CN106452245B - A kind of gray prediction TSM control method for permanent magnet synchronous motor - Google Patents
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- H—ELECTRICITY
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- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
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- H—ELECTRICITY
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Abstract
The present invention provides a kind of gray prediction TSM control method for permanent magnet synchronous motor, is related to the control technology field of ac motor.This method includes establishing permanent magnet synchronous motor mathematical model, selecting suitable m again with genetic algorithm*And n*, selected terminal sliding mode sliding-mode surface, adjustment item introduced according to gray prediction principle and TSM control principle, obtains final control item.A kind of gray prediction TSM control method for permanent magnet synchronous motor provided by the invention, two parameters (m and n) during prediction algorithm are selected again using principle of genetic algorithm, so that the two parameters are more reasonable, obtain more appropriate error prediction value, permanent magnet synchronous motor is set to control Process Precision higher, the advantages of buffeting and reduce and reduce, and not influencing quick response effect and strong robustness that TSM control itself has, and there is real-time.
Description
The technical field is as follows:
the invention relates to the technical field of control of alternating current motors, in particular to a gray prediction terminal sliding mode control method for a permanent magnet synchronous motor.
Background art:
the permanent magnet synchronous motor has the advantages of simple structure, small volume, high power density, low processing and assembling cost, no electric ring electric brush and the like, and is applied to a plurality of fields.
With the widespread use of permanent magnet synchronous motors in recent years, many researches are made on algorithms of control methods of permanent magnet synchronous motors, wherein vector control methods and direct torque control methods are widely used. The application of the terminal sliding mode control method in permanent magnet synchronous motor control enables the motor control to be very convenient and fast, the maximum advantage is that the terminal sliding mode control does not depend on parameters of the motor and complex coupling relations between the parameters and the parameters, the purpose of controlling the motor can be achieved by properly introducing the parameters according to the running condition of the motor through the terminal sliding mode control, the algorithm is easy to realize, the response speed is high, the calculated amount is small, and the accuracy is high. However, the terminal sliding mode control depends on errors, that is, if the terminal sliding mode control cannot be realized without the errors, the application of the terminal sliding mode control is limited.
The learners improve the terminal sliding mode control by using a gray prediction method, predict and judge the running trend of the motor in the running process in real time in the control process, and make adjustment in time to obtain a good effect. However, the problem is that the adjustment value given in the gray prediction process is too large due to the limitation of the prediction method itself, which causes large buffeting, or causes a stable error, so that the terminal sliding mode control with prediction function still has a place to be improved.
The invention content is as follows:
aiming at the defects of the prior art, the invention provides a gray prediction terminal sliding mode control method for a permanent magnet synchronous motor, which reselects two parameters (m and n) in the prediction algorithm process by using a genetic algorithm principle, so that the two parameters are more reasonable, a more proper error prediction value is obtained, the precision of the permanent magnet synchronous motor control process is higher, buffeting is reduced, and the quick response effect and the strong robustness of the terminal sliding mode control are not influenced.
A gray prediction terminal sliding mode control method for a permanent magnet synchronous motor comprises the following steps:
step 1, establishing a mathematical model of the permanent magnet synchronous motor, namely a torque and motion equation of a discrete permanent magnet synchronous motor system, as shown in formulas (1) and (2):
wherein,is derived from the speed of rotation, TeFor electromagnetic torque, TlFor load torque, npIs a logarithm of poles,. psiaFlux linkage, i, for permanent magnet interlinking with statorq，kIs the sampling value of the current component of the quadrature axis in the k period, J is the moment of inertia, omegakSampling value of rotation speed, omega, of rotor electrical angular velocity in k periodk-1The rotating speed sampling value of the rotor electrical angular speed in the previous period of k is shown, B is the viscous friction coefficient, and T is the sampling period.
Step 2, selecting proper parameter m by using genetic algorithm*And n*The method specifically comprises the following steps:
step 2.1, generating an expression of the parameters m and n according to a grey prediction principle, a rotating speed error and accumulation of the rotating speed error, wherein the expression is shown as a formula (3);
wherein, the parameter matrixes X and Y are respectively shown as a formula (4) and a formula (5);
wherein,k＝1、2、3、4、5，is the rotation speed error between the moment k and the previous period,the accumulated summation form is Representing the original error sequence;
step 2.2, determining the optimal values m of the parameters m and n by using a genetic algorithm*And n*The specific method comprises the following steps:
step 2.2.1, determining a target function as shown in a formula (6) and a formula (7);
wherein, Mape _ m and Mape _ n are absolute errors of parameters m and n respectively, and m isk-1And mkThe screening values of the parameter m obtained in the k-1 th period and the k-th period in the genetic algorithm are respectively nk-1And nkScreening values of the parameter n obtained in the k-1 th period and the k-1 th period obtained by a genetic algorithm respectively;
step 2.2.2, determining the size of the particle group in the genetic algorithm;
2.2.3, selecting proper crossing rate and variation rate, and calculating crossing and variation;
step 2.2.4, judging whether the absolute errors Mape _ m and Mape _ n in the target function areWhen the preset error range is reached, if yes, the optimal values of the parameters m and n are obtained, the step 2.3 is executed, if not, the step 2.2.3 is returned, the calculation of crossing and variation is carried out again, and finally the optimal m is obtained*And n*；
Step 2.3, gray prediction solution based on genetic algorithm optimization is carried out;
solving a grey prediction equation (8) to obtain a rotating speed errorPredicted value of next cycleAs shown in formula (9);
wherein m is*And n*Is the optimal value of the parameter obtained by the genetic algorithm optimization of the step 2.2;
finally obtaining the original error sequencePredicted value of next cycleAs 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, determining a rotating speed error and a derivative error signal thereof according to the permanent magnet synchronous motor model, as shown in a formula (11);
wherein e is1，kIs the rotational speed error signal in the k period, e2，kIs the calculation of the derivative of the k-period speed error signal, i.e. the first derivative error signal,is a given rotational speed, ωkIs the actual rotational speed sample, e1，k-1And e2，k-1Are each e1，kAnd e2，kThe value at k-1 period;
according to the mathematical model formula (1) and formula (2) of the permanent magnet synchronous motor, solving a second derivative of the rotating speed error to obtain first and second derivative error signals of the rotating speed, as shown in formula (12);
wherein,is to the rotating speed error signal e1，kThe first derivative of (a) is,is the second derivative, u, of the speed error signalkIs a controlled quantity expression, T, derived from terminal sliding mode controll，kAnd Tl，k-1Respectively, uncertain disturbance load in a k period and a k-1 period;
according to the terminal sliding mode control principle, the following equation is satisfied:
wherein,dkis an external uncertain disturbance of the system;
step 3.2, determining the sliding mode surface of the terminal sliding mode control as shown in a formula (14);
wherein s is2，kIs the sliding mode surface equation, s1，k＝e1，k，Δs1，k＝s1，k-s1，k-1，Is to s1，kIs derived fromp, q and α are parameters adjusted according to actual conditions;
step 3.3, determining a control quantity expression of sliding mode control of the gray prediction terminal, as shown in a formula (15);
uk＝ueq，k+us，k+uga，k(15)
wherein u iskA control quantity expression for terminal sliding mode control; u. ofeq，kIs an equivalent equation of terminal sliding mode control, as shown in formula (16); u. ofs，kA nonlinear switching surface equation, as shown in equation (17); u. ofga，kIs an adjustment equation of the gray prediction after improvement, as shown in formula (18);
us，k＝-b-1[K1sgn(s2，k-1)](17)
wherein,is a sliding mode surface equation calculated according to a predicted value,i.e., the result predicted by equation (10),is toDerivation is carried out; symbolic functionσ1Is a very small normal number, K1、K2The method is a value to be designed, the value is adjusted according to the actual situation, and epsilon is the sliding mode surface operation range.
According to the technical scheme, the invention has the beneficial effects that: the gray prediction terminal sliding mode control method for the permanent magnet synchronous motor optimizes two parameters (m and n) in the prediction algorithm process by using the genetic algorithm principle, and uses a more reasonable parameter m*And n*A more proper error predicted value is obtained, and the prediction judgment of the next adjustment is more accurately carried out, so that the precision of the control process of the permanent magnet synchronous motor is higher, the buffeting is reduced, and the robustness of terminal sliding mode control is kept; because the terminal sliding mode control has the characteristic that the control parameters can be irrelevant to the motor parameters, the control and debugging process of the terminal sliding mode control does not influence the advantages of quick response effect and strong robustness of the terminal sliding mode control, and the terminal sliding mode control has real-time property,the debugging can be continuously carried out until an ideal control effect is achieved.
Description of the drawings:
fig. 1 is a flowchart of a gray prediction terminal sliding-mode control method for a permanent magnet synchronous motor according to an embodiment of the present invention;
fig. 2 is a sliding mode control structure diagram of a gray prediction terminal according to an embodiment of the present invention.
The specific implementation mode is as follows:
the following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
As shown in fig. 1, a flow chart of a gray prediction terminal sliding-mode control method for a permanent magnet synchronous motor provided for this embodiment includes establishing a mathematical model of the permanent magnet synchronous motor, and reselecting a suitable m by using a genetic algorithm*And n*Selecting a sliding mode surface of a terminal sliding mode, introducing an adjustment item according to a gray prediction principle and a terminal sliding mode control principle to obtain a final control item, and FIG. 2 is a controller structure diagram determined by the control method of the embodiment, and the method comprises the steps of calculating main deviation, deriving the main deviation, predicting gray, processing a genetic algorithm, designing a terminal sliding mode control signal, and firstly subtracting an input expected speed signal and the speed of the permanent magnet synchronous motor measured by a speed sensor to obtain an error quantity e1，kThen calculate e1，kFirst derivative e of2，kE by gray online prediction method1，kTo make a prediction. And then, the predicted value is processed by a genetic algorithm, so that buffeting of the system caused by overlarge overshoot caused by the predicted value is prevented, and the genetic algorithm has the advantages of being artificially judged and having convergence and accuracy. The result obtained by gray prediction and genetic algorithm processing is uga，kAnd (6) controlling items. Control equation u obtained by terminal sliding mode processings，k+ueq，kAnd adding the two to obtain a new control equation to be introduced into the permanent magnet synchronous motor control system. The specific method is as follows.
Step 1, establishing a mathematical model of the permanent magnet synchronous motor, namely a torque and a motion equation of a discrete permanent magnet synchronous motor system, which are respectively shown as a formula (1) and a formula (2);
wherein,is derived from the speed of rotation, TeFor electromagnetic torque, TlFor load torque, npIs a logarithm of poles,. psiaFlux linkage, i, for permanent magnet interlinking with statorq，kIs the sampling value of the current component of the quadrature axis in the k period, J is the moment of inertia, omegakSampling value of rotation speed, omega, of rotor electrical angular velocity in k periodk-1The rotating speed sampling value of the rotor electrical angular speed in the previous period of k is shown, B is the viscous friction coefficient, and T is the sampling period.
In this embodiment, the parameters of the permanent magnet synchronous motor are as follows: number of pole pairs np4, moment of inertia J0.0006329, flux linkage psia0.175wb, and 0.0003035.
Step 2, reselecting the parameters m and n by using a genetic algorithm, measuring the adjacent period rotating speed of the motor by using a photoelectric encoder, solving the rotating speed error when programming by using DSP software, then accumulating and summing the obtained errors, and then introducing the parameters X and Y to obtain the proper parameter m*And n*The method specifically comprises the following steps:
step 2.1, obtaining an expression of the parameters m and n according to a grey prediction principle, a rotating speed error and accumulation generation of the rotating speed error;
the gray prediction differential equation in the gray prediction theory isWherein the expressions of the parameters m and n are shown as formula (3);
wherein, the introduced X and Y parameter matrixes are respectively shown as a formula (4) and a formula (5);
wherein,k is 1, 2, 3, 4, 5, in the specific implementation, the number of k values can be determined according to the actual situation,is the rotation speed error of the k time period and the previous period,the accumulated summation form isFrom the original error seriesIs accumulated intoA sequence;
step 2.2, determining the optimal values m of the parameters m and n by using a genetic algorithm*And n*The specific method comprises the following steps:
step 2.2.1, determining target functions of the parameters m and n, as shown in a formula (6) and a formula (7);
wherein, Mape _ m and Mape _ n are absolute errors of parameters m and n respectively, and m isk-1And mkThe screening values of the parameter m obtained in the k-1 th period and the k-th period in the genetic algorithm are respectively nk-1And nk-1Screening values of the parameter n obtained in the k-1 th period and the k-1 th period obtained by a genetic algorithm respectively;
step 2.2.2, determining the size of the particle group in the genetic algorithm;
the size of the population determines the convergence rate of the genetic algorithm, so the size of the population must be considered, the larger the number of the population, the more excellent genetic genes are retained, and in the embodiment, the size of the population is 40;
2.2.3, selecting proper crossing rate and variation rate, and calculating crossing and variation;
the genetic algorithm is suitable for solving a global optimization problem, and in the process of the evolution of an original population, excellent chromosomes are reserved, and inappropriate chromosomes are eliminated and replaced by new chromosome copies. The probability of a new chromosome replacing a rejected chromosome is called the crossover rate. In the process of evolution, mutation can also occur, and the first generation of chromosome genes are directly changed, so that the problem can be prevented from falling into local optimization. In this embodiment, the crossover rate is 0.9, and the variation rate is 0.01, and crossover and variation are calculated;
step 2.2.4, judging whether the absolute errors Mape _ m and Mape _ n in the target function reach a preset error range, if so, obtaining the optimal values of the parameters m and n, executing the step 2.3, if not, returning to the step 2.2.3, carrying out cross and variation calculation again, and finally obtaining the optimal m*And n*；
Step 2.3, gray prediction solution based on genetic algorithm optimization is carried out;
solving a grey prediction equation (8) to obtain a rotating speed errorPredicted value of next cycleAs shown in formula (9);
wherein m is*And n*The optimal value of the parameter is obtained through the genetic algorithm optimization in the step 2, and the original error sequence is finally obtainedPredicted value of next cycleAs shown in equation (10).
Step 3, determining a terminal sliding mode control expression according to the permanent magnet synchronous motor model, and improving the terminal sliding mode control of the gray prediction algorithm based on the genetic algorithm, wherein the specific method comprises the following steps:
step 3.1, determining a rotation speed error and a derivative error signal thereof;
setting the error of the rotation speed and the error signal of the first derivative thereof as
Wherein,is a given rotational speed, ωkIs the actual rotational speed sample, e1，kRepresenting the error signal of the rotation speed in k periods, e2，kIs a derivative calculation of a k-period speed error signal, i.e. a first derivative error signal, e1，k-1And e2，k-1Are each e1，kAnd e2，kThe value at k-1 period;
due to the fact thatIs to the rotating speed error signal e1，kThe derivation calculation of (a) is performed,solving a second derivative of the speed error signal, and bringing the formula (1) and the formula (2) into the formula (11) to obtain a formula (12);
wherein u iskIs a controlled quantity expression, T, derived from terminal sliding mode controll，kAnd Tl，k-1Respectively, uncertain disturbance load in a k period and a k-1 period;
according to the terminal sliding mode control principle, the following equation is satisfied:
wherein,dkis an external uncertain disturbance of the system;
in this example, motor parameters are taken in, and a ═ 0.48, b ═ 166;
step 3.2, determining the sliding mode surface of the terminal sliding mode control as shown in a formula (14);
wherein s is2，kIs the sliding mode surface equation, s1，k＝e1，k，Δs1，k＝s1，k-s1，k-1，Is to s1，kIs derived fromp, q and α are parameters adjusted according to actual conditions, are parameters designed according to a terminal sliding mode control principle, can be continuously adjusted to obtain a final determined value, have no actual physical significance, are only parameter symbols, and have the advantage that some parameters can be designed for adjustment without depending on system parameters;
step 3.3, determining a control quantity expression of sliding mode control of the gray prediction terminal, as shown in a formula (15);
uk＝ueq，k+us，k+uga，k(15)
wherein u iskA control quantity expression for terminal sliding mode control; u. ofeq，kIs an equivalent equation of terminal sliding mode control, as shown in formula (16); u. ofs，kA nonlinear switching surface equation, as shown in equation (17); u. ofga，kIs an adjustment equation of the gray prediction after improvement, as shown in formula (18);
us，k＝-b-1[K1sgn(s2，k-1)](17)
wherein,is a sliding mode surface equation calculated according to a predicted value,whileThat is, the result obtained by the prediction of the formula (10),is toDerivation is carried out; symbolic functionσ1Is a very small normal number, K1、K2The method is a value to be designed, the value can be adjusted according to the actual situation, and epsilon is the sliding mode surface operation range.
in the present embodiment, the parameter α is 2, σ1＝0.0001，ε＝0.5，K1＝2，K1＝10。
In the process of test debugging, due to the characteristics of terminal sliding mode control, namely control parameters can be irrelevant to motor parameters, and debugging is continuously carried out until an ideal control effect is achieved.
And (4) carrying out adjustment judgment on the next step of prediction by using the error prediction value processed by the genetic algorithm and the original error value. The reason that the terminal sliding mode generates buffeting is that the moving state reaches the position near the sliding mode surface and then passes back through the sliding mode surface, so when the estimated state point is outside the boundary and moves towards the direction far away from the boundary, the gray prediction terminal sliding mode control can predict positive one-step adjustment, and the state point is promoted to move towards the sliding mode surface s which is equal to 0; when the estimated state point is outside the boundary and moves towards the boundary surface, the gray predictive terminal sliding mode control predicts that a negative one-step adjustment is obtained, and the state point is caused to move towards the sliding mode surface s which is 0, so that buffeting is reduced.
According to the improved gray prediction terminal sliding mode control and the adjustment item u generated by the sliding mode surface action in the actual operation processga，kIn combination with the terminal sliding mode control principle, feasibility analysis is made on the gray prediction terminal sliding mode control method for the permanent magnet synchronous motor provided in this embodiment as follows:
the adjustment items are as follows:
if s2，k> 0 and predict valueIt is necessary to give a negative adjustment,thenDue to the fact thatTherefore, it is not only easy to use
If s2，k> 0 and predict valueIt is necessary to give a negative adjustment,thenDue to the fact thatTherefore, it is not only easy to use
Both of the above cases belong to the case "when the estimated state point is outside the boundary and moving toward the boundary surface", and a negative adjustment is required to make the state point want to move in the slip-form surface.
If s2，k< 0 and predicted valueIt is necessary to give a positive adjustment,thenDue to the fact thatTherefore, it is not only easy to use
If s2，k< 0 and predicted valueIt is necessary to give a positive adjustment,thenDue to the fact thatWhat is needed is
Both of these cases are the case when the estimated state point is outside the boundary and moving away from the boundary, and positive adjustment needs to be given to move the state point towards the slip-form face.
From the above analysis, it can be seen that the adjustment items given by the control method provided by the embodiment completely meet the system control requirements.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.
Claims (1)
1. A gray prediction terminal sliding mode control method for a permanent magnet synchronous motor is characterized by comprising the following steps:
step 1, establishing a mathematical model of the permanent magnet synchronous motor, namely a torque and motion equation of a discrete permanent magnet synchronous motor system, as shown in formulas (1) and (2):
wherein,is derived from the speed of rotation, TeFor electromagnetic torque, TlFor load torque, npIs a logarithm of poles,. psiaFlux linkage, i, for permanent magnet interlinking with statorq，kIs the sampling value of the current component of the quadrature axis in the k period, J is the moment of inertia, omegakSampling value of rotation speed, omega, of rotor electrical angular velocity in k periodk-1A rotating speed sampling value of the rotor electrical angular speed in the previous period of k is obtained, B is a viscous friction coefficient, and T is a sampling period;
step 2, selecting proper parameter m by using genetic algorithm*And n*The method specifically comprises the following steps:
step 2.1, generating an expression of the parameters m and n according to a grey prediction principle, a rotating speed error and accumulation of the rotating speed error, wherein the expression is shown as a formula (3);
wherein, the parameter matrixes X and Y are respectively shown as a formula (4) and a formula (5);
wherein, is the rotation speed error between the moment k and the previous period,the accumulated summation form is Representing the original error sequence;
step 2.2, determining the optimal values m of the parameters m and n by using a genetic algorithm*And n*The specific method comprises the following steps:
step 2.2.1, determining a target function as shown in a formula (6) and a formula (7);
wherein, Mape _ m and Mape _ n are absolute errors of parameters m and n respectively, and m isk-1And mkThe screening values of the parameter m obtained in the k-1 th period and the k-th period in the genetic algorithm are respectively nk-1And nkScreening values of the parameter n obtained in the k-1 th period and the k-1 th period obtained by a genetic algorithm respectively;
step 2.2.2, determining the size of the particle group in the genetic algorithm;
2.2.3, selecting proper crossing rate and variation rate, and calculating crossing and variation;
step 2.2.4, judging whether the absolute errors Mape _ m and Mape _ n in the target function reach a preset error range, if so, obtaining the optimal values of the parameters m and n, executing the step 2.3, if not, returning to the step 2.2.3, carrying out cross and variation calculation again, and finally obtaining the optimal m*And n*；
Step 2.3, gray prediction solution based on genetic algorithm optimization is carried out;
solving a grey prediction equation (8) to obtain a rotating speed errorPredicted value of next cycleAs shown in formula (9);
wherein m is*And n*Is the optimal value of the parameter obtained by the genetic algorithm optimization of the step 2.2;
finally obtaining the original error sequencePredicted value of next cycleAs 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, determining a rotating speed error and a derivative error signal thereof according to the permanent magnet synchronous motor model, as shown in a formula (11);
wherein e is1，kIs the rotational speed error signal in the k period, e2，kIs the calculation of the derivative of the k-period speed error signal, i.e. the first derivative error signal,is a given rotational speed, ωkIs the actual rotational speed sample, e1，k-1And e2，k-1Are each e1，kAnd e2，kThe value at k-1 period;
according to the mathematical model formula (1) and formula (2) of the permanent magnet synchronous motor, solving a second derivative of the rotating speed error to obtain first and second derivative error signals of the rotating speed, as shown in formula (12);
wherein,is to the rotating speed error signal e1，kThe first derivative of (a) is,is the second derivative, u, of the speed error signalkIs a controlled quantity expression, T, derived from terminal sliding mode controll，kAnd Tl，k-1Respectively, uncertain disturbance load in a k period and a k-1 period;
according to the terminal sliding mode control principle, the following equation is satisfied:
wherein,dkis an external uncertain disturbance of the system;
step 3.2, determining the sliding mode surface of the terminal sliding mode control as shown in a formula (14);
wherein s is2，kIs the sliding mode surface equation, s1，k＝e1，k，Δs1，k＝s1，k-s1，k-1，Is to s1，kIs derived fromp, q and α are parameters adjusted according to actual conditions;
step 3.3, determining a control quantity expression of sliding mode control of the gray prediction terminal, as shown in a formula (15);
uk＝ueq，k+us，k+uga，k(15)
wherein u iskA control quantity expression for terminal sliding mode control; u. ofeq，kIs an equivalent equation of terminal sliding mode control, as shown in formula (16); u. ofs，kA nonlinear switching surface equation, as shown in equation (17); u. ofga，kIs an adjustment equation of the gray prediction after improvement, as shown in formula (18);
us，k＝-b-1[K1sgn(s2，k-1)](17)
wherein,is a sliding mode surface equation calculated according to a predicted value,i.e., the result predicted by equation (10),is toDerivation is carried out; symbolic functionσ1Is a very small normal number, K1、K2The method is a value to be designed, the value is adjusted according to the actual situation, and epsilon is the sliding mode surface operation range.
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