## 1 Introduction
Considering the phenomenon of magnetic saturation and its dependence on the rotor position and the current, a PI controller with variable gains was proposed by [PERSON] et al. in 2011. This controller compensated the inductance variation and maintained the dynamics of the closed-loop system constant. Simulations and experimental results showed the advantages of gain adaptation compared to fixed gains [11]. In 2012, [PERSON] et al. applied a method for continuous gain scheduling proportional integral (GSPI) control to perform on-line control of a large sudden unbalanced vibration response of a rotor with an active elastic support/dry friction damper, with the parameters of the rotor being unknown or inaccurate [12]. In 2013, a gain phase modifier (GPM) was proposed by [PERSON] et al. to achieve a precise synchronous control current and to compensate the gain and phase errors caused by the power amplifier. The GPM was incorporated into the feed-forward controller to formulate two closed loops, which could adaptively tune the gain and phase of the synchronous control current, respectively [13]. In 2017, based on the single neuron proportion integration differentiation (PID) control method, fuzzy control theory was introduced by [PERSON] et al. to adjust the output gain K of single neuron PID control to realize single neuron PID control with variable step size. Experiments and simulation results showed that the fuzzy self-tuning single neuron PID control method had the advantages of faster response time, less overshoot amount, fewer oscillation times, extreme robustness, and good stability [14]. Based on the dynamic model of a rotor system with time-delay, a strictly positive real system was built to satisfy the stability conditions of the adaptive control system. A feed-forward gain adaptive controller was designed to improve the balance control of a rotor system under both variable speed and constant speed [15]. Based on the above analysis, the following points can be summarized. 1. The influence coefficient method is the common method to calculate the correcting vectors of the correcting faces in online dynamic balance control. In practical application, affected by the precision of signal measurement and analysis, the actual vectors of the influence coefficients are very difficult to measure and calculate. So the dynamic balance accuracy is low and difficult to improve based on the traditional influence coefficient method. 2. On the other hand, with the transformation of speed, service time, environment condition, temperature field, abrasion, and lubrication condition of supporting components etc., the kinetic parameters of the rotor system may be changed, but the original influence coefficients cannot meet the requirement of high accuracy dynamic balance control. 3. The gain scheduling control is perfect for the rotor system in which the kinetic parameters transform with the working conditions. Comparing with the influence coefficient method, the actual vectors of the influence coefficients of the dynamic balance system are not necessary to know based on the gain scheduling method, and ideal balancing accuracy can be gained based on the estimated value of influence coefficients and gain parameters. 4. The traditional gain scheduling control method is based on the fact that the influence coefficient has been estimated and the gain calculated under the offline state. Also, it belongs to open loop control and there is no feedback and compensation mechanism for the inaccurate gain, which could interfere with the online dynamic balance precision. Based on the above analysis, the gain scheduling control method and the adaptive method of influence coefficient are combined in the paper, and an adaptive method of gain parameters is proposed based on the online estimation and update of influence coefficients.