## 3 Design of ACM Controller
### Fuzzy Control  
The goal of an ACM system is to minimize or zero the force transmitted through the ACM to chassis. The fuzzy control design is simple, easy to apply, and robust [31]. The input of the fuzzy controller is the error \(e(t)\) between the desired minimum transmitted force and the actual transmitted force and the change rate of the difference \(\mathrm{d}e(t)\). The output \(u(t)\) of the fuzzy controller is the current acting on the actuator, which is then converted into active control force, and its composition is shown in Figure 7.  
\(E\), \(DE\) and \(U\) are used to denote the fuzzy sets of variables \(e(t)\), \(\mathrm{d}e(t)\) and \(u(t)\), respectively. The domain of the input fuzzy sets \(E\) and \(DE\) are all normalized to \(\{-6,-4,-2,0,\) 2, 4, 6\(\}\), and the corresponding fuzzy subset is {negative big, negative middle, negative small, zero, positive small, positive middle, positive big} denoted as {NB, NM, NS, ZR, PS, PM, PB}, {DNB, DNM, DNS, DZR, DPS, DPM, DPB}, respectively. In order to reduce the structural complexity of the fuzzy controller and increase the calculation speed, the fuzzy subsets on the left and right sides use Z-type and S-type membership functions respectively, and the rest of the fuzzy subsets use triangular membership functions. The distribution method of membership functions is adopted evenly distributed. The membership functions are shown in Figure 8a,b. The domain of the output fuzzy set \(U\) is normalized to \(\{-6,-4,\)\(-2,0,\)\(2,4,\)\(6\}\), and the corresponding fuzzy subset is the same as \(E\), membership function is shown in Figure 8c. The fuzzy control rules for the ACM control system are obtained from experience. The essence is to formulate the output of the fuzzy controller according to the different conditions of \(E\) and \(DE\). When \(E\) and \(DE\) have the same signs, it means that the system output is far away from the reference signal. The main task of formulating the control variable \(U\) should be to eliminate the error as soon as possible; when \(E\) and \(DE\) have opposite signs, it means that the system output is close to the reference signal. As the distance between the system output and the reference signal changes from large to small,  
Figure 6: PID feedback control block diagram. Figure 7: Fuzzy control block diagram. the control variable \(U\) is formulated to change from quickly eliminating errors to preventing overshoot. The fuzzy control rules as shown in Table 2.  
The function of the quantization factor (\(k_{\text{e}}\), \(k_{\text{de}}\)) and the scale factor (\(k_{\text{u}}\)) is equivalent to the external interface of the fuzzy controller. The function of the quantization factor is to map any input quantity to a fixed and finite interval, that is, the fuzzy domain. The function of the scale factor is to convert the value on the fuzzy domain into a value that can directly act on the controlled system. Use the trial-and-error method to determine the value of quantization factor and scale factor. The [PERSON]'s maximum-minimum reasoning method is applied. The area centre method, which is commonly used in engineering, is used to decompose the fuzzy problem. The input-output relationship of fuzzy controller is shown in Figure 9. It is a smooth surface, which shows that the fuzzy control system has good robustness and stability. The fuzzy control simulation is carried out by using the fuzzy toolbox of MATLAB. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(DE\)\(E\) & **NB** & **NM** & **NS** & **ZR** & **PS** & **PM** & **PB** \\ \hline DNB & PB & PB & PB & PM & PS & PS & ZR \\ DNM & PB & PB & PM & PS & PS & ZR & NS \\ DNS & PB & PM & PS & PS & ZR & NS & NS \\ DZR & PM & PS & PS & ZR & NS & NM \\ DPS & PS & PS & ZR & NS & NS & NM & NB \\ DPM & PS & ZR & NS & NS & NM & NB & NB \\ DPB & ZR & NS & NS & NM & NB & NB & NB \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fuzzy control rules.