Direct Torque Control System of Induction Motor Based on Fuzzy Control

Abstract: Based on the direct torque control theory, a simulation model of an induction motor direct torque control system was constructed under Matlab 6.5/Simulink. In order to improve the dynamic and static quality of the induction motor system, a fuzzy adaptive PI speed regulator was designed. According to the speed deviation and the deviation change rate, the PI parameters were adjusted online through fuzzy reasoning to improve the speed regulation performance of the system. The simulation results show that this fuzzy controller has better control effect than the conventional PID controller.
Keywords: fuzzy control; direct torque control; induction motor; speed regulator

0 Introduction
Direct torque control (DTC) is another advanced motor control technology after vector control technology. It is widely used due to its simple structure, insensitivity to motor parameters and rapid torque response. In the direct torque control system of induction motor, the speed controller is mostly a PID controller. The traditional PID control technology cannot effectively overcome the influence caused by the change of motor parameters, load changes and nonlinear factors, while fuzzy control adapts to the control of nonlinear time-varying and hysteresis systems and has the advantage of strong robustness. When the conventional PID speed regulator cannot meet the requirements of high-performance speed regulation of the system due to fixed parameters, fuzzy control technology is introduced to construct a speed fuzzy controller, and a fuzzy adaptive PI speed regulator is designed. According to the speed deviation and the deviation change rate, the PI parameters are adjusted online through fuzzy reasoning, which effectively improves the performance of the direct torque control system and achieves a better control effect.

1 Basic principles of direct torque control
The core idea of ​​direct torque control is to carry out comprehensive control of flux and torque with torque as the center. It does not need to decouple the mathematical model of the motor, but emphasizes direct control of the motor torque, that is, using the space vector analysis method to directly calculate and control the torque of the AC motor in the stator coordinate system. The structural principle of direct torque control is shown in Figure 1. It consists of flux estimation, torque estimation, flux position estimation, switch table and regulator, inverter and other parts. Its working process is as follows: First, the detection unit detects the motor stator current and voltage value, actual speed ω, and then inputs it into the induction motor mathematical model module to calculate ψα, ψβ and actual torque value Te. ψα and ψβ pass through the flux calculation unit to obtain the amplitude |ψs| of the stator flux ψs and the interval signal SN. The actual speed ω and the given speed ω* are used by the speed regulator to obtain the torque set value. The actual torque Te and the torque set value are processed by the torque regulator to obtain the torque switch signal TQ. The flux set value and the flux feedback value |ψs| are processed by the flux regulator to generate the flux switch signal ψQ. The switch signal selection unit integrates ψQ, TQ and SN, and obtains the inverter switch signal SUabc by looking up the table to control the inverter to provide a suitable voltage to drive the induction motor to operate.

2 Design of fuzzy direct torque control system
Fuzzy control is a typical intelligent control method, a computer digital control based on fuzzy set theory, fuzzy language variables and fuzzy logic reasoning. Its basic idea is to summarize the control strategy of human experts for a specific controlled object or process into a series of control rules, and obtain the control action set through fuzzy reasoning, which acts on the controlled object or process. Compared with traditional control methods, fuzzy logic control does not require an accurate mathematical model of the system, has the advantages of strong robustness and good control performance, and is more suitable for the control of complex, nonlinear time-varying and hysteresis systems. The fuzzy adaptive PI speed regulator consists of a conventional PI controller and a fuzzy controller. Its principle is as follows: the fuzzy controller selects the speed error e and the speed error change rate ec as input variables, and uses fuzzy rules through fuzzy reasoning to output the proportional correction coefficient △KP and the integral correction coefficient △KI to adjust the parameters of the PI controller online in real time, thereby generating a given torque signal, which is sent to the DTC control system to control the speed of the induction motor. Figure 2 shows the schematic diagram of the system.
2.1 Fuzzy variables
This fuzzy controller uses two input variables and two output control quantities. The two fuzzy input variables are speed error and speed error change rate, represented by e and ec respectively, and the output control quantity is the proportional correction coefficient and the integral correction coefficient, represented by △KP and △KI respectively. e contains 7 fuzzy subsets, and the corresponding linguistic variables are: negative large (NB), negative medium (NM), negative small (NS), zero (Z), positive small (PS), positive medium (PM) and positive large (PB). The domain is [-1, +1], and the membership distribution function is shown in Figure 3.

ec contains three fuzzy subsets, and the corresponding linguistic variables are: negative (N), zero (z) and positive (P). The domain is also [-1, +1], and the membership function is shown in Figure 4.

△KP and △KI contain four fuzzy subsets respectively, and the corresponding linguistic variables are: zero (Z), small (S), medium (M), and large (B). The domain is [0, 1], and the membership function is shown in Figure 5.
2.2 Fuzzy control rules
The basic principles of fuzzy PI parameter self-tuning are as follows:
(1) When the system deviation (|e|) is large, in order to eliminate the deviation as quickly as possible, regardless of the sign of ec, larger KP and KI should be taken to achieve the purpose of reducing the deviation.
(2) When the system deviation (|e|) is moderate, in order to prevent the system from overshooting, a smaller KP should be taken. At the same time, in order to ensure a certain response speed, KI should be selected with a moderate value.
(3) When the system deviation (|e|) is small or zero, in order to shorten the adjustment time of the system, a moderate KP and a smaller KI value should be selected. According to the above adjustment rules and multiple simulation results, the control rules of the fuzzy controller are shown in Table 1.

2.3 Fuzzy reasoning and fuzzy decision-making
Fuzzy reasoning adopts the Mamdani reasoning method, and uses the output corresponding to the maximum membership as the control quantity to obtain the final output value of KP and KI. Its control rule adopts the form of "If e=E and ec=Ec then △KP and△KI".
Referring to Table 1, 21 control rules can be obtained.
For example, "If e=PB and ec=P then △KP=B and △KI=Z", the output is the proportional correction coefficient △KP and the integral correction coefficient △KI, and the PI parameters are adjusted online to achieve the purpose of real-time control.

3 Simulation results
In order to verify the correctness and superiority of the new control system, the parameters of the three-phase squirrel cage induction motor are selected as follows: Pn=2.5kw, us=380V, f=50Hz, nr=1400r/min, Rs=1.85Ω, Rr=2.658Ω, Ls=0.294H, Lr=0.2898H, Lm=0.2838H, np=2, J=0.01kg·m2. In Matlab 6.5, the modules provided by the Simulink library and the Power Sys-tem Blocket library are used to construct the system simulation model. Referring to the previous analysis, the constructed simulation model is shown in Figure 6.

In order to verify the effectiveness of the fuzzy adaptive PI speed regulator, it was compared with the conventional PI speed regulator under two identical working conditions.

Figure 7 and Figure 8 show the speed response waveforms of fuzzy adaptive PI and conventional PI when the given speed changes (1 000-100-500) r/min and the load changes (0-15-5) N·m. By comparing the results, it can be found that the DTC system using fuzzy adaptive PI speed regulator has fast speed response, small overshoot, good steady-state performance, good interference suppression ability and robustness, and significantly improved speed regulation performance. Fuzzy adaptive PI control has better control effect.

4 Conclusion
This paper applies the fuzzy control method to the direct torque control system of the induction motor. In view of the fact that the conventional PI speed regulator cannot meet the requirements of high-performance speed regulation of the system due to fixed parameters, a fuzzy adaptive PI speed regulator control system combining fuzzy control and PI control is designed to replace the traditional PID control. The simulation model of the system is established in the Matlab/Simulink environment. The simulation results show that this method can not only improve the speed regulation performance of the system, but also improve the anti-interference ability of the system, proving the feasibility and correctness of the system.