CN106712626B - A kind of asynchronous motor forecast Control Algorithm - Google Patents

Abstract

The invention discloses a model predictive control method for an asynchronous motor, specifically: firstly, linearize and discretely process the equation of the control object, and obtain the predicted value of the state variable and The system outputs the predicted value, and then obtains the optimal control quantity and real-time control quantity for the control object, so as to obtain the predicted value of the state variable at the next moment, and applies the real-time control quantity to the asynchronous motor for control. In the present invention, on the basis of analyzing the rolling time-domain characteristics of model predictive control and deriving and discussing its mathematical model in detail, according to the internal relationship between system variables and their differences and system equations, the state and output are formed by expanding and converting the state variables The dual-state feedback structure speeds up the output convergence speed, effectively reducing the control domain and reducing the online calculation amount of the entire system on the basis of no constraints and processing of system control information.

Description

A Model Predictive Control Method for Asynchronous Motor

technical field

The invention belongs to the technical field of motor control and relates to a model predictive control method for an asynchronous motor.

Background technique

Asynchronous motors have nonlinear, strong coupling, and multivariable properties. Generally, PI regulators are used to regulate the system. Its structure is simple, easy to implement, and has good dynamic performance. However, the system has shortcomings such as being easily affected by system parameter changes, poor adaptability to load changes, and weak anti-interference ability. In addition, in the process of controller parameter tuning, it often needs to rely on a lot of engineering experience for repeated debugging. Therefore, in the case of high dynamic performance requirements, the use of traditional PI regulators will be subject to certain limitations and cannot meet the relevant performance requirements.

Model predictive control was born in the 1970s. From the initial industrial application heuristic control algorithm, it has now developed into a new branch of discipline with rich theory and continuous expansion of practical content. Predictive control is aimed at control problems with optimization requirements. Since the birth and development of this control method, it has achieved some success in complex industrial systems, especially the model predictive control algorithm has unique advantages in dealing with nonlinear constraints. After decades of development, model predictive control has been gradually applied in various fields, especially in recent years with the rapid development of digital signal processors, model predictive control strategies have been rapidly developed and applied in the field of motor control. Looking at the motor model predictive control strategy in recent years, to a large extent, it is the algorithm improvement, development and combination with other algorithms, using their respective advantages to improve the control performance of the entire system. Although the model predictive control method has many advantages, the biggest obstacle before it is applied to the field of motor control is that the algorithm is relatively complex and the amount of online calculation is relatively large, which cannot be accepted by this application field. The development level of the processor at that time could hardly meet the dynamic performance requirements of the system, which delayed the application and development of the algorithm in the field of motor control. Therefore, the focus of the present invention is to study a more efficient and simple control strategy for the problem of large calculation amount of the model predictive control algorithm.

Contents of the invention

The purpose of the present invention is to provide a model predictive control method for an asynchronous motor, which solves the problem of large amount of calculation and poor real-time performance when the model predictive control algorithm is implemented on-line in the existing motor control.

The technical solution adopted in the present invention is a model predictive control method for asynchronous motors, specifically implemented according to the following steps:

Step 1, linearize and discretize the voltage equation of the control object:

Suppose the discrete mathematical model of the research object is:

Among them, x(k) is the state variable, y(k) is the output variable of the system, u(k) is the input variable of the system, A is the system matrix, B is the input matrix, C is the output matrix, k is the current sampling time ;

Linearize and discretize the voltage equation of the control object and abstract it into the form of formula (1);

Step 2, according to the discrete mathematical model of the control object, obtain the predicted value of the state variable and the predicted value of the system output at different times in the prediction domain at time k;

The predicted values of state variables at different times are:

x(k+p|k)＝A ^p x(k)+A ^p-1 Bu(k)+A ^p-2 Bu(k+1)+…+A ^pl Bu(k+l-1) (2 )

The predicted value of the system output is:

In order to describe the output expression more concisely, define variables 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)

Use the above definition to re-describe the output recursively:

Y=Gx(k)+HU (6)

in,

Here it is assumed that the control quantity of the system can be expressed as the following form:

The objective function to obtain the optimal control quantity is:

J*＝(R _r -Y)(R _r -Y) ^T +U ^T RU (8)

Among them, R is the weight matrix of the influence of the input on the objective function, is a unit vector whose dimension is equal to the prediction time domain, Y is the output variable of the system, and U is the input variable of the system.

Substituting the formula Y=Gx(k)+HU into formula (8), the following expression can be obtained:

In order to make J* obtain the best input control variable u(k), it can be obtained by obtaining the necessary condition dJ*/dU=0 of the minimum value:

U＝(H ^T H+R) ^-1 H ^T (R _r -Gx(k)) (10)

From the formula (10), it is possible to calculate all the predicted values in the forecast time domain at time k, but the predictive control does not apply all the control variables to the control object, but the real-time control value, that is, the optimal control value The first element acts on the control object, so when the input variable acts on the object at time k, the predicted value of the system output is:

Step 3: Mathematically transform the discrete mathematical model of the control object in step 1, and combine the predicted value of the state variable and the predicted value of the system output obtained in step 2 to obtain the optimal control amount and real-time control amount for the control object.

Step 4, according to the optimal control amount and the immediate control amount of the control object obtained in step 3, combined with formula (2), the predicted value of the state variable at the next moment is obtained;

Step 5, apply the immediate control quantity obtained in step 4 to the asynchronous motor for control and use the predicted value of the state variable at the next moment to perform a new round of cyclic solution.

The present invention is also characterized in that,

The system equation of the state expansion after the mathematical transformation of the discrete mathematical model of the control object is:

Among them, O is a zero vector.

The optimal control quantity is:

The current real-time control amount is:

The predicted value of the state variable at the next moment is:

definition for the first element of The elements in the first row of (H ^T H+R) ^-1 H ^T G are:

The beneficial effect of the present invention is that, on the basis of analyzing the rolling time-domain characteristics of the model predictive control and deriving and discussing the mathematical model in detail, according to the internal relationship between the system variables and their differences and the system equations, by expanding and converting the state variables , so that the converted system presents a state and output dual-state feedback structure in the form of predictive control. By this means, the output feedback that is not in the original control structure is introduced into the control structure, forming a double-state feedback closed-loop structure. From this structure, it can be easily concluded that the output state feedback speeds up the convergence speed of the output, so that on the basis of the system control information without any constraints and processing, the double feedback control structure can effectively reduce the control domain and reduce the online calculation of the entire system. quantity.

Description of drawings

Fig. 1 is the control system block diagram of the asynchronous motor model predictive control method of the present invention;

Fig. 2 is a structural block diagram of model predictive control based on single-state feedback;

Figure 3 is a structural block diagram of model predictive control based on dual-state feedback.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

The invention provides a model predictive control method of an asynchronous motor, which adopts a double closed-loop vector control system. The vector control system includes two parts: the speed outer loop and the current inner loop. As shown in Figure 1: the current signal detection circuit 3 detects the three-phase current of the motor in the three-phase static coordinate system through the Hall sensor, and after 3s/2s conversion 4, it is converted into the current value i _sα , the current value in the static two-phase coordinate system i _sβ , and the error of comparing the given speed ω ^* in the speed outer loop with the encoder feedback speed ω _r is adjusted by the speed outer loop controller to output the q-axis current i _q ^* in the rotor rotating coordinate system, i _q ^* and the _d -axis given excitation current id ^* pass through the slip calculation module 7 to obtain the slip ω _s and the feedback speed ω _r , and after the rotation angle calculation 8, the motor rotor angle θ is output. The current value is _α , is _β and motor rotor angle θ in the stationary two-phase coordinate system are transformed into the two-phase feedback calculation excitation current _id and torque current i _q in the rotor rotating coordinate system after 2r/2s. Given excitation current id ^* and feedback calculation excitation current _id , torque current i _q ^* and feedback calculation torque current _{i q ,} the results u _sd ^* and u _sq ^* are obtained through the calculation of model predictive controller 6 . The two-phase voltages u _sd ^* and u _sq ^* in the rotating coordinate system are transformed into two-phase voltages u _sα ^* and u _sβ ^* in the stationary two-phase coordinate system after 2r/2s inverse transformation, and after being adjusted by the PWM generating module 10, A PWM wave is generated, and the generated PWM wave is applied to the three-phase inverter 1 to drive the asynchronous motor module 2 to work.

The invention provides a model predictive control method for an asynchronous motor, which is specifically implemented according to the following steps:

Step 1. Taking the squirrel-cage asynchronous motor as the research object, the stator voltage equation of the asynchronous motor in the synchronous rotating coordinate system (d-q coordinate system) of its rotor field orientation is used as the control object, and its form is as follows:

In the above formula, R _s is the stator resistance, L _m is the mutual inductance between the stator and rotor, L _s , L _r are the stator inductance and rotor inductance respectively, L _σ = σL _s is the total leakage inductance, ω _s is the synchronous angular velocity, ψ _r is the rotor flux amplitude, u _sd , u _sq are d-axis stator voltage, q-axis stator voltage respectively, i _sd , i _sq are d-axis stator current, q-axis stator current respectively.

Through linearization and discrete processing, the following expression can be obtained:

In the formula, T _s is the sampling time.

In order to facilitate subsequent analysis, the formula (2) is abstracted into the following form:

Among them, x(k) is the state variable, y(k) is the output variable of the system, u(k) is the input variable of the system, A is the system matrix, B is the input matrix, C is the output matrix, k is the current sampling time .

Assuming that the scope of the prediction domain is p, and the scope of the control domain is l, according to the predictive control theory, it can be concluded that the two should satisfy the relationship: p≥l. General definition: If time k is taken as the starting point, the input control sequence is u(k), u(k+1),...,u(k+l-1), and the predicted output state sequence is x under the action of the control sequence (k+1|k), x(k+2|k),...,x(k+p|k), where x(k+p|k) means to predict based on the state at k time Predicted value at time k+p in the domain.

Step 2, obtain the predicted value of the state variable and the predicted value of the system output at different times in the prediction domain at time k:

Based on the discrete mathematical model of the control object in step 1, the predicted value of the state variable at different times in the prediction domain at time k can be deduced:

x(k+p|k)＝A ^p x(k)+A ^p-1 Bu(k)+A ^p-2 Bu(k+1)+…+A ^pl Bu(k+l-1) (4 )

Based on the state prediction, the system output prediction value can be obtained:

Through the recursion (4) and (5), it can be concluded that within the scope of the prediction domain, the state quantity and the output prediction sequence depend on the starting time x(k) and the control sequence u(k+i), where i=0 ,1,...l-1.

In order to describe the output expression more concisely, define variables 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)

Use the above definition to re-describe the output recursively:

Y=Gx(k)+HU (8)

in,

Suppose the control vector of the system is:

The objective function of the optimal control quantity is:

J ^* ＝(R _r -Y)(R _r -Y) ^T + U ^T RU (10)

Among them, R is the weight matrix of the influence of the input on the objective function, is a unit vector of dimension equal to the forecast horizon.

Substituting the formula Y=Gx(k)+HU into the formula (10), the following expression can be obtained:

In order to make the minimum value u(k) obtained by J*, it can be obtained through the minimum value necessary condition dJ ^* /dU=0:

U＝(H ^T H+R) ^-1 H ^T (R _r -Gx(k)) (12)

From formula (12), it is possible to calculate all the predicted values within the forecast time domain at time k, but the predictive control does not apply all the control variables to the control objects, but applies the immediate control variables to the control objects, so at time k The input variables when acting on an object are:

Due to the special form of G, H, coupled with the control amount finally implemented in the control object, some connections can be obtained through careful derivation, and the definition:

α is The first element, β is the first row element of (H ^T H+R) ^-1 H ^T G.

According to this, the predicted value of the state variable at the next moment can be obtained as:

Step 3, through step 2, a model predictive control mode for seeking the optimal control target can be obtained as shown in Figure 2, which is a single-state feedback structure in the normal state. At the same time, it is considered that the size of the control domain of the system is an important constraint on the online calculation amount of the algorithm. Therefore, under the premise of keeping the output performance index unchanged, reducing the control range of the control domain will be an effective method to solve the problem of online implementation of model predictive control.

Mathematically change the discrete model of the system described in step 1:

Substituting Equation (15) for the original state equation, and adopting the method of state expansion, the following system equation of state expansion can be obtained:

Among them, O is a zero vector.

According to the new state equation to describe and predict the form of the input and output sequence of the process, and according to formula (11), the optimal control quantity can be deduced:

Similarly, the current real-time control amount can be obtained as:

in the formula It is similar to the corresponding structure of G and H in step 2, just to show the difference, define for the first element of The elements in the first row of (H ^T H+R) ^-1 H ^T G are:

By analyzing the structure of the output matrix C and the system matrix A after state expansion, the following conclusions are drawn: The last column of the matrix is the same as are the same, and it follows that equal the last column of . According to this relationship, perform matrix transformation can be described by this formula Combined with (19), we can get is the feedback gain related to the state quantity, is the feedback gain related to the output.

Through step 4, the improved state feedback predictive control block diagram can be obtained as shown in Figure 3. From the block diagram, it can be clearly seen that the improved method introduces the feedback of the output to the input to speed up the convergence of the output.

The present invention is mainly aimed at the fact that the amount of calculation in the rolling optimization process of the model predictive control cannot meet the requirements, and then the real-time performance of the system control cannot be satisfied. By starting from the basic single-state structure and adopting the idea of state conversion and expansion, The original single-state feedback control structure is improved to form a two-state feedback control structure in the present invention, and the feedback of the output is introduced, thereby reducing the length of the control domain and reducing the amount of calculation. It is easy to get the parameters in the control equation by comparing the motor equation with the control equation of the final control quantity, so it has universality in practical applications.

Claims (4)

1. A model predictive control method for asynchronous motors, specifically implemented in the following steps: Step 1, linearize and discretize the voltage equation of the control object: Suppose the discrete mathematical model of the research object is: Among them, x(k) is the state variable, y(k) is the output variable of the system, u(k) is the input variable of the system, A is the system matrix, B is the input matrix, C is the output matrix, k is the current sampling time ; Linearize and discretize the voltage equation of the control object and abstract it into the form of formula (1); Step 2, according to the discrete mathematical model of the control object, obtain the predicted value of the state variable and the predicted value of the system output at different times in the prediction domain at time k; The predicted values of state variables at different times are: x(k+p|k)＝A ^p x(k)+A ^p-1 Bu(k)+A ^p-2 Bu(k+1)+…+A ^{p- l} Bu(k+ l -1) ( 2) The predicted value of the system output is: In order to describe the output expression more concisely, define variables 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) Use the above definition to re-describe the output recursively: Y=Gx(k)+HU (6) in, Here it is assumed that the control quantity of the system can be expressed as the following form: The objective function to obtain the optimal control quantity is: J ^* ＝(R _r -Y)(R _r -Y) ^T +U ^T RU (8) Among them, R is the weight matrix of the influence of the input on the objective function, is a unit vector whose dimension is equal to the prediction time domain, Y is the output variable of the system, and U is the input variable of the system; Substituting the formula Y=Gx(k)+HU into formula (8), the following expression can be obtained: In order to obtain the optimal input control quantity u(k) obtained by J ^* , it can be obtained by obtaining the minimum value of the necessary condition dJ ^* /dU=0: U＝(H ^T H+R) ^-1 H ^T (R _r -Gx(k)) (10) From the formula (10), it is possible to calculate all the predicted values within the forecast time domain at time k, but the predictive control does not apply all the control variables to the control object, but uses the immediate control quantity, which is the first priority to obtain the optimal control quantity. The element acts on the control object, so when the input variable acts on the object at time k, the predicted value of the system output is: Step 3: Mathematically transform the discrete mathematical model of the control object in step 1, and combine the predicted value of the state variable and the predicted value of the system output obtained in step 2 to obtain the optimal control amount and real-time control amount for the control object. Step 4, according to the optimal control amount and the immediate control amount of the control object obtained in step 3, combined with formula (2), the predicted value of the state variable at the next moment is obtained; Step 5, apply the immediate control quantity obtained in step 4 to the asynchronous motor for control and use the predicted value of the state variable at the next moment to perform a new round of cyclic solution. 2. a kind of asynchronous motor model predictive control method according to claim 1, is characterized in that, the system equation of the state expansion after the discrete mathematical model of described control object carries out mathematical transformation is: Among them, O is a zero vector. 3. A kind of asynchronous motor model predictive control method according to claim 1, is characterized in that, described optimal control amount is: The current real-time control amount is: 4. A kind of asynchronous motor model predictive control method according to claim 3, is characterized in that, the state variable predictive value of described next moment is: definition for the first element of The elements in the first row of (H ^T H+R) ^-1 H ^T G are: