CN106712626B - A kind of asynchronous motor forecast Control Algorithm - Google Patents
A kind of asynchronous motor forecast Control Algorithm Download PDFInfo
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- CN106712626B CN106712626B CN201710056940.6A CN201710056940A CN106712626B CN 106712626 B CN106712626 B CN 106712626B CN 201710056940 A CN201710056940 A CN 201710056940A CN 106712626 B CN106712626 B CN 106712626B
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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
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
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 motor control technology fields, are related to a kind of asynchronous motor forecast Control Algorithm.
Background technique
Asynchronous machine has the property of non-linear, close coupling, multivariable, is generally used pi regulator and adjusts to system
Section, its structure is simple, easy to accomplish, there is preferable dynamic property.But system exists vulnerable to system parameter variations influence, to negative
The disadvantages of carrying variation adaptability difference and weak anti-interference ability, and during attitude conirol, it generally requires to rely on
A large amount of engineering experiences are debugged repeatedly.It therefore, will using traditional pi regulator to the higher occasion of dynamic performance requirements
By certain limitation, it is not able to satisfy the requirement of correlated performance.
Model Predictive Control is born in 1970s, from initial industrial application heuristic control algorithm through sending out
The exhibition new discipline branch that abundant, practice content is constantly expanded for a theory.PREDICTIVE CONTROL is directed to the control for having optimization demand
Problem obtains some successes, especially model since the control method is born and is developed so far in Complex Industrial Systems
Predictive control algorithm has unique advantage to nonlinear restriction issue handling.Develop by recent decades, Model Predictive Control is
Through gradually being applied in every field, especially in recent years as digital signal processor develops rapidly, Model Predictive Control plan
Application is slightly rapidly developed in the field of motor control.Make a general survey of in recent years about motor model predictive control strategy largely
It is exactly combined to algorithm improvement, development and with other algorithms, improves whole system control performance using respective advantage.Although
Model predictive control method has many advantages, but before not being applied to Motor Control Field, maximum hinders to be exactly the calculation
Method is relatively complicated, and on-line calculation is bigger, can not be received by the application field.With the development level of processor at that time
The dynamic performance requirements that hardly can satisfy system have delayed the algorithm middle application and development in the field of motor control.So
The emphasis point of the present invention problem computationally intensive aiming at Model Predictive Control Algorithm studies a kind of highly efficient, simple control
System strategy.
Summary of the invention
The object of the present invention is to provide a kind of asynchronous motor forecast Control Algorithms, solve mould in existing motor control
Type predictive control algorithm roll online implementation when it is computationally intensive, real-time is poor.
The technical scheme adopted by the invention is that a kind of asynchronous motor forecast Control Algorithm, specifically according to the following steps
Implement：
Step 1, linearisation and discrete processes are carried out to control object voltage equation：
Assuming that the discrete models of research object are：
Wherein, x (k) is state variable, and y (k) is the output variable of system, and u (k) is the input variable of system, and A is to be
System matrix, B is input matrix, and C is output matrix, and k is current sample time；
By the linearisation of control object voltage equation and discrete processes and the form for being abstracted as formula (1)；
Step 2, it according to the discrete models of control object, obtains different moments state of the k moment in prediction domain and becomes
It measures predicted value and system exports predicted value；
Different moments state variable predicted value is：
X (k+p | k)=Apx(k)+Ap-1Bu(k)+Ap-2Bu(k+1)+…+Ap-lBu(k+l-1) (2)
System exports predicted value：
Output expression formula is described in order to conciser, in this defined variable：
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)
It carries out redescribing expression by stepping type is exported using above-mentioned definition：
Y=Gx (k)+HU (6)
Wherein,
It is assumed herein that the control amount of system can be expressed as form：
The objective function for taking optimum control amount is：
J*=(Rr-Y)(Rr-Y)T+UTRU (8)
Wherein, R is the weight matrix that input influences objective function,For dimension and the equal unit of prediction time domain to
Amount, Y are the output variable of system, and U is the input variable of system.
Formula Y=Gx (k)+HU is substituted into formula (8), available following expression：
It, can be by seeking the necessary condition dJ*/dU=0 of minimum in order to enable J* obtains best input control quantity u (k)
It acquires：
U=(HTH+R)-1HT(Rr-Gx(k)) (10)
It can be calculated by formula (10) at the k moment, predict all predicted values in time domain scale, but PREDICTIVE CONTROL not will
All control amounts are applied to control object, but by instant control amount, that is, the header element of Optimal Control amount is sought, control is acted on
Object processed, so the input variable when acting on object at the k moment, system output predicted value are：
Step 3, mathematic(al) manipulation, the shape obtained in conjunction with step 2 are carried out to the discrete models of control object in step 1
State variable predicted value and system export predicted value, obtain the optimum control amount and instant control amount for control object.
Step 4, the optimum control amount and instant control amount of the control object obtained according to step 3 are obtained in conjunction with formula (2)
To the state variable predicted value of subsequent time；
Step 5, asynchronous machine is applied to according to the instant control amount that step 4 obtains control and using subsequent time
State variable predicted value carry out a new wheel circulation and solve.
The features of the present invention also characterized in that
The system equation that the discrete models of control object carry out the conditional extensions after mathematic(al) manipulation is：
Wherein, O is null vector.
Optimum control amount is：
Currently control amount is immediately：
The state variable predicted value of subsequent time is：
DefinitionForHeader element,For (HTH+R)-1HTThe first trip element of G then has：
The invention has the advantages that by detailed to Model Predictive Control rolling time horizon signature analysis and to its mathematical model
Thin derivation is developed on the basis of discussion, according to system variable and its difference and system equation inner link, by state variable
Extension and conversion, so that system is presented under PREDICTIVE CONTROL form and done well and output pair state feedback structures after conversion.Pass through
The output not having in former control structure feedback is introduced into control structure by the means, forms double state feedback closed loop configurations.
It is readily able to obtain from the structure, by accelerating output quantity convergence rate to output state feedback, so that in system control
On the basis of information processed is without any constraint and processing, double back feedback control structure can effectively reduce control domain, reduce whole system and exist
Line computation amount.
Detailed description of the invention
Fig. 1 is the control system block diagram of asynchronous motor forecast Control Algorithm of the present invention；
Fig. 2 is the Model Predictive Control structural block diagram based on single state feedback；
Fig. 3 is the Model Predictive Control structural block diagram based on double state feedbacks.
Specific embodiment
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
The present invention provides a kind of asynchronous motor forecast Control Algorithms, using two close cycles vector control system.Vector
Control system includes speed outer ring and current inner loop two parts.As shown in Figure 1：Current signal detection circuit 3 passes through hall sensing
Device detects three-phase current of the motor under three-phase static coordinate system, by 3s/2s transformation 4, under two phase coordinate system of convert to static
Current value isα、isβ, then by the given rotating speed ω in speed outer ring*With encoder feedback speed omegarThe error to compare is passed through
After speed outer ring controller is adjusted, the q shaft current i under output rotor rotating coordinate systemq *, iq *Exciting current i is given with d axisd *Through
It crosses slip computing module 7 and obtains slip ωsWith feedback speed ωrIt is added the output motor rotor angle θ after rotating angle calculation 8.
Current value i under static two phase coordinate systemsα、isβAnd rotor angle of electric machine θ is converted under rotor rotating coordinate system by 2r/2s
Two-phase feedback calculate exciting current electric current idWith torque current iq.Given exciting current id *Exciting current i is calculated with feedbackd, turn
Square electric current iq *With feedback calculating torque electric current iq, result u is calculated by model predictive controller 6sd *And usq *.Rotation is sat
Two-phase voltage u under mark systemsd *With usq *Two-phase voltage after 2r/2s inverse transformation under two phase coordinate system of convert to static
usα *、 usβ *, by PWM occur module 10 adjusting, generate PWM wave, by the PWM wave of generation act on three-phase inverter 1 it
Afterwards, driving asynchronous machine module 2 works.
The present invention provides a kind of asynchronous motor forecast Control Algorithms, are specifically implemented according to the following steps：
Step 1, using Squirrel Cage Asynchronous Motors as research object, its rotor field-oriented synchronous rotating frame is utilized
Asynchronous machine stator voltage equation is control object under (d-q coordinate system), and form is as follows：
In above formula, RsFor stator resistance, LmThe mutual inductance between rotor, Ls,LrRespectively stator inductance, inductor rotor, Lσ
=σ LsFor total leakage inductance, ωsFor synchronous angular velocity, ψrFor rotor flux amplitude, usd,usqRespectively d axis stator voltage, q axis stator
Voltage, isd,isqRespectively d axis stator current, q axis stator current.
The expression-form shaped like following formula can be obtained by linearisation and discrete processes：
In formula, TsFor the sampling time.
In order to which formula (2) is just abstracted as following form with subsequent analysis：
Wherein, x (k) is state variable, and y (k) is the output variable of system, and u (k) is the input variable of system, and A is system
Matrix, B are input matrix, and C is output matrix, and k is current sample time.
Assuming that prediction domain range is p, control domain range is l, according to predictive control theory it can be concluded that the two should meet pass
System：p≥l.General definition：If using the k moment as starting point, input control sequence be u (k), u (k+1) ..., u (k+l-1),
The lower prediction output state sequence of control sequence effect is x (k+1 | k), x (k+2 | k) ..., x (k+p | k), wherein x (k+p | k)
Represented meaning is that k+p moment predicted value in domain is predicted on the basis of k moment state.
Step 2, different moments state variable predicted value and system of the k moment in prediction domain are obtained and exports predicted value：
Based on control object discrete models in step 1, different moments shape of the k moment in prediction domain can be gone out with recursion
State variable predicted value：
X (k+p | k)=Apx(k)+Ap-1Bu(k)+Ap-2Bu(k+1)+…+Ap-lBu(k+l-1) (4)
It can be concluded that system exports predicted value on the basis of obtaining status predication：
Pass through stepping type (4) and (5) available conclusion：Within the scope of prediction domain, quantity of state and output forecasting sequence
Depending on initial time x (k) and control sequence u (k+i), wherein i=0,1 ... l-1.
Output expression formula is described in order to conciser, in this defined variable：
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)
It carries out redescribing expression by stepping type is exported using above-mentioned definition：
Y=Gx (k)+HU (8)
Wherein,
Assuming that the dominant vector of system is：
The objective function of optimum control amount is：
J*=(Rr-Y)(Rr-Y)T+UTRU (10)
Wherein, R is the weight matrix that input influences objective function,For dimension and the equal unit of prediction time domain to
Amount.
Formula Y=Gx (k)+HU is substituted into formula (10), available following expression：
In order to enable the minimum u (k) that J* is obtained, can pass through minimum necessary condition dJ*/ dU=0 is acquired：
U=(HTH+R)-1HT(Rr-Gx(k)) (12)
It can be calculated by formula (12) at the k moment, predict all predicted values in time domain scale, but PREDICTIVE CONTROL not will
All control amounts are applied to control object, but instant control amount is acted on control object, so acting on pair at the k moment
As when input variable be：
Due to G, the special shape of H can be obtained along with the control amount for being finally implemented on control object by carefully deriving
Certain connection connections present in it out, and define：
α isHeader element, β are (HTH+R)-1HTG first trip element.
Available subsequent time state variable predicted value is accordingly:
Step 3, by the available one kind of step 2 as shown in Fig. 2, seeking the Model Predictive Control mould of optimal control target
Formula shows as the structure type of single state feedback in the normal state.At the same time in view of the control domain size of system is algorithm
The important restrictions condition of on-line calculation.Therefore, under the premise of guaranteeing that output performance index is constant, reduce the control of control domain
Range will be the effective ways for solving the problems, such as Model Predictive Control on-line implement.
System discrete model described in step 1 is subjected to variation mathematically：
Formula (15) are replaced into reset condition equation, and the method available following conditional extensions of adoption status extension
System equation：
Wherein, O is null vector.
According to the form of new state equation description and prediction process kind input and output sequence, and according to formula (11)
Optimum control amount can be pushed over out：
Similarly available current control amount immediately is：
In formulaWith G in step 2, H counter structure has similitude, only to show difference, definitionForHeader element,For (HTH+R)-1HTThe first trip element of G then has：
Analysis is carried out by the structure to the output matrix C and sytem matrix A after progress conditional extensions to draw the following conclusions：Matrix last column withIt is the same, and then it can be concluded thatIt is equal toLast column.According to this relationship, square is carried out
Battle array transformationIt can be described with the formulaCombined again with (19) formula it can be concluded thatIt is related with quantity of state
Feedback oscillator,It is feedback oscillator related with output quantity.
As shown in figure 3, it can be bright by block diagram by the available improved state feedback predictive control block diagram of step 4
Aobvious finds out, output quantity is carried out feedback and is introduced into input quantity quickening output quantity convergence rate by improved method.
The present invention is implementing rolling optimization process calculation amount it is impossible to meet requiring primarily directed to Model Predictive Control, into
And to the effect that cannot be satisfied with of real-time of system control, by from basic single status architecture adoption status conversion with
The thought of extension improves original single state feedback control structure, forms the control structure of double state feedbacks in the present invention, will
The feedback of output quantity introduces, to reduce the length of control domain, reduces calculation amount.By by motor equation and final control amount
Governing equation comparison be easy to obtain parameter in governing equation, so having versatility in practical applications.
Claims (4)
1. a kind of asynchronous motor forecast Control Algorithm, specifically implements according to the following steps：
Step 1, linearisation and discrete processes are carried out to control object voltage equation：
Assuming that the discrete models of research object are：
Wherein, x (k) is state variable, and y (k) is the output variable of system, and u (k) is the input variable of system, and A is system square
Battle array, B is input matrix, and C is output matrix, and k is current sample time；
By the linearisation of control object voltage equation and discrete processes and the form for being abstracted as formula (1)；
Step 2, according to the discrete models of control object, it is pre- to obtain different moments state variable of the k moment in prediction domain
Measured value and system export predicted value；
Different moments state variable predicted value is：
X (k+p | k)=Apx(k)+Ap-1Bu(k)+Ap-2Bu(k+1)+…+Ap-l Bu(k+l-1) (2)
System exports predicted value：
Output expression formula is described in order to conciser, in this defined variable：
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)
It carries out redescribing expression by stepping type is exported using above-mentioned definition：
Y=Gx (k)+HU (6)
Wherein,
It is assumed herein that the control amount of system can be expressed as form：
The objective function for taking optimum control amount is：
J*=(Rr-Y)(Rr-Y)T+UTRU (8)
Wherein, R is the weight matrix that input influences objective function,For the dimension unit vector equal with prediction time domain, Y
For the output variable of system, U is the input variable of system；
Formula Y=Gx (k)+HU is substituted into formula (8), available following expression：
In order to enable J*The best input control quantity u (k) obtained, can be by seeking the necessary condition dJ of minimum*/ dU=0 is asked
?：
U=(HTH+R)-1HT(Rr-Gx(k)) (10)
It can be calculated by formula (10) at the k moment, predict all predicted values in time domain scale, but PREDICTIVE CONTROL will not own
Control amount be applied to control object, but be to seek the header element of Optimal Control amount by instant control amount, act on control pair
As so the input variable when acting on object at the k moment, system output predicted value are：
Step 3, mathematic(al) manipulation, the state variable obtained in conjunction with step 2 are carried out to the discrete models of control object in step 1
Predicted value and system export predicted value, obtain the optimum control amount and instant control amount for control object.
Step 4, the optimum control amount and instant control amount of the control object obtained according to step 3 obtain down in conjunction with formula (2)
The state variable predicted value at one moment；
Step 5, the shape that asynchronous machine control and utilize subsequent time is applied to according to the instant control amount that step 4 obtains
State variable predicted value carries out a new wheel circulation and solves.
2. a kind of asynchronous motor forecast Control Algorithm according to claim 1, which is characterized in that the control object
The system equation of conditional extensions that carries out after mathematic(al) manipulation of discrete models be：
Wherein, O is null vector.
3. a kind of asynchronous motor forecast Control Algorithm according to claim 1, which is characterized in that the optimum control
Amount is：
Currently control amount is immediately：
4. a kind of asynchronous motor forecast Control Algorithm according to claim 3, which is characterized in that the subsequent time
State variable predicted value be：
DefinitionForHeader element,For (HTH+R)-1HTThe first trip element of G then has：
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| CN107872182B (en) * | 2017-11-16 | 2020-11-27 | 东南大学 | Permanent magnet synchronous motor control method based on generalized model prediction |
| CN108054972B (en) * | 2017-12-28 | 2020-11-17 | 西安理工大学 | Method for improving dynamic control performance of permanent magnet synchronous linear motor |
| 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 |
| CN110247592B (en) * | 2019-06-28 | 2020-12-18 | 西安理工大学 | Multivariable second-order nonsingular terminal sliding mode current control method introducing approach law |
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