1PMSM mathematical model
Permanent magnet motors can be divided into two types: one with a square wave input current, also known as a brushless DC motor (BLDCM); and the other with a sine wave input current, also known as...
Permanent magnet synchronous motor (PMSM). This paper focuses on the system design of the latter. To establish the mathematical model of the rotor shaft (dq axis) of the permanent magnet synchronous motor, the following is done.
assumed:
1) Ignore the saturation of the motor core;
2) Ignore eddy current and hysteresis losses in the motor;
3) The rotor has no damping winding.
Under the above assumptions, the motor voltage equation expressed in rotor reference coordinates (axis) is as follows:
Stator voltage equation
ud=Rsid+pψd－ωeψq (1)
uq=Rsiq＋pψq＋ωeψd (2)
Stator flux linkage equation
ψd = Ldid + ψf (3)
ψq=Lqiq（4）
Electromagnetic torque equation
Tem=3/2Pn[ψfiq＋(Ld－Lq)idiq]（5）
Equation of motion of the electric motor
J(dwm/dt)=Tem－TL（6）
In the formula: ud and uq are the d-axis and q-axis voltages, respectively;
id and iq are the d-axis and q-axis currents, respectively; Ld and Lq are the equivalent inductances of the stator inductance in the d-axis and q-axis, respectively.
Rs is the stator resistance;
ωe is the rotor's electrical angular velocity;
ψf is the magnetic flux linkage of the rotor excitation magnetic field through the stator winding;
p is a differential operator;
Pn is the number of pole pairs of the motor;
ωm is the rotor mechanical speed;
J is the moment of inertia;
TL represents the load torque.
2 Vector Control Strategy
The above equations are obtained by transforming the a, b, c coordinate system to the d, q rotor coordinate system. Here, the rotor axis is taken as the d-axis, and the q-axis leads in the direction of rotation.
The d-axis is 90° electrical angle. Its coordinate transformation is as follows.
2.1 Clarke Transform
2.2 Park Transformation
From the rotor coordinate perspective, the stator current can be divided into two parts: the torque current iq and the excitation current id. Therefore, vector control typically uses...
id=0 is used to ensure that the maximum output torque is obtained with the minimum current amplitude. At this time, the motor torque expression of equation (6) is:
Tem = (3/2)Pnψfiq (11)
As can be seen from equation (11), Pn and ψf are internal parameters of the motor, and their values are constant. To obtain a constant torque output, it is only necessary to control iq to a constant value. From the above dq
Analysis of the shaft shows that the direction of iq can be determined by detecting the rotor shaft. This greatly simplifies the vector control of the permanent magnet synchronous motor. Figure 1 shows the system.
The control block diagram shows that the system can operate in both speed-given and position-given modes, and the PWM modulation method uses space vector modulation.
3 System Hardware and Software Design
3.1 Hardware Design
3.1.1 DSP and peripheral resources
The hardware of the servo system based on a DSP is shown in Figure 2. The control circuit of the entire system is composed of the DSP. The DSP acts as the control core, receiving external information and then making judgments.
The servo system's operating mode is switched off and converted into a switching signal output by the inverter. This signal, after being isolated by a circuit, directly drives the IPM module to supply power to the motor. Additionally...
External EEPROM is used for saving parameters and storing user information.
3.1.2 Power Circuit
The entire main circuit first undergoes uncontrolled rectification, then outputs via a full-bridge inverter. The inverter utilizes an IGBT intelligent control module. The module integrates the drive circuitry, and...
The design includes fault detection and protection circuits for overvoltage, overcurrent, overheating, and undervoltage. The system's auxiliary power supply uses a switching power supply, primarily powering six switching circuits.
The power supply for the power-on transistor, the DSP, the power supply for the I/O interface control chip, and the sampling LEM.
3.1.3 Current Sampling Circuit
The system design requires at least two-phase current sampling. Due to the symmetry of the load, both ib and ic phases are sampled. The sampling circuit uses Hall effect sensors and...
After being processed by analog circuitry within a voltage range of ±5V, the signal is then sent to the DSP via a bipolar A/D converter chip.
3.1.4 Rotor Position Detection Circuit
The motor feedback uses an incremental photoelectric encoder with a resolution of 2500 pulses/revolution. The output signal includes A, B, Z, U, V, and W pulses.
Signals A and B are 90° out of phase (electrical angle). The DSP can determine the motor's direction of rotation and speed by judging the phase and number of signals A and B. This is achieved by acquiring these signals...
The position of the motor rotor and the speed of the motor are determined. Additionally, the U, V, and W axes are 120° (electrical degrees) apart, used to determine the rotor position during motor startup.
Place.
3.1.5 Protection Circuit
The system incorporates overvoltage, undervoltage, IGBT fault, motor overheating, IPM overheating, and encoder fault detection protections in its main circuit. Fault signals are processed via logic circuits.
The switch pulse can be directly blocked after the circuit is closed, and the system protection can be achieved through software detection via DSP I/O input.
3.2 Software Design
The DSP servo control program consists of three parts: the main program, the timing sampling program, and the data exchange program between the DSP and peripheral resources.
3.2.1 Main Program
The main program completes system initialization, I/O interface control signals, and settings of registers for various control modules within the DSP, before entering a loop program.
3.2.2 Timed Sampling Procedure
The timing sampling program is the core of the entire servo control program. It implements sampling of the current loop and speed loop, as well as vector control, PWM signal generation, and various other functions.
Operating mode selection and I/O cyclic scanning. Each sampling cycle includes current loop sampling, switch signal output, speed loop control, and position loop control.
The PWM control signal is generated using a regular sampling PWM modulation method. In each sampling cycle, an error judgment is performed on the current of each phase to determine the next cycle.
The duty cycle of the switching transistor.
3.2.3 Data Exchange Procedure
The data exchange program mainly includes a communication program with the host computer, a program for storing parameters in the EEPROM, and a program for reading and displaying keyboard values on the controller. The communication...
It adopts a serial communication interface, accepts instructions from the host computer according to a specific communication protocol, and transmits parameters as required. The keyboard is scanned every 0.2ms .
New display.
4. Experimental Results
The aforementioned servo system uses an AC permanent magnet synchronous servo motor with a rated power of 2.5kW , a rated current of 10A, a rated speed of 2000r/min, and a rated torque of 6N·m.
The stator inductance is 8.5 mH and the stator resistance is 2.8 Ω. Figure 3 shows the starting waveform of the motor at rated speed under no-load conditions, obtained through simulation. Figure 4 shows the dq of the stator current.
The component starting waveforms were obtained through simulation. Figure 5 shows the B-phase current waveform during no-load starting. Figure 6 shows the B-phase current waveform during steady-state operation of the motor under load.
Simulation and experimental results show that the system has a fast dynamic response and high control accuracy, fully meeting the requirements of a servo system. Furthermore, this system...
It has been successfully applied to the servo control system of CNC lathes and performs well.
5 Conclusion
The system employs a DSP control structure in its hardware, featuring a simple and compact circuit design that meets the requirements of vector control. Furthermore, the fully digital control enables…
The system has seen significant improvements in control precision, functionality, and anti-interference capabilities. Furthermore, by fully utilizing the internal resources of the DSP, only a small amount of additional...
With few circuit components, the system can achieve its intended functions. Its low cost and high-performance control characteristics give it excellent market application prospects. Furthermore...
In addition, the rational design of the system software structure also ensures the real-time performance and stability of the system.
