## 3 Design of Suspension Controller
### Integrated Fuzzy Control Design of LADRC Controller  
In practical application, the parameter tuning in LSEF is similar to the parameter tuning in PID controller, which requires manual adjustment of parameters for different control states, which shows poor adaptability [27]. Conversely, fuzzy control uses control rules and reasoning to adaptively adjust the gain parameters \(k_{\rm p},k_{\rm d}\) in LSEF according to the error \(e\) and error change \(de\) between the given air gap and the actual air gap, so that the active disturbance rejection parameters can meet the needs of \(e\) and \(de\), and improve the control performance of the active disturbance rejection controller [28; 29; 30]. First of all, according to the debugging experience of PID and ADRC, set the input variables \(e\) and \(de\) of the fuzzy controller--whose universe is [\(-\)0.2, 1.4] and [\(-\)8, 8], respectively--and the corresponding language variables are \(E\) and \(EC\). According to the parameters of the control law in the LADRC experiment, the output variables \(\Delta k_{\rm p}\) and of the fuzzy controller are set with the universe of \([-200,\,200]\) and \([-10,\,10]\), respectively, and the corresponding language variables are \(\Delta k_{\rm p}\) and \(\Delta k_{\rm d}\), respectively. Secondly, in order to improve the control accuracy, seven subsets of fuzzy language are defined within the universe of the input and output variables of each fuzzy controller, which are {negative large (NB), negative middle (NM), negative small (NS), zero (ZO), positive small (PS), positive middle (PM), positive large (PB)}. In the levitation control experiment, the defined fuzzy language sublets represent the description of the deviation distance and speed of the levitation air gap from the set air gap and the range of the fuzzy output value, where positive and negative represent the direction of the deviation. Large, medium and small indicate the degree of deviation. According to expert experience method and common fuzzy distribution function, \(e,de\) and \(\Delta k_{\rm p},\Delta k_{d}\) are connected with fuzzy language using triangular membership function. Then, use fuzzy reasoning combined with the Mamdani interface system to realize the rules of 'if A and B, then C', and its reasoning is simple and intuitive. It can be obtained according to the dynamic rules and control experience of the suspension control unit. The control rules of the inputs \(E,EC\) and outputs \(\Delta k_{\rm p},\Delta k_{\rm d}\) are established, which are shown in Table 1.  
Finally, the centroid method is selected to solve the ambiguity, which can take all the information in the fuzzy subset into account and more accurately convert the fuzzy value obtained by fuzzy reasoning into the accurate value expressed in the range of the output \(\Delta k_{\rm p},\Delta k_{\rm d}\). The three-dimension effect picture is obtained and shown in Figure 5. Through scale change and superposition of initial parameters, the actual parameters \(k_{\rm p}\) and \(k_{\rm d}\), which are input to the error feedback control law, are obtained:  
\[\left\{ \begin{array}{l}k_{\rm p}=k_{\rm p0}+l_{\rm p}\times\Delta k_{\rm p}\\ k_{\rm d}=k_{\rm d0}+l_{\rm d}\times\Delta k_{\rm d}\end{array} \right. \tag{17}\]  
where \(k_{\rm p0},k_{\rm d0}\) are the initial values of gain parameters in LESF and \(l_{\rm p},l_{\rm d}\) are scale factors. Combined with the LADRC parameter-tuning principle, the fuzzy linear active disturbance rejection controller of the suspension control unit can be obtained. The other three suspension control units can follow the same design method to complete the controllers design. In particular, the extended state observer can accurately estimate the total disturbance, modify the control object and simplify the control object into an integrator series system so that the ADRC can achieve static error-free control.