CN106712626B - A kind of asynchronous motor forecast Control Algorithm - Google Patents
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
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Abstract
The invention discloses a kind of asynchronous motor forecast Control Algorithms, specially：Linearisation and discrete processes are carried out to control object equation first, according to the discrete models of control object, it obtains different moments state variable predicted value and system of the k moment in prediction domain and exports predicted value, and then obtain the optimum control amount and instant control amount for control object, to obtain the state variable predicted value of subsequent time, instant control amount is applied to asynchronous machine and is controlled.The present invention by derived in detail to Model Predictive Control rolling time horizon signature analysis and to its mathematical model develop discuss on the basis of, according to system variable and its difference and system equation inner link, by extending and converting to state variable, formation state and the double state feedback structures of output, accelerate output quantity convergence rate, so that effectively reducing control domain on the basis of system control information is without any constraint and processing, reducing whole system on-line calculation.
Description
Technical Field
The invention belongs to the technical field of motor control, and relates to an asynchronous motor model prediction control method.
Background
The asynchronous motor has the properties of nonlinearity, strong coupling and multivariable, generally adopts a PI regulator to regulate a system, and has the advantages of simple structure, easy realization and better dynamic performance. However, the system has the defects of being easily influenced by system parameter changes, poor adaptability to load changes, weak anti-interference capability and the like, and in the parameter setting process of the controller, repeated debugging is often required to be carried out depending on a large amount of engineering experience. Therefore, in the situation with high requirement on dynamic performance, the traditional PI regulator is limited and cannot meet the requirement on relevant performance.
Model predictive control was born in the last 70 th century, and a heuristic control algorithm applied in the first industry has been developed into a novel disciplinary branch with rich theory and continuously expanded practical contents. The predictive control aims at the control problem with optimization requirements, the control method has been successful in a complex industrial system since the birth and the development of the control method, and particularly, a model predictive control algorithm has unique advantages on nonlinear constraint problem processing. Through the development of decades, model predictive control is gradually applied to various fields, and particularly, along with the rapid development of a digital signal processor in recent years, a model predictive control strategy is rapidly applied to the field of motor control. In recent years, the predictive control strategy related to the motor model is to improve, develop and combine the algorithm with other algorithms to a great extent, and the respective advantages are utilized to improve the control performance of the whole system. Although the model predictive control method has many advantages, before the model predictive control method is not applied to the field of motor control, the biggest obstacle is that the algorithm is relatively complex, the online calculation amount is large, and the method cannot be accepted by the application field. The development level of the processor at that time can hardly meet the dynamic performance requirement of the system, and the application and development of the algorithm in the field of motor control are delayed. Therefore, the invention focuses on the problem of large calculation amount of the model predictive control algorithm and researches a more efficient and simple control strategy.
Disclosure of Invention
The invention aims to provide a model predictive control method for an asynchronous motor, which solves the problems of large calculated amount and poor real-time performance when a model predictive control algorithm is implemented in an online rolling mode in the existing motor control.
The technical scheme adopted by the invention is that the model predictive control method of the asynchronous motor is implemented according to the following steps:
step 1, carrying out linearization and discrete processing on a voltage equation of a control object:
assume that the discrete mathematical model of the study object is:
wherein x (k) is a state variable, y (k) is an output variable of the system, u (k) is an input variable of the system, A is a system matrix, B is an input matrix, C is an output matrix, and k is the current sampling time;
linearizing and discretely processing a voltage equation of a control object and abstracting the voltage equation into a form of formula (1);
step 2, acquiring state variable predicted values and system output predicted values of the k moment in a prediction domain at different moments according to the discrete mathematical model of the control object;
the predicted values of the state variables at different moments are as follows:
x(k+p|k)＝Apx(k)+Ap-1Bu(k)+Ap-2Bu(k+1)+…+Ap-lBu(k+l-1) (2)
the system outputs the predicted value as:
for a more concise description of the output expression, the variables are defined here:
Y＝[y(k+1|k),y(k+2|k),y(k+3|k),…,y(k+p|k)]T(4)
U＝[u(k+1|k),u(k+2|k),u(k+3|k),…,u(k+l-1|k)]T(5)
the output recursion is represented by the re-description using the above definition:
Y＝Gx(k)+HU (6)
wherein,
it is assumed here that the control quantity of the system can be expressed in the form:
taking the objective function of the optimal control quantity as follows:
J*＝(Rr-Y)(Rr-Y)T+UTRU (8)
wherein R is a weight matrix of the influence of the input on the objective function,for a single dimension equal to the prediction time domainBit vector, Y is the output variable of the system, and U is the input variable of the system.
By substituting formula (8) with formula Y ═ Gx (k) + HU, the following expression can be obtained:
in order to obtain the optimum input control quantity u (k) by J, the minimum requirement dJ/dU is 0:
U＝(HTH+R)-1HT(Rr-Gx(k)) (10)
although all the predicted values in the time domain range at time k can be calculated by equation (10), since the prediction control does not apply all the controlled variables to the controlled object but applies the immediate controlled variable, i.e., the first element of the optimal controlled variable, to the controlled object, the system output predicted value is the input variable at time k when the immediate controlled variable acts on the object:
and 3, performing mathematical transformation on the discrete mathematical model of the control object in the step 1, and combining the state variable predicted value and the system output predicted value obtained in the step 2 to obtain the optimal control quantity and the instant control quantity aiming at the control object.
Step 4, obtaining a state variable predicted value at the next moment according to the optimal control quantity and the instant control quantity of the control object obtained in the step 3 and by combining the formula (2);
and 5, applying the instant control quantity obtained in the step 4 to the asynchronous motor for control, and performing new round of loop solution by using the state variable predicted value at the next moment.
The present invention is also characterized in that,
the system equation of state expansion after the discrete mathematical model of the control object is mathematically transformed is as follows:
wherein O is a zero vector.
The optimal control quantity is as follows:
the current instant control quantity is as follows:
the predicted value of the state variable at the next moment is:
definition ofIs composed ofThe first element of (a) is,is (H)TH+R)-1HTThe first row elements of G are:
the invention has the advantages that on the basis of the rolling time domain characteristic analysis of model predictive control and the detailed derivation evolution discussion of the mathematical model, the state variable is expanded and converted according to the internal relation of the system variable and the difference value thereof and the system equation, so that the converted system presents a state and output dual-state feedback structure in a predictive control mode. By the means, the output feedback which is not in the original control structure is introduced into the control structure, and a dual-state feedback closed-loop structure is formed. The structure can be easily obtained, the output quantity convergence speed is accelerated by feeding back the output state, so that the double-feedback control structure can effectively reduce the control domain and reduce the online calculated quantity of the whole system on the basis of no constraint and processing of system control information.
Drawings
FIG. 1 is a block diagram of a control system for an asynchronous machine model predictive control method of the present invention;
FIG. 2 is a block diagram of a model predictive control architecture based on single-state feedback;
FIG. 3 is a block diagram of a model predictive control architecture based on two-state feedback.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention provides a model prediction control method for an asynchronous motor, which adopts a double closed-loop vector control system. The vector control system comprises a speed outer loop and a current inner loop. As shown in fig. 1: the current signal detection circuit 3 detects the three-phase current of the motor under a three-phase static coordinate system through the Hall sensor, converts the three-phase current into a current value i under a static two-phase coordinate system through 3s/2s conversion 4sα、isβThen the given rotation speed omega in the speed outer ring is set*And encoder feedback speed omegarThe compared error is regulated by a speed outer loop controller, and q-axis current i under a rotor rotating coordinate system is outputq *，iq *And d-axis given excitation current id *The slip omega is obtained by the slip calculation module 7sWith feedback speed omegarAnd adding the rotation angles, calculating 8, and outputting a motor rotor angle theta. Current value i under static two-phase coordinate systemsα、isβAnd converting the rotor angle theta of the motor into two-phase feedback calculation exciting current i under a rotor rotating coordinate system through 2r/2sdAnd torque current iq. Given exciting current id *And feedback calculating exciting current idTorque current iq *And feedback calculating torque current iqThe result u is obtained by calculation of the model predictive controller 6sd *And usq *. Two-phase voltage u under rotating coordinate systemsd *And usq *After 2r/2s inverse transformation, the two-phase voltage u is converted into a static two-phase coordinate systemsα *、 usβ *And after the PWM wave is generated through the regulation of the PWM generation module 10, the generated PWM wave acts on the three-phase inverter 1 to drive the asynchronous motor module 2 to work.
The invention provides an asynchronous motor model prediction control method, which is implemented according to the following steps:
step 1, a squirrel-cage asynchronous motor is taken as a research object, a stator voltage equation of the asynchronous motor under a synchronous rotating coordinate system (d-q coordinate system) with oriented rotor magnetic field is taken as a control object, and the form of the stator voltage equation is as follows:
in the above formula, RsIs stator resistance, LmFor mutual inductance between stator and rotor, Ls,LrRespectively stator inductance, rotor inductance, Lσ＝σLsTotal leakage inductance, ωsFor synchronous angular velocity, #rIs the rotor flux linkage amplitude, usd,usqD-axis stator voltage, q-axis stator voltage, isd,isqD-axis stator current and q-axis stator current.
Through linearization and discrete processing, an expression form of the following formula can be obtained:
in the formula, TsIs the sampling time.
To facilitate subsequent analysis, equation (2) is abstracted into the following form:
wherein x (k) is a state variable, y (k) is an output variable of the system, u (k) is an input variable of the system, A is a system matrix, B is an input matrix, C is an output matrix, and k is the current sampling time.
Assuming that the prediction domain range is p and the control domain range is l, the relationship between the two ranges can be obtained according to the prediction control theory: p is more than or equal to l. General definition: when the time k is taken as a starting point, the input control sequence is u (k), u (k +1), …, u (k + l-1), and the output state sequence is predicted under the action of the control sequence to be x (k +1| k), x (k +2| k), …, x (k + p | k), wherein the meaning of x (k + p | k) is that the predicted value of the time k + p in the domain is predicted on the basis of the state of the time k.
Step 2, obtaining state variable predicted values and system output predicted values of the k time in the prediction domain at different times:
based on the discrete mathematical model of the control object in the step 1, the predicted values of the state variables at different moments in the prediction domain at the moment k can be deduced:
x(k+p|k)＝Apx(k)+Ap-1Bu(k)+Ap-2Bu(k+1)+…+Ap-lBu(k+l-1) (4)
the system output prediction value can be obtained on the basis of obtaining the state prediction:
the conclusion can be reached by recursions (4) and (5): in the prediction domain, the state variables and the output prediction sequence depend on the starting time x (k) and the control sequence u (k + i), i being 0,1, … l-1.
For a more concise description of the output expression, the variables are defined here:
Y＝[y(k+1|k),y(k+2|k),y(k+3|k),…,y(k+p|k)]T(6)
U＝[u(k+1|k),u(k+2|k),u(k+3|k),…,u(k+l-1|k)]T(7)
the output recursion is represented by the re-description using the above definition:
Y＝Gx(k)+HU (8)
wherein,
assume that the control vector for the system is:
the objective function of the optimal control quantity is:
J*＝(Rr-Y)(Rr-Y)T+UTRU (10)
wherein R is a weight matrix of the influence of the input on the objective function,is a unit vector with dimension equal to the prediction time domain.
By substituting formula (10) with formula Y ═ Gx (k) + HU, the following expression can be obtained:
in order to make J take a minimum u (k), the minimum requirement dJ can be passed*The value/dU is determined as 0:
U＝(HTH+R)-1HT(Rr-Gx(k)) (12)
although all predicted values in the prediction time domain range at the time k can be calculated by equation (12), the input variables when acting on the target at the time k are:
due to the special form of G, H, together with the control quantities ultimately applied to the control objects, it is possible to derive, through careful derivation, certain link relationships that exist therein, and to define:
alpha isa first element, β is (H)TH+R)-1HTG head line element.
Therefore, the predicted value of the state variable at the next moment can be obtained as follows:
step 3, as shown in fig. 2, a model predictive control mode that seeks an optimal control target can be obtained through step 2, and is represented as a structural form of single-state feedback in a normal state. Meanwhile, the control domain size of the system is considered to be an important constraint condition of the online calculation amount of the algorithm. Therefore, on the premise of ensuring that the output performance index is not changed, reducing the control range of the control domain is an effective method for solving the problem of online implementation of model predictive control.
Mathematically varying the discrete model of the system described in step 1:
the original state equation is replaced by equation (15), and the following state-extended system equation can be obtained by using the state extension method:
wherein O is a zero vector.
The form of the input and output sequence is described and predicted according to the new state equation, and the optimal control quantity can be deduced according to equation (11):
in the same way, the current instant control quantity can be obtained as follows:
in the formulaHas similarity with the corresponding structures of G and H in the step 2, only shows differences, definesIs composed ofThe first element of (a) is,is (H)TH+R)-1HTThe first row elements of G are:
the following conclusion is obtained by analyzing the structures of the output matrix C and the system matrix A after state expansion:last column of the matrix andare identical, and can thus be derivedIs equal toThe last column of (2). According to the relation, matrix transformation is performedCan be described by this formulaAnd then combined with the formula (19) to obtainIs the feedback gain in relation to the state quantity,is the feedback gain related to the output quantity.
The improved state feedback prediction control block diagram obtained through step 4 is shown in fig. 3, and it is obvious from the block diagram that the improved method introduces the output quantity feedback to the input quantity to accelerate the convergence speed of the output quantity.
The invention mainly aims at the problem that the calculated quantity of model predictive control in the process of implementing rolling optimization can not meet the requirements and further can not obtain satisfactory real-time effect on system control, improves the original single-state feedback control structure by adopting the ideas of state conversion and expansion from the basic single-state structure, forms the control structure of dual-state feedback in the invention, and introduces the feedback of the output quantity, thereby reducing the length of a control domain and reducing the calculated quantity. The parameters in the control equation can be easily obtained by comparing the motor equation with the control equation of the final controlled variable, so that the method has universality in practical application.
Claims (4)
1. A model predictive control method for an asynchronous motor is implemented by the following steps:
step 1, carrying out linearization and discrete processing on a voltage equation of a control object:
assume that the discrete mathematical model of the study object is:
wherein x (k) is a state variable, y (k) is an output variable of the system, u (k) is an input variable of the system, A is a system matrix, B is an input matrix, C is an output matrix, and k is the current sampling time;
linearizing and discretely processing a voltage equation of a control object and abstracting the voltage equation into a form of formula (1);
step 2, acquiring state variable predicted values and system output predicted values of the k moment in a prediction domain at different moments according to the discrete mathematical model of the control object;
the predicted values of the state variables at different moments are as follows:
x(k+p|k)＝Apx(k)+Ap-1Bu(k)+Ap-2Bu(k+1)+…+A lp-Bu(k+l-1) (2)
the system outputs the predicted value as:
for a more concise description of the output expression, the variables are defined here:
Y＝[y(k+1|k),y(k+2|k),y(k+3|k),…,y(k+p|k)]T(4)
U＝[u(k+1|k),u(k+2|k),u(k+3|k),…,u(k+l-1|k)]T(5)
the output recursion is represented by the re-description using the above definition:
Y＝Gx(k)+HU (6)
wherein,
it is assumed here that the control quantity of the system can be expressed in the form:
taking the objective function of the optimal control quantity as follows:
J*＝(Rr-Y)(Rr-Y)T+UTRU (8)
where R is the weight moment of the influence of the input on the objective functionThe number of the arrays is determined,the unit vector with the dimension equal to the prediction time domain, Y is the output variable of the system, and U is the input variable of the system;
by substituting formula (8) with formula Y ═ Gx (k) + HU, the following expression can be obtained:
to make J*The optimum input control amount u (k) can be obtained by determining the minimum required condition dJ*The value/dU is determined as 0:
U＝(HTH+R)-1HT(Rr-Gx(k)) (10)
although all the predicted values in the time domain range at time k can be calculated by equation (10), since the prediction control does not apply all the controlled variables to the controlled object but applies the first element of the optimum controlled variable, which is the immediate controlled variable, to the controlled object, the system output predicted value is the input variable when the input variable acts on the object at time k:
and 3, performing mathematical transformation on the discrete mathematical model of the control object in the step 1, and combining the state variable predicted value and the system output predicted value obtained in the step 2 to obtain the optimal control quantity and the instant control quantity aiming at the control object.
Step 4, obtaining a state variable predicted value at the next moment according to the optimal control quantity and the instant control quantity of the control object obtained in the step 3 and by combining the formula (2);
and 5, applying the instant control quantity obtained in the step 4 to the asynchronous motor for control, and performing new round of loop solution by using the state variable predicted value at the next moment.
2. The model predictive control method of the asynchronous machine according to claim 1, characterized in that the system equation of state expansion after the mathematical transformation of the discrete mathematical model of the control object is:
wherein O is a zero vector.
3. The model predictive control method of an asynchronous machine according to claim 1, characterized in that the optimal control quantity is:
the current instant control quantity is as follows:
4. the asynchronous motor model predictive control method of claim 3, wherein the predicted value of the state variable at the next moment is:
definition ofIs composed ofThe first element of (a) is,is (H)TH+R)-1HTThe first row elements of G are:
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| CN108365785B (en) * | 2018-01-12 | 2020-11-17 | 西安理工大学 | Asynchronous motor repeated prediction control method |
| CN109004878B (en) * | 2018-08-21 | 2022-05-27 | 上海应用技术大学 | Dynamic matrix control method for asynchronous motor |
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