torso & 15.66 & 14.47 & 7.59 \\  & Lower Torso & 14.93 & 13.76 & 7.83 \\  & Thigh & 14.86 & 13.30 & 10.49 \\ \hline \multirow{4}{*}{50 Km/h} & Head & 12.83 & 11.88 & 7.40 \\  & Upper Torso & 12.71 & 11.64 & 8.41 \\ \cline{1-1}  & Lower Torso & 12.04 & 11.00 & 8.56 \\ \cline{1-1}  & Thigh & 12.22 & 10.96 & 10.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Peak-to-peak value of acceleration of body parts. Figure 6: Human head acceleration for the bump profile with an amplitude of 0.07 m and speed of 3.04 km/h). From Figure 8 it can be observed that the stroke length for the MR damper is within the range of \(\pm 20\) mm which is acceptable for the seat suspension [19]. The calculated values of the PID gains with the time for the bump input are shown in Figure 9.  
Figure 8: Seat suspension stroke length. Figure 7: Force generated by MR damper. Figure 9: Variation of proportional–integral–derivative gains. The FLST-PID can easily be implemented to design the suspension module and can be integrated with the electronic control unit (ECU) of the car which is responsible for other electronic controls in the vehicles. The three phases of fuzzy logic, i.e., fuzzification, fuzzy inference engine and defuzzification, can be embedded into the circuit. The suspension model receives the feedback from the accelerometer or velocity sensors fitted at the sprung mass and the seat of the drivers. Thus, for FLST-PID, the inputs coming from such sensors can be directed to the fuzzification board. Then, in the fuzzy inference engine, the fuzzy logic rules that depend on the analogue signals' input voltages ranging from \(-\) 5 V to + 5 V can be implemented, generating an analogue voltage distribution on the signal lines. Such a voltage distribution is characterized by the membership functions of the individual inference result. The membership function of the final fuzzy inference result can be applied to the buffer amplifier array (input stage of defuzzifier), through a data bus of analogue signal lines (rules) and, then, the outputs fed to the two resistor arrays, one of which produces a weighted sum of the membership function, and the other, a normal sum of two output data (scalar values).