## 4 Switching Adaptive Notch Filter Vibration Control Strategy Based on Fuzzy Control
### Fuzzy Control Based on Adaptive ANF  
Compared to traditional notch filters, the adaptive bipolar notch filter offers the following two advantages:  
1. It is possible to simultaneously take into account the rotor unbalanced vibration control of AMB rigid rotor systems in the presence of rigid body translational modes and rigid body conical modes;
2. By avoiding the design of an interference observer and controlling the polarity switching, transient vibrations produced during the switching instant can be effectively reduced. The fuzzy control of adaptive ANF for AMB high-speed motors with rigid rotor systems includes the following steps: Firstly, the input variables of the fuzzy controller are determined to be the error \(E\) between the rotor vibration signal \(x_{A}\) collected by the eddy current displacement sensor and the reference position \(r_{xA}\), as well as its rate of change \(R\), while the output variable is the power amplifier control signal \(U\). Secondly, the variation range of rotor vibration displacement is \(\pm 0.3\) mm, and the corresponding variation range of eddy current displacement sensor output voltage is \(6\) V; thus, the basic domain of \(x_{A}\) is chosen to be \([-0.003,\,0.003]\), and at this time, the corresponding quantization factor is \(k_{1}=2000\). The fundamental domain of the rotor vibration rate of change is \([-0.003,\,0.003]\), and its corresponding quantization factor is \(k_{2}=2000\). The output variable is the amplifier current, and its fuzzy variable thesis domain is selected as \([-6,\,6]\); then, the fuzzy control rules are formulated. When the rotor vibration \(x_{A}\) is much smaller than the reference position \(r_{xA}\), the corresponding error signal \(E\) is PB, and the control variable corresponds to the maximum value in order to ensure that the rotor position is rapidly approaching the reference position. When the rotor vibration \(x_{A}\) is much larger than the reference position \(r_{xA}\), the control variable corresponds to the minimum value. As the rotor vibration decreases, the vibration error signal \(E\) is PS. To ensure that the rotor can run stably, the output should not be too large; thus, the output variable is PS. Finally, taking the fuzzy rules of \(\Delta K_{p}\) as an example, a Mamdani inference-based fuzzy controller is employed. For instance, if the fuzzy quantities of rotor vibration error E and its rate of change R are 3 and \(-3\), respectively, it can be inferred from Figure 4c that \(E\) and \(EC\) belong to (PS and PM) and (NM and NS), respectively. Therefore, based on the Appendix A, the fuzzy rules for \(\Delta K_{p}\) are as follows:  
Rule 1: if E is PS and R are NM, then U1 is PS. Rule 2: if E is PS and R are NS, then U2 is ZO. Rule 3: if E is PM and R are NM, then U3 is ZO. Rule 4: if E is PM and R are NS, then U4 is ZS. Using [PERSON]'s criterion, the fuzzy value \(U_{1}\) of U is calculated as follows:  
\[U_{1}=\rho_{1}(U)\vee\rho_{2}(U)\vee\rho_{3}(U)\vee\rho_{4}(U), \tag{9}\]  
where \(\rho_{i}(U),\ i=1,2,3,4\) denotes the fuzzy value of U in rule i. \(\rho_{i}(U),\ i=1,2,3,4\) is expressed as follows:  
\[\rho_{i}(U)=(\rho_{i}(E)\wedge\rho_{i}(R))\wedge\rho_{i}(U_{0}), \tag{10}\]  
where \"\(\wedge\)\" and \"\(\vee\)\" are the minimum and maximum values, respectively. Rule 1 is used to interpret Equation (8). When input \(E=3\), the affiliation degree of its fuzzy linguistic variable PS is 0.5 according to the affiliation function of \(E\), and \(\rho_{1}(E)\) is defined as follows:  
\[\rho_{1}(E)=0.5, \tag{11}\]  
By combining Equations (9)-(11), the fuzzy value of the fuzzy output \(U\) under the conditions of rule 1 is as follows:  
\[\rho_{1}(U)=(0.5\wedge 0.5)\vee\rho(U_{0}=\text{NM}), \tag{12}\]  
According to the center of gravity method, the exact amount of amplifier current control is obtained by defuzzifying the solution of (12). After obtaining the current control amount, the vibration control effect of the ANF is adjusted.