## 4 System Simulation and Comparison  
MATLAB/Simulink is used to simulate the vibration characteristics of engine mount and the AVC performance of ACM controller. The simulation models of the nine active control algorithms above are established. In this study, the range of engine speed \(n\) is 1000-6000 rpm. It is assumed that three mounts are used and the force\(f_{1}\), i.e., the input of the model, is calculated by Equation (36):  
\[f_{1}=\frac{1}{3}F_{\mathrm{e}}=\frac{1}{3}\frac{4m_{\mathrm{i}}R^{2}\omega^{2} }{L}\cos(2\omega t) \tag{36}\]  
where \(F_{\mathrm{e}}\) is vertical vibration force of the four-cylinder four-stroke in-line engine and \(\omega\) is angular velocity of the crankshaft and calculated by \(\omega=2\pi n/60\). Other relevant parameters in the formula are shown in Table 1.  
As shown in Figure 12, the simulation results of time domain response of the force transmitted to the chassis side are obtained. Considering the engine speed at 3000 rpm, and the vibration in the vertical direction, with and without active control. Figure 12a,b,d-f,h are simulations under the control of LMS, RLS, LQR, H\({}_{2}\), H\({}_{\infty}\), and Fuzzy, respectively. The results show that the effectiveness of above control algorithms. Figure 12c,g,i are simulations under the control of FxLMS, PID, and Fuzzy PID algorithms, respectively. After controlling the current to drive the actuator to work, the force transmitted to the chassis side is greatly reduced compared to when there is no control. In order to compare the active vibration isolation performance of nine control algorithms more intuitively, the force transmissibility is used to represent the vibration isolation performance of nine control algorithms and compared with the case of no control, as shown in Table 4.  
It can be seen from Table 4 that the force transmissibility of ACM with nine control algorithms is much smaller than that without control. Figure 13a,b show the change of the force transmitted to the chassis and the controlled current at different engine speeds under nine active control algorithms, respectively. It could be seen that in the range of 1000-6000 rpm the force transmitted to the vehicle body  
after the control of eight algorithms except LMS is less than that before control. The control effect of LMS adaptive algorithm is effective at speeds below 5000 rpm and poor above 5000 rpm, and it is not even as good as passive engine mount. The reason lies in that LMS adaptive algorithm is extremely sensitive to phase errors, and excessive phase errors cause the algorithm to be unstable, which greatly reduces the control effect. On the other hand, the results show that different algorithms have different control effects at different speeds. The LQR algorithm takes into account the system performance and control energy at the same time, so that the comprehensive index is optimized. Therefore, it may not be very prominent from the perspective of the vibration isolation effect. This characteristic is also reflected in the simulation results. However, compared with other algorithms, FxLMS, PID and Fuzzy PID control algorithms can reduce the force transmitted to the vehicle chassis more effectively in the range of 1000-6000 rpm, the force transmission is an order of magnitude lower than other control algorithms, and the control current at different speeds is also within a reasonable range. Meanwhile the PID controller is easily affected by the external environment in practical applications. Therefore, the advantages of PID applied to the ACM system that stimulates rapid changes are not prominent. The rules of the fuzzy PID controller need to be determined based on experience, the calculation is complicated and time-consuming. In addition, the scale factor and the quantization factor are determined by trial and error, which has a strong uncertainty, and needs to be debugged in practical applications. By contrast, the FxLMS adaptive control has the advantage of small amount of calculation, strong robustness and easy implementation by hardware.