Abstract : This paper elucidates the vector control principle of asynchronous motors, analyzes the dynamic electromagnetic relationships and coordinate transformation principle of asynchronous motors, establishes a mathematical model of asynchronous motors in a rotating coordinate system, explains the decoupling effect of the mathematical model of three-phase asynchronous motors, and presents the vector control system diagram and simulation diagram of the motor.
Keywords : induction motor vector control decoupling
VectorControlofInductionMotorDrivebasedonMatlab
Liyihui
(CSU, School of Information Science and Engineering, Changsha, 410083)
Abstract: This article laborates the inductionmotorvectorcontrolprinciple,hasanalyzedasynchronousmachine'sdynamicelectromagnetismrelationsandthecoordinatetransformationprinciple,hasestablishedasynchronousmotor'sinrevolvingcoordinatesystemmathematicalmodel,explainedthethree-phaseasynchronousmachinemathematicalmodel'sdecouplingfunction,hasgiventheelectricalmachineryvectorcontroldiagramandthesimulationchart.
KeyWords:inductionmotor,vectorcontrol,decoupling
1. Research Background
With the continuous development of frequency conversion technology, new methods for controlling induction motors are constantly emerging. Among them, vector control is currently the main method for achieving high-performance control of induction motors. Vector control, also known as field-oriented control (FOC), is the decoupled control of torque and rotor flux linkage in a two-phase coordinate system that rotates synchronously with the rotor magnetic field. This allows for independent control of torque and flux linkage, thus achieving speed regulation performance similar to that of a DC motor. The vector control method, proposed in the early 1970s, decomposes the stator current of an AC motor into a magnetic field current component in the field-oriented coordinate system and a torque current component perpendicular to it through coordinate transformation and field-oriented control. This decoupling between the two results in a torque model similar to that of a DC motor, enabling rapid torque and flux control similar to that of a DC motor. This significantly improves the dynamic performance of the system, leading to a breakthrough in AC motor speed regulation technology. Currently, vector control has become the mainstream method for AC variable frequency speed regulation systems. MATLAB's SIMULINK is a software package for modeling, simulating, and analyzing dynamic systems. It features modularity, reloadability, encapsulation, block diagram-oriented programming, and visualization, greatly improving the efficiency and reliability of system simulation. Among various vector control methods, rotor magnetic field-oriented vector control is widely used. This paper combines this vector control with the features of SIMULINK to introduce a modeling and simulation method for a rotor magnetic field-oriented vector control system of an induction motor. Using the simulation model, simulation experiments of the control system are conducted. This provides an effective and reliable basis for research and analysis of similar speed control systems.
K. Hasse proposed the Indirect Field-Oriented Control (IFOC) method in 1969, and F. Blaschke proposed the Direct Field-Oriented Control (DFOC) method in 1971. These two control methods differ significantly. Indirect vector control, also known as slip-type vector control, uses an open-loop flux linkage control method. Therefore, it does not require calculating the amplitude and phase of the actual rotor flux linkage. Instead, it relies on the slip formula in the vector control equation to obtain the slip frequency, thus forming a slip-type vector control system. This slip frequency is added to the motor speed, and the rotor flux linkage position relative to the stator is calculated through integration. This method has a relatively simple structure, and its dynamic performance can essentially reach the level of a DC dual-closed-loop control system. Direct vector control, on the other hand, uses a closed-loop flux linkage control method. It relies on measuring or observing the rotor flux linkage to obtain its position information, thereby achieving decoupled control of torque and flux linkage.
The key to vector control technology lies in field orientation, and a crucial factor affecting field orientation is the motor parameters. During actual operation, the operating conditions of an induction motor change, such as variations in rotor temperature and magnetic circuit saturation. These changes cause deviations in motor parameters, with the rotor resistance parameter showing the most significant variation. For indirect vector control systems, because rotor flux linkage is controlled in an open-loop manner, implementation is relatively easy; however, the controller's design performance depends heavily on the motor parameters. When the rotor resistance parameter setting in the vector controller deviates from the actual motor parameter value, the slip calculated from the slip formula in the vector control equation becomes inaccurate, disrupting flux linkage orientation and degrading the motor's dynamic performance. Direct field-oriented control of rotor flux linkage employs closed-loop control. Obtaining rotor flux linkage using direct measurement methods is difficult and prone to measurement errors, limiting its widespread adoption. Estimating rotor flux linkage using an observer relies on the mathematical model of the induction motor.
2. Mathematical Model of Induction Motor in Two-Phase Arbitrary Rotating Coordinate System (dq Coordinate System)
The change in the relative position between the stator and rotor of an induction motor causes a change in the coupling factor. Decoupling this coupling factor in a synchronous rotating coordinate system yields the time-invariant coupling factor and independent control variables. Representing variables such as voltage, current, and flux linkage in a two-phase synchronous rotating coordinate system simplifies calculations and facilitates the analysis of the motor's dynamic characteristics.
The dq model is used for the design and analysis of vector control systems. The voltage and flux linkage equations of the induction motor in the dq coordinate system, after simplification, yield the following vector control model in the dq coordinate system:
In the formula,
w—motor angular velocity;
s—motor leakage flux coefficient,
.
3. Vector control equations based on rotor flux orientation and their decoupling effect
If we take the d-axis along the rotor total flux linkage vector
The direction of the q-axis is 90° counterclockwise, which is perpendicular to the direction of the q-axis.
When the two-phase synchronous rotating coordinate system is oriented according to the rotor flux linkage, the following should be true:
Substituting the torque equation (2-6) and the above equations, we can obtain:
From equations (3-2) and (3-3), it can be seen that the rotor flux linkage is generated only by the excitation component of the stator current and is independent of the torque component. In this sense, the excitation component of the stator current and the torque component are decoupled.
Equation (3-4) also shows that the transfer function between and is a first-order inertial element, and its time constant Tr is the rotor flux excitation time constant. When the excitation current component changes abruptly, the change of is hindered by the excitation inertia, which is consistent with the inertial effect of the excitation winding of the DC motor.
Therefore, by controlling the excitation components separately
By combining the torque component, a control effect similar to that of a DC motor can be obtained, and the design of the controller is relatively simple.
4. Vector Control Model for Induction Motors
An induction motor module was built based on the Matlab/Simulink simulation platform. The induction motor module includes calculations of current, flux linkage, electromagnetic torque, speed, and position, as shown in Figure 4-1.
Figure 4-1 Induction Motor Model
In the MATLAB/Simulink environment, an indirect vector control system for the induction motor was designed based on the established induction motor model, laying the foundation for subsequent research. The system speed loop employs PI control, and other main functional modules include a decoupling module, a coordinate transformation module, and a current hysteresis controller module. The rotor flux linkage is directly given, and the entire system has only two loops: a speed loop and a voltage loop. The decoupling control of the induction motor starts from the mathematical model of the induction motor and applies decoupling control methods from modern control theory. Through state feedback, the originally complex, multivariable, nonlinear, and strongly coupled system is decoupled and linearized to achieve dynamic decoupling between the motor speed and the rotor flux linkage. The simulation model of the indirect vector control system for the induction motor is shown in Figure 4-2.
Figure 4-2 Simulation model of induction motor indirect vector control system
The decoupling module of the induction motor indirect vector control system is shown in Figure 4-3:
Figure 4-3 Decoupling module of induction motor indirect vector control system
5. Simulation Results
To verify the dynamic and static performance of the designed induction motor indirect vector control system under sudden changes in load torque and given speed, a simulation experiment was conducted on the control system. The motor parameters are shown in Table 5-1.
Table 5-1. Motor Parameters
The proportional gain of the PI controller is set to 1, the integral gain to 0.1, and the upper and lower limits of the integral, as well as the upper and lower limits of the controller output, are set to 1 and -1, respectively. The DC voltage is 240V, the speed setpoint is 100 r/min, the rotor flux setpoint is 0.5 Wb, and the motor starts with a 5 Nm load. After 1.5 seconds, the speed setpoint changes to 150 r/min. The speed response waveform, rotor flux waveform, and electromagnetic torque waveform of the control system are shown in Figure 5-1.
(a) Rotational speed waveform
(b) Electromagnetic torque waveform
(c) Rotor flux waveform
6. Conclusion
Simulation Figure 4-1 shows that the motor's speed response roughly follows the given speed change and reaches a steady state within a short time. The motor torque and flux linkage then reach a steady state. The figure also shows that the overshoot is too large at the beginning of system operation, and changing the PI parameters has little effect. Analysis suggests this may be related to the selection of motor parameters.
7. References
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About the author:
Wang Suiping (1956-), male, is a professor in the Department of Control Engineering, School of Information Science, Central South University. His research areas include deep-sea robotics, motor control, and metallurgical process control.
Li Yihui (1987–), male, from Yueyang, Hunan Province, holds a Master's degree and is a student at the School of Information Science and Technology, Central South University. His research areas include industrial process control, computer control, and fieldbus.
