## 1 Introduction
employed genetic algorithm to isolate vibration of viscoelastic damped structures and verify the applicability of genetic algorithm to vibration isolation of a simple beam structure [21]. The aforementioned works demonstrate that the intelligent control algorithms can improve effect of vibration control. However, the problems of the intelligent control algorithms are twofold. On the one hand, those intelligent control algorithms are sometimes too complex and the computational time of the above algorithms is sometimes very long, which result in limiting their engineering application. On the other hand, control results of the intelligent control algorithms may be different under identical initial parameters. Aimed at such dilemmas, the PID controller which is a direct output feedback method has been widely applied to control vibration. The parameter tuning of the PID controller is the key step in the process of designing the controller. The selection of \(K_{p}\), \(K_{i}\) and \(K_{d}\) parameters will directly affect the performance of the PID controller. The parameter tuning methods of the PID controller can be divided into experimental method and intelligent tuning method. [PERSON] et al. chose the appropriate parameters of the PID controller for the isolation platform to reduce the disturbances [22]. The parameter tuning based on the experimental method needs to do many experiments, which is not beneficial for practical engineering application. The intelligent tuning method, an effective PID parameter tuning method, usually used in the PID controller of active isolation systems. [PERSON] et al. exploited genetic algorithm to obtain parameters of the PID controller for magnetic suspension system [PERSON] et al. (2019). [PERSON] et al. employed an iterative learning algorithm to select parameters for the PID controller of flexible beam structure [PERSON] et al. (2019). [PERSON] et al. utilized ant colony optimization to tune parameters of the PID controller to find optimal required force for wind turbine tower [PERSON] et al. (2019). Although the above intelligent tuning methods make the PID controller have good control performance, the intelligent algorithms are usually complex and time-consuming, which again limits their application. All of the above PID controllers can effectively control vibration based on experimental methods and intelligent tuning methods. However, these aforementioned methods need to conduct many experiments or employ complex algorithms with computation burden and time. For these reasons, the present study investigates an active control method based on equivalent stiffness and damping coefficient, which can be used for practical engineering application. In this paper, a new active control method with equivalent stiffness and damping coefficient is proposed for the electromagnetic isolation system. In this method, the range of equivalent stiffness coefficient and damping coefficient of the electromagnetic force are calculated based on the required range of dynamic performance indexes. The equivalent stiffness and damping coefficient are similar to the \(K_{p}\) and \(K_{d}\) parameters of a PID controller, which can avoid the parameter tuning problem in the PID controller. According to the established nonlinear relationship between electromagnetic force and coil current and gap in the our own previous paper [PERSON] et al. (2019), the equivalent stiffness coefficient and damping coefficient can be satisfied by the controlled current in different gaps for achieving the better vibration isolation performance. Moreover, the control diagram is presented. Finally, simulations and experiments are implemented for verifying the effectiveness of the proposed active control method.