Research and design of brushless DC motor control system based on DSP

Introduction
In recent years, with the rapid development of power electronic devices and modern control theory, brushless DC motors have been widely used in optical drives, intelligent robots, electric vehicles and other fields because they have no contact commutation device and no sparks caused by commutation. They have many advantages such as high efficiency, speed not limited by mechanical commutation, strong maintainability and high safety. DSP (digital signal processor) has been widely used in the control field with its high-speed data processing capability, rich internal resources, high integration and low power consumption. This paper proposes a design scheme for a brushless DC motor control system based on DSP. The design combines fuzzy control methods to realize the intelligent control of brushless DC motors.

1 Mathematical model of brushless DC motor
According to the physics formula, when a single conductor cuts the magnetic lines of force in a magnetic field, the electromotive force e generated is: where

B is the magnetic field induction intensity, l is the effective length of the conductor in the magnetic field, and v is the linear velocity of the conductor moving perpendicular to the magnetic lines of force. In the motor, the relationship between v and the speed n is:

In this way, the magnitude of the induced electromotive force induced by the brushless DC motor during operation is:

Wherein, E is the induced electromotive force generated by the brushless DC motor; p is the number of pole pairs of the motor; α is the pole arc coefficient; W is the number of winding turns of each phase of the point winding; ψ is the magnetic flux of each pole; n is the speed of the motor.
Assume that the winding of the brushless DC motor adopts a three-phase star structure, the three phases of the stator are completely symmetrical, and the electrical angle is 120° apart in space, and the inductance parameters of the three-phase winding resistance are the same. At the same time, the mutual inductance generated between the armature windings is ignored, the air gap magnetic permeability of the motor is uniform, the magnetic circuit is not saturated, and the eddy current loss is ignored. The mathematical model of the brushless DC motor is as follows:

Wherein, Va, Vb, and Vc are the three-phase terminal voltages respectively; R is the three-phase winding resistance; L is the three-phase winding inductance; Ea, Eb, and Ec are the three-phase induced electromotive force of the motor respectively; ia, ib, and ic are the currents flowing through the three-phase windings respectively. In this way, the expression of its electromagnetic torque can be expressed as:

According to the law of kinematics. The expression of electromagnetic torque can also be expressed as:

Where T1 is the load torque of the motor, J is the moment of inertia of the rotor, and Z is the damping coefficient of the motor rotation.

2 System hardware design
2.1 Overall system hardware design
This system can be roughly divided into power drive part, DSP control core part, A/D signal detection part, etc. Figure 1 shows the overall hardware system block diagram of a DC brushless motor control system based on DSP.

2.2 Design of power drive part
Figure 2 shows the power conversion bridge circuit diagram of the three-phase brushless DC motor introduced in this article. In the figure, 6 N-channel MOSFET power elements IRF540 are used to form a three-phase bridge circuit as an electronic commutator of the brushless DC motor. The function it performs is consistent with the function of the commutator of the traditional brushed DC motor. Resistor R107 is used as a sampling resistor for overcurrent protection. In fact, it is a small manganese copper shunt with a value of 0.01Ω, which can ensure that no large voltage will be generated when the normal working current and rated starting current pass through the resistor. When the motor is blocked, short-circuited somewhere, or the upper and lower MOSFETs are turned on and short-circuited at the same time, the resistor can generate a large current. When the voltage drop on this resistor reaches a certain level, the circuit can quickly activate the overcurrent protection circuit to stop the operation of all MOSFETs and disconnect the main circuit power supply to prevent the situation from further deteriorating.

2.3 DSP part design
According to the analysis of the motor mathematical model. In order to achieve high-precision and reliable control of the brushless DC motor speed, this system uses T1's mature DSP product TMS320LF2407 . This digital signal processor not only has the characteristics of the architecture required for high-speed signal processing and digital functions, but also its low cost, low power consumption and high-performance processing capabilities and rich internal resources are very useful for the digital control of the motor. In addition, the digital signal processor (DSP) also has a high-precision 10-bit ADC analog-to-digital conversion module and a pulse modulation PWM module. 2.4 A/D signal detection design The detection function of the A/D signal can be completed through the dedicated high-end current measurement chip AD8206 and high-precision sampling resistors. That is, after Coil_A, Coil_ B, and Coil_C led out from the three-phase power conversion bridge pass through high-precision ultra-low resistance 0.01Ω sampling resistors, the three wires U, V, and W are connected to the A, B, and C three-phase coils of the stator armature respectively. In this way, the current passing through the armature windings of each phase can be detected by detecting the voltage on the sampling resistor. The method for testing the voltage of each phase relative to the ground is relatively simple, and can be tested by the resistor voltage division method. The voltage on the A, B, and C three-phase coils can also be obtained by the resistor voltage division method at the U, V, and W test points. Figure 3 shows the sampling circuit of the voltage and current of phase A.

3 System software design
3.1 System control diagram
Figure 4 shows the control block diagram of this system. According to the control block diagram, the system can be divided into several subtasks. These include system initialization tasks, system parameter sampling tasks, system protection tasks, fuzzy control calculation tasks, motor control tasks, communication tasks, etc. At any time, only one subtask can be selected by the system scheduler and enter the main loop of the system to run. At this time, other tasks are in a dormant or suspended state. Waiting for the system to call. Each subtask appears in the form of a dead loop function and is called by the system. The interruption and switching of the dead loop of each subtask is generally based on the system beat clock. The block diagram of the subtask that should be called next, determined by the system scheduler, is shown in Figure 5.

3.2 Selection of fuzzy control parameters
This fuzzy controller uses the deviation e between the motor speed output and the expected speed output and the rate of change of the deviation ec as input variables to output the change value of the motor control value. In the fuzzy control area, the speed deviation and the rate of change of the deviation can be quantified into 7 fuzzy subsets, namely the fuzzy linguistic variables {negative large, negative medium, negative small, zero, positive small, positive medium, positive large}, abbreviated as {NL, NM, NS, ZO, PS, PM, PL}.
Considering the two signals of speed deviation and speed deviation change rate, the following fuzzy thrust rules can be adopted:

Since e and ec each have a fuzzy subset, there are 49 fuzzy rules in total, and their specific rules are listed in Table 1.

3.3 System parameter sampling
The voltage and current sampling unit collects a total of 7 data, namely three-phase voltage, three-phase current and stator armature total current. These parameters correspond to the 7 sampling channels in A/D. During each sampling process, the program samples 7 data in sequence according to the sampling channel at one time, and puts the sampling results into the data buffer for other programs to read and call. If the maximum speed of the controlled motor is 3000 rpm, that is, 50 rpm, and there are 6 commutation intervals in each electrical cycle, then in order to ensure the commutation control accuracy <15°, each commutation interval is sampled 5 times. The number of samples per second is 5x6x50=1500 times/second, and the interval time of each sampling is about 660μs. Figure 6 shows the flow chart of the voltage and current sampling program of the system.

4 System simulation model
The simulation can be completed using the Simulink function in Matlab software. Simulink is an integrated software package that can perform dynamic system modeling, simulation and comprehensive analysis. The systems it can handle include linear and nonlinear systems, discrete, continuous and hybrid systems, single-task and multi-task discrete event systems. Figure 7 shows a simulation model of a brushless DC motor body.

5 Conclusion
Based on the analysis of the mathematical model of brushless DC motor, this paper proposes a solution for permanent magnet brushless DC motor control system based on TMS320LF2407 A. This solution makes full use of the powerful computing function and rich internal resources of DSP. And introduces fuzzy control algorithm into the control system. The simulation results show that the control waveform of the system is consistent with the theoretical analysis, the whole system runs smoothly, and has good static and dynamic characteristics.