With correction factor fuzzy PID control of PMSM AC servo system (1)

Abstract: in order to overcome the permanent magnet synchronous motor (PMSM) servo system with nonlinear and uncertainty factors that improve servo system control precision and performance characteristics, presented with correction factor of fuzzy-proportional, integral and differential (PID) control.

It is set PID and fuzzy control advantages in one control system, depending on the speed deviation to determine the speed controller used fuzzy control algorithm or PID control algorithm, and under the control of the system's speed and velocity error rate, using the correction factor for fuzzy controller for online modification of parameters. Simulation results show: correction factor of fuzzy-PID control optimized the system of dynamic and static characteristics that meet the system requirements of high-performance, verify that the control strategy of superiority and reliability.

Keywords: permanent magnet synchronous motor, servo systems; fuzzy control; correction factor

Servo system is automatic control system of a type of closed-loop control, usually applied to control the structure of the controlled object in a State that allows it to automatic, continuous, accurate reproduction of the input signal changes, often used for rapid, precise position control and speed control applications.

With the rapid development of modern industry, accuracy and reliability of control at increasingly higher demands. To this end, a variety of control methods, one of the most common is proportional, integral and differential (PID) control method, the algorithm is simple, good stability, wide application, theory of mature and widely used in industrial control field, apply to establish precise mathematical model of linear time-invariant parameters of the system. The actual permanent magnet synchronous motor (PMSM) itself when with nonlinear, transgender, uncertainties, it is difficult to establish precise mathematical model, coupled with a system run time also from different levels of interference, PID control strategy to meet the high performance PMSM servo system control requirements.

Unlike traditional PID control methods, fuzzy control does not depend on exact charged object model, system dynamic response better robustness, but more difficult to eliminate system adjustment at the end of the error, and the stability of the PID control methods can be a good solution to this.

Therefore, this article will combine both can effectively solve fuzzy control of steady-state error. However, the fixed parameters of fuzzy controller cannot guarantee that the system of dynamic and static characteristics in a wide range for optimum. In order to improve the performance of fuzzy controller, under the control of the system's speed error error ec e and speed on fuzzy controller for online modification of the parameters, namely the correction factor.

L Fuzzy-PID controller design

1.1 system control structure

Servo speed controller consists of two parts: the fuzzy controller and PID controller.

Controller under speed deviation e to determine the speed controller used to control algorithm to achieve closed-loop speed control. When speed deviation of e is greater than a threshold ε, you should be to improve system responsiveness, more control, allowing the actual speed as soon as possible to reach a given speed, at which point the use of fuzzy control algorithm; when speed deviation e is less than threshold ε, close to the speed of the rotor speed, you should be given to improve the system of static characteristics, improve system stability precision, you should use PID control algorithm. At the same time for fuzzy control controller, the system of dynamic and static characteristics, the use of coarse and fine tune parameters, solves adjust speed and stability precision.

Figure l is fuzzy PID speed control principle.

Two-dimensional fuzzy controller input variable is the speed given and speed feedback between e and error variation ec output variable for current loop of a given u. And definitions:

　　

　　

1.2 control rules

Fuzzy rule selection is at the core of the design of fuzzy controller, fuzzy controller input output is passed between Fuzzy rules linked to the table, and the selection of fuzzy inference rule is based on the error and the error rate of change on the basis of size.

When the error is large, select control to eliminate the error; if the error is low, the volume of the selected control to the system stable, and you want to pay attention to preventing the overshoot, the selected membership function curve more pointed, the higher the sensitivity of the control. To do this select the normal distribution function as fuzzy variable membership function, using the focus method of fuzzy decision.

Located in Figure 1 E and Ec's basic on domain-[6 June], errors and error rate is 13-fuzz, that is, E = Ec = {6, 5, 4, 3, 2 l, O, a, l, 2, 3, 4, 5, 6}.

Speed of fuzzy controller output U of universes is [0, 6], and is divided into seven quantization level, that is, U = {1, 2, 3, 4, 5, 6); E, Ec and U fuzzy set {negative (NB), negative (NM), small (NS), zero (0), are small (PS), the median (PM), Chia Tai (PB)}. As a rule of thumb, you can summarize fuzzy controllers control rules, see table 1. Table amount for the entry in the results as E and Ec by fuzzy logic reasoning be U output, which is essentially the operator's control to summarize the experience of a series of "IF-THEN" type of conditional statements. The first thing a conditional statement to enter the variable E and Ec, after U is the output variable.

There shall be a speed deviation e and speed deviation change quantitative factor ec respectively, K1 and K2: output U factor of K3.

These three factors on the control of a direct impact on results, K1 too large easy to produce overshoot, and prone to limit cycle, too little will make the system response time; the larger the conducive to K2-harmonic oscillation suppression, but too large system should slow down, and K2 too much or too little will make the overshoot, and prone to limit cycles; K3 's OK on fuzzy controller for controlling the performance of very large, its selection and actual control object. K3 is too small will make the system of dynamic response process have variable length, K3 overshoot the Assembly so that larger, causing the system oscillation. For the system to respond quickly and non-Adjustment, General, online modify parameters factor K1, K2 and K3, thus amended Basic universe e, ec and "and on the domain E, Ec and U, relationships.

Correction factor n adjustment principle is: as e and ec is large, the system should reduce errors, speed up the process, you should select a larger amount, i.e. increase control K3, decrease the K1 and K2; when e and ec more hours, that is, the system close to the steady state value, you should reduce the K1 and K3, increase, decrease the overshoot K2, improve system stability precision.

Set correction factor to n, fuzzy variable n, fuzzy set {high on (AB), in the (AM), low drop (AS), unchanged (OK), small shrinkage (CS), indent (CM), large shrinkage (CB)); N domain N = {1/8, 1/4, 1/2, 1, 2, 4, 8}.

Set basic fuzzy controller ratio of the original quantization factor, namely, according to the factor of quantized E and Ec are fixed factor, correction factor n adjustment rules table and under the table are shown in table 2 and table 3, control rules are similar to real are the same as in table 1. At this point quantization factor, the scaling factor is adjusted to, are:

　　

　　

　　

　　

2 system simulation model

The system adopts the powerful features of MATLAB7.0 Simulink simulation module for simulation.

Simulation setting PMSM parameters are as follows:

Stator resistance R = 2.875 Ω; armature inductance Ld = Lq = 8.510-3H; flux φ = 0.175 Wb; p = 4 pole.

And set the motor torque at O.2 s from 4 to 7 Nm Nm mutation; speed given as 700 r/min. Figure 2 shows the system block diagram.

　　

　　

This system is based on the digital signal processor (DSP) full digital AC servo system.

This control functions are available through the software programming in DSP implementation, rather than in the other building hardware circuit, makes the whole system becomes simple and compact structure. And full digital control makes servo system reliability, control parameters more easily than hardware circuits.

The system mainly includes:

1) pole position detection and current measurement module module;

2) speed and current loop control;

3) coordinate transformation module;

4) space vector modulation (SVPWM) module;

5) rectifier and the inverter module.

System power module driven by far the most common pulse width modulation (PWM) optimization SVPWM, it can significantly reduce the inverter output current of the harmonic components and motor loss, lowering of harmonic pulse of torque.

With the DSP technology, computing capabilities to enhance the storage capacity increases, making the Digital PWM increasingly convenient.

Current loop using PI control algorithm, speed loop with fuzzy-PID control, current regulator and speed regulator uses the belt saturation limit of PI regulator.

Current loop armature current feedback values and current command signals are compared to current error, the current loop regulator control by errors in the current fast follow instruction value change, steady-state current no static errors.

Current controller output of rotated coordinate system transformation to rest/static coordinates V V α and β, then through the power-driven modules get motor voltage three-phase winding Va, Vb and Vc; detection of winding current after rotating the coordinate system transformation rest/to rotate [1] [2]