## 5 Conclusions  
Comparative research work of control algorithms for ACM is divided into three steps. Firstly, mechanical and mathematical models of ACM are established. Then, basing on the working principle of each control algorithm, the ACM controller is designed in the MATLAB/Simulink simulation environment. Finally, the simulation model of nine control algorithms for ACM are established to implement vibration isolation performance simulations for ACM. For rotating machinery such as engines, FrLMS algorithm has been applied to the ACM system and the control effect has been obtained. This paper intends to study the feasibility and control effect of other algorithms in the ACM system. After experimental verification, it is possible to select several control algorithms that consume less computing resources to improve the economics of the product. The three control algorithms of LMS, RLS, and FrLMS all belong to feedforward control, and the relevant information of the disturbance source needs to be measured. The RLS algorithm has a large amount of calculation, while the FrLMS has a small amount of calculation, strong robustness and good control effect, which is suitable for the ACM system. The LQR, H\({}_{2}\), and H\({}_{\infty}\) algorithms all have restrictions on the state space form, otherwise the controller cannot be solved, so some pre-processing of the state space model of the ACM system is required. PID algorithm can be applied to most systems, and its most important part is the adjustment of three parameters. The widely used empirical formula method, the Ziegler--Nichols method, as well as the critical oscillation method and damped oscillation method, are not suitable for this ACM system; therefore, three parameters are obtained by using frequency domain performance settings. Subsequent tests may be affected by the external environment, so fine-tuning will be made on this basis. Fuzzy control algorithms belong to the advanced control field, but the design of fuzzy rules requires prior knowledge and expert experience, and its structure is also relatively complex. Therefore, in actual application, it will be considered to be converted into an offline look-up table to reduce the calculation amount and running time of the controller. The simulation results of different engine speeds from 1000 rpm to 6000 rpm show that except the LMS algorithm, the other eight algorithms have good control effect in the whole speed range, and the control current is in a reasonable range. FrLMS adaptive control algorithm, PID control algorithm and fuzzy PID control algorithm have the best vibration isolation performance among nine control algorithms. Furthermore, considering cost, implementation difficulty and stability, FrLMS adaptive control algorithm is more  
Figure 13: The force transmitted to the chassis and the control current at different engine speeds under nine control algorithms: (**a**) The force transmitted to the chassis; (**b**) The control current. suitable for active control mount field than the fuzzy PID and PID control algorithms. Therefore, the FxLMS adaptive control algorithm can be selected and applied to ACM. The active mounting system development process includes offline simulation, semi-physical simulation and full-physical simulation. In this paper, the offline simulations of nine control algorithms for the ACM system are studied. The latter simulation will be completed: semi-physical simulation (rapid control prototype, referred to as RCP), the control system is composed of a dSPACE simulation platform and a computer to complete the smooth transition from prototype controller to production controller; in full-physical simulation, the control system consists of a development board and computer composition, confirm the consistency of the functions completed by the controller and RCP.