CN106452245B - A kind of gray prediction TSM control method for permanent magnet synchronous motor - Google Patents

Abstract

The invention provides a gray prediction terminal sliding mode control method for a permanent magnet synchronous motor, and relates to the technical field of control of an AC motor. The method includes establishing the mathematical model of permanent magnet synchronous motor, using genetic algorithm to reselect the appropriate m ^* and n ^* , selecting the sliding surface of the terminal sliding mode, introducing adjustment items according to the principle of gray prediction and terminal sliding mode control, Get the final control term. The present invention provides a gray predictive terminal sliding mode control method for permanent magnet synchronous motors, using the principle of genetic algorithm to reselect the two parameters (m and n) in the predictive algorithm process, so that these two parameters are more accurate In order to be reasonable, a more appropriate error prediction value can be obtained, so that the control process of the permanent magnet synchronous motor has higher precision, the chattering is reduced and reduced, and it does not affect the fast response effect and strong robustness of the terminal sliding mode control itself. , and is real-time.

Description

A Gray Predictive Terminal Sliding Mode Control Method for Permanent Magnet Synchronous Motor

Technical field:

The invention relates to the technical field of control of AC motors, in particular to a gray prediction terminal sliding mode control method for permanent magnet synchronous motors.

Background technique:

The permanent magnet synchronous motor has the advantages of simple structure, small size, high power density, low processing and assembly costs, no electric ring brushes, etc., and is used in many fields. However, the permanent magnet synchronous motor has multivariable, strong coupling and nonlinear Problems make the control of permanent magnet synchronous motors complicated, especially the system parameter changes, the disturbance of external uncertain factors makes the control equation complex and difficult to implement, and the accuracy is not high, and the real-time performance is not strong.

With the widespread use of permanent magnet synchronous motors in recent years, there has been a lot of research on the control method algorithms of permanent magnet synchronous motors, among which vector control methods and direct torque control methods are widely used. The application of the terminal sliding mode control method in the permanent magnet synchronous motor control makes the motor control very convenient. Its biggest advantage is that the terminal sliding mode control does not depend on the parameters of the motor and the complex coupling relationship between them. Sliding mode control can achieve the purpose of controlling the motor by properly introducing parameters according to the running conditions of the motor. The algorithm is easy to implement, the response speed is fast, the calculation amount is small, and the accuracy is high. However, the terminal sliding mode control depends on the error, that is, if there is no error, the terminal sliding mode control cannot be realized, which limits the application of the terminal sliding mode control.

Some scholars use the gray prediction method to improve the terminal sliding mode control. During the control process, real-time prediction is made to judge the running trend of the motor during operation, and timely adjustments are made to achieve good results. But the problem is that the adjustment value given in the gray forecasting process is due to the limitations of the forecasting method itself, the overshoot is too large, causing large chattering, or causing stability errors, so the terminal sliding mode control with forecasting function still exists. Areas for improvement.

Invention content:

Aiming at the defects of the prior art, the present invention provides a gray prediction terminal sliding mode control method for permanent magnet synchronous motors, using the principle of genetic algorithm to reselect the two parameters (m and n) in the prediction algorithm process, These two parameters are more reasonable, a more appropriate error prediction value is obtained, the control process of the permanent magnet synchronous motor is more accurate, chattering is reduced and reduced, and it does not affect the fast response effect and The advantages of strong robustness and real-time performance.

A gray predictive terminal sliding mode control method for permanent magnet synchronous motors, comprising the following steps:

Step 1. Establish the permanent magnet synchronous motor mathematical model, that is, the torque and motion equation of the discrete permanent magnet synchronous motor system, such as formulas (1) and (2):

in, is the derivation of the rotational speed, T _e is the electromagnetic torque, T _l is the load torque, n _p is the number of pole pairs, ψ _a is the flux linkage between the permanent magnet and the stator, i _{q, k} is the current of the quadrature axis The sampling value of the component in period k, J is the moment of inertia, ω _k is the sampling value of the rotational speed of the rotor electrical angular velocity in k period, ω _k-1 is the sampling value of the rotational speed of the rotor electrical angular velocity in the previous period k, B is the viscous Friction coefficient, T is the sampling period.

Step 2, using a genetic algorithm to select suitable parameters m ^* and n ^* , specifically including the following steps:

Step 2.1, according to the gray prediction principle and the speed error and its accumulation, generate the expressions of the parameters m and n, as shown in formula (3);

Among them, the parameter matrix X and Y are as formula (4) and formula (5) respectively;

in, k=1, 2, 3, 4, 5, is the rotational speed error between time k and the previous cycle, Its cumulative sum form is Represents the original error sequence;

Step 2.2, determine the optimum value m ^* and n ^* of parameter m and n with genetic algorithm, concrete method is:

Step 2.2.1, determine the objective function, such as formula (6) and formula (7);

Among them, Mape_m and Mape_n are the absolute errors of the parameters m and n respectively, m _k-1 and m _k are the screening values of the parameter m obtained in the k-1th cycle and the k-th cycle of the genetic algorithm respectively, n _k-1 and n _k is the screening value of the parameter n obtained from the k-1th cycle and the kth cycle obtained by the genetic algorithm, respectively;

Step 2.2.2, determine the size of the particle swarm population in the genetic algorithm;

Step 2.2.3, select the appropriate crossover rate and mutation rate, and carry out the calculation of crossover and mutation;

Step 2.2.4. Determine whether the absolute errors Mape_m and Mape_n in the objective function reach the preset error range. If yes, obtain the optimal values of parameters m and n, and execute step 2.3. If not, return to step 2.2.3 and start again. Carry out the calculation of crossover and mutation, and finally get the optimal m ^* and n ^* ;

Step 2.3, carry out the gray prediction solution based on genetic algorithm optimization;

Solve the gray prediction equation (8) to get the speed error Predicted value for the next period As shown in formula (9);

Among them, m ^* and n ^* are the optimal values of the parameters obtained through the optimization of the genetic algorithm in step 2.2;

Finally, the original error sequence is obtained Predicted value for the next period As shown in formula (10);

Step 3, improving the terminal sliding mode control of the gray prediction algorithm based on the genetic algorithm;

Step 3.1, determine the speed error and its derivative error signal according to the permanent magnet synchronous motor model, as shown in formula (11);

Among them, e _{1, k} is the rotational speed error signal in the k period, e _{2, k} is the derivation calculation of the rotational speed error signal in the k period, that is, the first-order derivative error signal, is the given speed, ω _k is the actual speed sampling, e _{1, k-1} and e _{2, k-1} are the values of e _{1, k} and e _{2, k} in the k-1 cycle respectively;

According to the mathematical model formula (1) and formula (2) of the permanent magnet synchronous motor, and calculate the second derivative of the speed error, the first-order and second-order derivative error signals of the speed are obtained, as shown in formula (12);

in, is the first derivative of the speed error signal e _1,k , is the second-order derivative of the speed error signal, u _k is the expression of the control quantity obtained by the terminal sliding mode control, T _{l, k} and T _{l, k-1} are the different values in the k period and the k-1th period, respectively Determine the disturbance load;

According to the principle of terminal sliding mode control, it is assumed that the following equations are satisfied:

in, d _k is the external uncertain disturbance of the system;

Step 3.2, determine the sliding mode surface of terminal sliding mode control as shown in formula (14);

Among them, s _{2, k} is the sliding mode surface equation, s _{1, k} = e _{1, k} , Δs _{1, k} = s _{1, k} -s _{1, k-1} , is the derivative of s _{1, k} , so there is p, q and α are parameters adjusted according to the actual situation;

Step 3.3, determine the control variable expression of the gray prediction terminal sliding mode control, as shown in formula (15);

u _k = u _{eq, k} + u _{s, k} + u _{ga, k} (15)

Among them, u _k is the control variable expression of terminal sliding mode control; u _{eq, k} is the equivalent equation of terminal sliding mode control, as shown in formula (16); u _{s, k} is the nonlinear switching surface equation, as in formula ( 17); u _{ga, k} is the adjustment equation of the improved gray prediction, as shown in formula (18);

u _{s, k} =-b ^-1 [K ₁ sgn(s _{2, k-1} )] (17)

in, is the sliding mode surface equation calculated from the predicted value, That is, the result predicted by formula (10), is true derivative; symbolic function σ ₁ is a small normal number, K ₁ and K ₂ are the values to be designed, and their values are adjusted according to the actual situation, and ε is the operating range of the sliding surface.

It can be seen from the above-mentioned technical scheme that the beneficial effect of the present invention is that: a kind of gray predictive terminal sliding mode control method for permanent magnet synchronous motor provided by the present invention uses the principle of genetic algorithm to predict the two parameters (m and n) to optimize and use more reasonable parameters m ^* and n ^* to obtain a more appropriate error prediction value, and more accurately predict and judge the next step of adjustment, so that the control process of the permanent magnet synchronous motor has higher precision, thereby reducing and reduced chattering, maintaining the robustness of the terminal sliding mode control; since the terminal sliding mode control has the characteristic that the control parameters can be independent of the motor parameters, the control debugging process does not affect the fast response effect of the terminal sliding mode control itself It has the advantages of strong robustness and real-time performance, and can be continuously debugged until the ideal control effect is achieved.

Description of drawings:

Fig. 1 is the flow chart of the gray predictive terminal sliding mode control method for permanent magnet synchronous motor provided by the embodiment of the present invention;

FIG. 2 is a structural diagram of a gray prediction terminal sliding mode control provided by an embodiment of the present invention.

Detailed ways:

The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

As shown in Figure 1, it is a flow chart of a gray predictive terminal sliding mode control method for permanent magnet synchronous motors provided by this embodiment, including establishing a mathematical model of permanent magnet synchronous motors and using genetic algorithms to reselect the appropriate m ^* and n ^* , the sliding mode surface of the selected terminal sliding mode, the adjustment item is introduced according to the gray prediction principle and the terminal sliding mode control principle, and the final control item is obtained. Fig. 2 is the determined controller of the control method of the present embodiment Structural diagram, including finding the main deviation, deriving the main deviation, gray prediction, genetic algorithm processing, and designing the terminal sliding mode control signal. First, the input expected speed signal is subtracted from the speed of the permanent magnet synchronous motor measured by the speed sensor. Error amount e _{1, k} , and then calculate the first derivative e 2 _{, k} of e _{1, k} , and predict the change of e _{1, k} through the gray online prediction method. Then carry out the genetic algorithm processing on the predicted value to prevent the chattering of the system caused by the excessive overshoot caused by the predicted value. The advantage of the genetic algorithm is that it has been artificially judged, and has convergence and accuracy. The result obtained through gray prediction and genetic algorithm processing is u _{ga, k} control item. At the same time, the control equation u _{s, k} +u _{eq, k} obtained through terminal sliding mode processing is brought into the permanent magnet synchronous motor control system by adding the two new control equations. The specific method is as follows.

Step 1, establish the mathematical model of the permanent magnet synchronous motor, that is, the torque and the equation of motion of the discrete permanent magnet synchronous motor system, as shown in formula (1) and formula (2) respectively;

in, is the derivation of the rotational speed, T _e is the electromagnetic torque, T _l is the load torque, n _p is the number of pole pairs, ψ _a is the flux linkage between the permanent magnet and the stator, i _{q, k} is the current of the quadrature axis The sampling value of the component in period k, J is the moment of inertia, ω _k is the sampling value of the rotational speed of the rotor electrical angular velocity in k period, ω _k-1 is the sampling value of the rotational speed of the rotor electrical angular velocity in the previous period k, B is the viscous Friction coefficient, T is the sampling period.

The parameters of the permanent magnet synchronous motor in this embodiment are: number of pole pairs n _p = 4, moment of inertia J = 0.0006329, flux linkage ψ _a = 0.175wb, viscous friction coefficient B = 0.0003035.

Step 2. Use the genetic algorithm to reselect the parameters m and n, use the photoelectric encoder to measure the rotational speed of the adjacent cycle of the motor, and calculate the rotational speed error when programming with DSP software, then accumulate and sum the obtained errors, and then introduce Parameters X and Y, obtain suitable parameters m ^* and n ^* , specifically include the following steps:

Step 2.1, according to the gray prediction principle and the speed error and its accumulation generation, the expressions of the parameters m and n are obtained;

In the gray forecasting theory, the gray forecasting differential equation is Wherein the expression of parameter m and n is as shown in formula (3);

Wherein, the introduced X and Y parameter matrices are as formula (4) and formula (5) respectively;

in, k=1, 2, 3, 4, 5, in specific implementation, the number of k values can be determined according to the actual situation, is the rotational speed error between the period k and the previous period, Its cumulative sum form is From the original error series accumulated into sequence;

Step 2.2, determine the optimum value m ^* and n ^* of parameter m and n with genetic algorithm, concrete method is:

Step 2.2.1, determine the objective function of parameter m and n, as formula (6) and formula (7);

Among them, Mape_m and Mape_n are the absolute errors of the parameters m and n respectively, m _k-1 and m _k are the screening values of the parameter m obtained in the k-1th cycle and the k-th cycle of the genetic algorithm respectively, n _k-1 and n _k-1 is the screening value of the parameter n obtained from the k-1th cycle and the k-th cycle obtained by the genetic algorithm, respectively;

Step 2.2.2, determine the size of the particle swarm population in the genetic algorithm;

The size of the group determines the convergence rate of the genetic algorithm, so the size of the group must be considered. The more the number of groups, the more excellent genetic genes that are retained. In this embodiment, the size of the group is 40;

Step 2.2.3, select the appropriate crossover rate and mutation rate, and carry out the calculation of crossover and mutation;

The genetic algorithm is suitable for solving the global optimization problem. During the evolution of the original population, the good chromosomes are preserved, and the unsuitable ones are eliminated and replaced by new chromosomes. The probability that a new chromosome replaces the eliminated one is called the crossover rate. In the process of evolution, mutations may also occur, directly changing the first-generation chromosomal genes can prevent the problem from falling into local optimum. In this embodiment, the crossover rate is 0.9, the mutation rate is 0.01, and the crossover and mutation are calculated;

Step 2.2.4. Determine whether the absolute errors Mape_m and Mape_n in the objective function reach the preset error range. If yes, obtain the optimal values of parameters m and n, and execute step 2.3. If not, return to step 2.2.3 and start again. Carry out the calculation of crossover and mutation, and finally get the optimal m ^* and n ^* ;

Step 2.3, carry out the gray prediction solution based on genetic algorithm optimization;

Solve the gray prediction equation (8) to get the speed error Predicted value for the next period As shown in formula (9);

Among them, m ^* and n ^* are the optimal values of the parameters obtained through the optimization of the genetic algorithm in step 2, and finally the original error sequence is obtained Predicted value for the next period As shown in formula (10).

Step 3. Determine the terminal sliding mode control variable expression according to the permanent magnet synchronous motor model, and improve the terminal sliding mode control of the gray prediction algorithm based on the genetic algorithm. The specific method is as follows:

Step 3.1, determining the speed error and its derivative error signal;

Set the speed error and its first order derivative error signal as

in, is the given rotational speed, ω _k is the actual rotational speed sampling, e _{1, k} represents the rotational speed error signal in the k period, e _{2, k} is the derivation calculation of the rotational speed error signal in the k period, that is, the first-order derivative error signal, e _{1 , k-1} and e _{2, k-1} are respectively e _{1, k} and e _{2, the value of k} in the k-1 period;

because is the derivative calculation of the rotational speed error signal e _1,k , is to calculate the second derivative of the speed error signal, and put the formulas (1) and (2) into the formula (11) to get the formula (12);

Among them, u _k is the control quantity expression obtained by the terminal sliding mode control, T _{l, k} and T _{l, k-1} are the uncertain disturbance loads in the k period and the k-1th period respectively;

According to the principle of terminal sliding mode control, it is assumed that the following equations are satisfied:

in, d _k is the external uncertain disturbance of the system;

In this example, bring in the motor parameters, you can get a=-0.48, b=-166;

Step 3.2, determine the sliding mode surface of terminal sliding mode control as shown in formula (14);

Among them, s _{2, k} is the sliding mode surface equation, s _{1, k} = e _{1, k} , Δs _{1, k} = s _{1, k} -s _{1, k-1} , is the derivative of s _{1, k} , so there is p, q, and α are parameters adjusted according to the actual situation. They are parameters designed according to the principle of terminal sliding mode control. They can be adjusted continuously to obtain the final definite value. They have no actual physical meaning, but only parameter symbols. The advantages of terminal sliding mode control It is that some parameters can be designed for adjustment without depending on the system parameters;

Step 3.3, determine the control variable expression of the gray prediction terminal sliding mode control, as shown in formula (15);

u _k = u _{eq, k} + u _{s, k} + u _{ga, k} (15)

Among them, u _k is the control variable expression of terminal sliding mode control; u _{eq, k} is the equivalent equation of terminal sliding mode control, as shown in formula (16); u _{s, k} is the nonlinear switching surface equation, as in formula ( 17); u _{ga, k} is the adjustment equation of the improved gray prediction, as shown in formula (18);

u _{s, k} =-b ^-1 [K ₁ sgn(s _{2, k-1} )] (17)

in, is the sliding mode surface equation calculated from the predicted value, and is the result predicted by formula (10), is true derivative; symbolic function σ ₁ is a small normal number, K ₁ and K ₂ are the values to be designed, which can be adjusted according to the actual situation, and ε is the operating range of the sliding surface.

In this embodiment, the parameters used are α=2, σ ₁ =0.0001, ε=0.5, K ₁ =2, K ₁ =10.

During the test and debugging process, due to the characteristics of the terminal sliding mode control, that is, the control parameters can be independent of the motor parameters, and the debugging is carried out continuously until the ideal control effect is achieved.

The error prediction value processed by the genetic algorithm and the original error value are used to predict the next adjustment judgment. The reason for chattering in the terminal sliding mode is that the motion state reaches the vicinity of the sliding mode surface and then passes through the sliding mode surface back and forth. Therefore, when the estimated state point is outside the boundary and moves away from the boundary, the gray prediction terminal sliding mode control will predict A positive one-step adjustment is obtained, which prompts the state point to move toward the sliding mode surface s=0; when the estimated state point is outside the boundary and moves toward the boundary surface, the gray prediction terminal sliding mode control will predict a negative one-step adjustment, prompting The state point moves towards the sliding mode surface s=0, thereby reducing chattering.

According to the adjustment item u _ga,k produced by the above-mentioned improved gray prediction terminal sliding mode control and the sliding mode surface in the actual operation process, combined with the principle of terminal sliding mode control, a kind of permanent magnet synchronous motor provided in this embodiment is used The feasibility analysis of the gray predictive terminal sliding mode control method is as follows:

The adjustments are:

If s _{2, k} > 0 and predicted value then a negative adjustment is required, but because so

If s _{2, k} > 0 and predicted value then a negative adjustment is required, but because so

Both of the above two cases belong to the situation of "when the estimated state point is outside the boundary and moves towards the boundary surface", a negative adjustment is required to make the state point move toward the sliding surface.

If s _{2, k} <0 and predicted value then a positive adjustment is required, but because so

If s _{2, k} <0 and predicted value then a positive adjustment is required, but because Place

Both of the above two cases belong to the situation of "when the estimated state point is outside the boundary and moves in a direction away from the boundary", a positive adjustment needs to be given to make the state point move toward the sliding mode surface.

It can be seen from the above analysis that the adjustment items provided by the control method provided by this embodiment fully meet the system control requirements.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: it can still be Modifications are made to the technical solutions described in the foregoing embodiments, or equivalent replacements are made to some or all of the technical features; these modifications or replacements do not make the essence of the corresponding technical solutions depart from the scope defined by the claims of the present invention.

Claims (1)

1. a gray predictive terminal sliding mode control method for permanent magnet synchronous motor, is characterized in that, comprises the following steps: Step 1. Establish the permanent magnet synchronous motor mathematical model, that is, the torque and motion equation of the discrete permanent magnet synchronous motor system, such as formulas (1) and (2): in, is the derivation of the rotational speed, T _e is the electromagnetic torque, T _l is the load torque, n _p is the number of pole pairs, ψ _a is the flux linkage between the permanent magnet and the stator, i _{q, k} is the current of the quadrature axis The sampling value of the component in period k, J is the moment of inertia, ω _k is the sampling value of the rotational speed of the rotor electrical angular velocity in k period, ω _k-1 is the sampling value of the rotational speed of the rotor electrical angular velocity in the previous period k, B is the viscous Friction coefficient, T is the sampling period; Step 2, using a genetic algorithm to select suitable parameters m ^* and n ^* , specifically including the following steps: Step 2.1, according to the gray prediction principle and the speed error and its accumulation, generate the expressions of the parameters m and n, as shown in formula (3); Among them, the parameter matrix X and Y are as formula (4) and formula (5) respectively; in, is the rotational speed error between time k and the previous cycle, Its cumulative sum form is Represents the original error sequence; Step 2.2, determine the optimum value m ^* and n ^* of parameter m and n with genetic algorithm, concrete method is: Step 2.2.1, determine the objective function, such as formula (6) and formula (7); Among them, Mape_m and Mape_n are the absolute errors of the parameters m and n respectively, m _k-1 and m _k are the screening values of the parameter m obtained in the k-1th cycle and the k-th cycle of the genetic algorithm respectively, and n _k-1 and n _k is the screening value of the parameter n obtained from the k-1th cycle and the kth cycle obtained by the genetic algorithm, respectively; Step 2.2.2, determine the size of the particle swarm population in the genetic algorithm; Step 2.2.3, select the appropriate crossover rate and mutation rate, and carry out the calculation of crossover and mutation; Step 2.2.4, judge whether the absolute errors Mape_m and Mape_n in the objective function reach the preset error range, if so, get the optimal values of parameters m and n, execute step 2.3, if not, return to step 2.2.3, and start again Carry out the calculation of crossover and mutation, and finally get the optimal m ^* and n ^* ; Step 2.3, carry out the gray prediction solution based on genetic algorithm optimization; Solve the gray prediction equation (8) to get the speed error Predicted value for the next period As shown in formula (9); Among them, m ^* and n ^* are the optimal values of the parameters obtained through the optimization of the genetic algorithm in step 2.2; Finally, the original error sequence is obtained Predicted value for the next period As shown in formula (10); Step 3, improving the terminal sliding mode control of the gray prediction algorithm based on the genetic algorithm; Step 3.1, determine the speed error and its derivative error signal according to the permanent magnet synchronous motor model, as shown in formula (11); Among them, e _{1, k} is the rotational speed error signal in the k period, e _{2, k} is the derivation calculation of the rotational speed error signal in the k period, that is, the first-order derivative error signal, is the given speed, ω _k is the actual speed sampling, e _{1, k-1} and e _{2, k-1} are the values of e _{1, k} and e _{2, k} in the k-1 cycle respectively; According to the mathematical model formula (1) and formula (2) of the permanent magnet synchronous motor, and calculate the second derivative of the speed error, the first-order and second-order derivative error signals of the speed are obtained, as shown in formula (12); in, is the first derivative of the speed error signal e _1,k , is the second-order derivative of the speed error signal, u _k is the expression of the control quantity obtained by the terminal sliding mode control, T _{l, k} and T _{l, k-1} are the different values in the k cycle and the k-1th cycle Determine the disturbance load; According to the principle of terminal sliding mode control, it is assumed that the following equations are satisfied: in, d _k is the external uncertain disturbance of the system; Step 3.2, determine the sliding mode surface of terminal sliding mode control as shown in formula (14); Among them, s _{2, k} is the sliding mode surface equation, s _{1, k} = e _{1, k} , Δs _{1, k} = s _{1, k} -s _{1, k-1} , is the derivative of s _{1, k} , so there is p, q and α are parameters adjusted according to the actual situation; Step 3.3, determine the control variable expression of the gray prediction terminal sliding mode control, as shown in formula (15); u _k = u _{eq, k} + u _{s, k} + u _{ga, k} (15) Among them, u _k is the control quantity expression of terminal sliding mode control; u _{eq, k} is the equivalent equation of terminal sliding mode control, as shown in formula (16); u _{s, k} is the nonlinear switching surface equation, as in formula ( 17); u _{ga, k} is the adjustment equation of the improved gray prediction, as shown in formula (18); u _{s, k} =-b ^-1 [K ₁ sgn(s _{2, k-1} )] (17) in, is the sliding mode surface equation calculated from the predicted value, That is, the result predicted by formula (10), is true derivative; symbolic function σ ₁ is a small normal number, K ₁ and K ₂ are the values to be designed, and their values are adjusted according to the actual situation, and ε is the operating range of the sliding surface.