## 3 Controller Design for the Semi-Active Seat Suspension  
To determine the desired force required to minimize the transmissibility of the vibration to the human body for a comfortable ride, a proper controller design is essential. Therefore, in this work, the self-tuning PID controller based on fuzzy logic has been implemented. The PID controller is one of the most popular and highly used control designs in the industry. The performance of the PID controller is based on the optimal values of gains. However, as the operating conditions change and the system parameters change, the PID controllers show unwanted overshoots, and this sometimes leads to a slow response when subjected to external disturbances [19]. To overcome such a drawback, the FLST-PID has been implemented in this work. The FLST-PID tunes the gain on the basis of fuzzy logic, which provides the advantage of the auto-tuning of the proportional, integral and derivative gains for the PID controller for a better performance when subjected to varying external disturbances [27]. This control takes the error and error derivative as the input and determines suitable values of the proportional gain (\(K_{p}\)), integral gain (\(K_{i}\)) and derivative gain (\(K_{d}\)) as the output [27; 28]. The values of \(K_{p}\), \(K_{i}\) and \(K_{d}\) were tuned by the fuzzy logic. The block diagram of the FLST-PID is shown in Figure 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Parameter** & **Value** \\ \hline \(\eta\) & Frequency & 190 (/s) \\ \hline \(c_{0a}\) & Viscous damping at high damper velocity & 784 (Ns/m) \\ \hline \(c_{0b}\) & Viscous damping at high damper velocity & 1803 (Ns/m) \\ \hline \(k_{0}\) & Stiffness at high damper velocity & 3610 (N/m) \\ \hline \(c_{1a}\) & Viscous damping at low damper velocity & 14,649 (Ns/m) \\ \hline \(c_{1b}\) & Viscous damping at low damper velocity & 34,622 (Ns/Vm) \\ \hline \(k_{1}\) & Accumulator stiffness & 840 (N/m) \\ \hline \(x_{0}\) & Effect of MR damper accumulator & 0 (m) \\ \hline \(a_{a}\) & Coefficient of stiffness & 12,441 (Nm) \\ \hline \(\alpha_{b}\) & Coefficient of stiffness & 38,430 (N/Vm) \\ \hline \(\gamma\) & Characteristics constant of Bouc-Wen model & 136,320 (m\({}^{-2}\)) \\ \hline \(\beta\) & Characteristics constant of Bouc-Wen model & 2,059,020 (m\({}^{-2}\)) \\ \hline \(\delta\) & Characteristics constant of Bouc-Wen model & 58 \\ \hline \(n\) & Characteristics constant of Bouc-Wen model & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the magneto-rheological damper. The state variables, sprung mass velocity and accelerations used in this work are measured by using velocity sensors or accelerometers. The sprung mass velocity and acceleration are measurable typically and, hence, considered as the input variables. Therefore, the sprung mass velocity \((z_{s})\) error, i.e., (\(z_{s}\)-0), is denoted as '\(V_{e}\)', and the error of derivative (\(\overset{\cdot}{z_{s}}\)-0) is denoted as '\(C_{e}\)', i.e., the sprung mass acceleration (\(\overset{\cdot}{z_{s}}\)), were chosen as inputs. For the fuzzy logic design, the linguistic variables of the input membership functions were taken as: Negative Large (NL), Negative Small (NS), Zero (ZE), Positive Small (PS) and Positive Large (PL). Similarly, the linguistic variables of the output membership functions were taken as: Positive Very Small (PVS), Positive Small (PS), Positive Medium Small (PMS), Positive Medium (PM), Positive Medium Large (PML), Positive Large (PL) and Positive Very Large (PVL). Membership functions were chosen on the basis of the literature [14; 18; 27; 28], the trial and error method and the experience of the authors and are shown in Figure 3.  
Figure 3: \(Cont.\)  
Figure 2: Block diagram of Fuzzy Logic based Self-Tuning Proportional-Integral-Differential Controller. The triangular membership functions were considered for the input as well as the output variables. The fuzzy rules for tuning and gain were based on the error and the derivative of the error.