# Induction Machine-Based EV Vector Control Model Using Mamdani Fuzzy Logic Controller
## 2 Materials and Methods
### Design of MFLC Speed Control Model  
The speed control model of the IM developed in Simulink with a fuzzy controller in place of a P-I controller is depicted in \"Figure 5\". However, \"Figure 6\" shows a general model for the indirect vector control of an induction machine developed and tested in the Simulink environment. The Vector control block consists of two controller options (PI controller and fuzzy logic controller). Reference speed and measured speed are applied at the input of the adder block. The reference speed is subtracted from the measured speed. The speed difference is connected with the input of the fuzzy logic controller block. However, the output of the fuzzy controller is the torque signal required to generate the three-phase current signal compared with measured current in the current regulator block to generate gate pulses of the IGBT inverter block. \"Figure 7\" presents the block diagram of the closed-loop MFLC speed controller operation. The design of FLC intends to provide better speed control in terms of desired speed applications. FLC design maps predecessor sets with consequential sets. Initially, the FLC controller fuzzifies input vectors in Equation (15) as:  
\[a=\left(a_{1}:\texttt{{{imm::::}}},a_{n}\right) \tag{15}\]  
where:  
\(a_{1}\): first variable;  
\(a_{n}\): \(n\)th variable. Here, T2U is performed by mapping input vector T towards fuzzy set U. This task is achieved by the selection of relevant membership functions (MFs) suitable to represent the variation of input parameter from a set of available MFs. The same procedure is followed to represent the output variable via the selection of the most appropriate member function from the available ones. After the selection of input and output MFs, connectivity between MFs needs to be established. If-then rules stored in the fuzzy controller database are used to relate the relationship of the input variable with the output variable. The formation of rules is based on logical operations but heavily depends on human expertise. Therefore, FLC handles system nonlinearities and the variation of parameters as input and output are mapped with the help of the rule base. The rules are designed after the careful observation \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Impedence Type** & **Value** \\ \hline P & rated power & 50 Hp \\ V & voltage & 460 V \\ \(R_{s}\) & stator winding resistance & 87 mH \\ \(L_{ls}\) & stator leakage inductance & 0.8 mH \\ \(L_{m}\) & excitation inductance & 34.7 mH \\ \(R_{r}\) & rotor resistance & 227 m\(\Omega\) \\ \(L_{lr}\) & rotor leakage inductance & 0.8 mH \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Induction machine parameter values. of datasets obtained by workspace named as measured speed (MS), reference speed (RS), and torque, respectively. Multiple inputs contribute to the selection of the output response based on rules designed in the fuzzy controllers. The number of rules in the fuzzy controller plays an important role in the derivation of output. As each input MF is mapped with the output MF, each rule thus contributes to the output value within the range of input defined in MF. The decisions taken by the fuzzy controllers are made on binary logic. If any rule from the rule base  
Figure 6: Simulink model of fuzzy logic controller-based vector control. Figure 7: Block diagram of closed-loop MFLC speed control operation. is true then output MF mapped with input MF will respond; otherwise, the controller traverses down towards the next rule sequentially. The MF for single input \"Speed_difference\" is the difference between measured speed (MS) and reference speed (RS) with a range of \([-40+5]\), whereas only output signal torque is in the range \([-30+330]\). Seven MFs are disseminated to fill intervals for both the input and output of the fuzzy inference system (FIS). R-type trapezoidal MF is placed at the lower end of the input and output interval. L-type trapezoidal MF is placed at the higher end of the input and output interval.