CN109412488A - A kind of permanent magnet synchronous motor dynamic matrix control method - Google Patents

Abstract

The invention discloses a dynamic matrix control method for a permanent magnet synchronous motor. The steps are as follows: 1. Establishing a dq-axis mathematical model of PMSM, using the extended Kalman filter EKF as a random observer, and using the extended Kalman filter algorithm to observe variables Correct the predicted variables to obtain the optimal predicted value; 2. Construct vector control with extended Kalman filter EKF; 3. Implement PMSM with DMC algorithm. DMC algorithm uses the step response of the object to realize the steps of model prediction and rolling. Optimization and feedback correction; 4. Construct the DMC vector control structure of permanent magnet motor based on EKF. The model after the variable replacement of the present invention can be appreciably and controllable, and the rotation speed predicted by the EKF replaces the sensor in the dynamic matrix control of the original permanent magnet synchronous motor to measure the rotation speed, so that the entire control process is completed by the computer, which improves the controllability of the system and facilitates Apply in more occasions.

Description

A dynamic matrix control method for permanent magnet synchronous motor

technical field

The invention relates to a dynamic matrix control method of a permanent magnet synchronous motor, belonging to the technical field of permanent magnet synchronous motor application.

Background technique

In the exploration and exploitation of oil drilling rig system, due to the complex environmental conditions and geological structure, it has the characteristics of non-linearity and uncertainty in actual work, and the drilling rig requires a good dynamic response in terms of driving motor, and it can be used in load changes. In order to maintain the stability of the rotational speed at all times, applying the DMC (dynamic matrix) in the predictive control to the PMSM (permanent magnet synchronous motor) drilling rig system will have a better control effect for these problems.

PMSM is known for its advantages of high dynamic performance, high efficiency and light weight. By combining microelectronic control technology and power electronic technology, it can design and manufacture many integrated electromechanical equipment and products with superior performance. Its energy saving characteristics It is also the first choice for the design of drive systems in today's world, and it is also used more and more in the field of oil drilling rigs. Based on the superiority of PMSM in structure, performance, especially control, the application of modern control theory and intelligent control strategy in motor control is increasing, and model predictive control, as a new computer control algorithm, is also being used more and more in PMSM .

In order to realize the DMC control of the PMSM of the oil drilling rig system, it is necessary to use a coaxial mechanical position sensor to measure the rotor position and speed information. However, this causes some disadvantages: 1. The increased weight and volume of the PMSM lead to an increase in cost; 2. Coaxial installation The accuracy requirements are high. If it does not match, it will seriously affect the normal operation of the PMSM, and because of the addition of components, the anti-disturbance performance of the PMSM will be reduced; 3. The use environment is strictly required, and the disturbance caused by external environmental changes will have a great impact on its accuracy. The impact of PMSM in oil rig systems is affected.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the defects existing in the prior art, provide a dynamic matrix control method for permanent magnet synchronous motor, adopt EKF (Extended Kalman Filter) to carry out PMSM sensorless design, and conduct the motor by observing the position and speed information of the motor. Closed-loop control simplifies the mechanical equipment of the drilling rig, thus making the drilling rig system more flexible and more reliable.

In order to achieve the above purpose, the technical solution adopted in the present invention is: a dynamic matrix control method for a permanent magnet synchronous motor, the steps are as follows:

1. Establish the dq-axis mathematical model of PMSM, use the extended Kalman filter EKF as a random observer, and correct the predicted variables through the observation variables of the extended Kalman filter algorithm, so as to obtain the optimal predicted value;

2. Use extended Kalman filter EKF to construct vector control, set rotor flux linkage, speed and rotor position angle as state variables, and set stator voltage as input variable. If the moment of inertia is large enough, the speed is constant in the sampling period, so that the speed estimation error is attributed to the system noise, and the accuracy of the motor model is not affected;

3. Realize PMSM with DMC algorithm. DMC algorithm uses the step response of the object, and the realization steps go through model prediction, rolling optimization and feedback correction;

Fourth, constitute the DMC vector control structure of permanent magnet motor based on EKF.

Further, the PMSM adopts a surface-mounted PMSM.

Further, the establishment of the dq-axis mathematical model of the PMSM refers to:

Voltage equation (1)

Electromagnetic torque equation (2)

Mechanical equation of motion(3)

In the formula, id , i _q and _ud , u _q are the _dq components of the stator current and voltage, respectively; L _d , L _q and ψ _d , ψ _q are the dq components of the stator inductance and flux linkage, respectively; R _S is the stator resistance; ω is the mechanical angular velocity of the rotor; _{n p} is the number of pole pairs; ψ _f is the permanent magnet flux linkage; Te and T _L are the electromagnetic torque and load torque of the motor, respectively; J is the moment of inertia; P is the viscous friction coefficient.

Further, the extended Kalman filter algorithm is:

x(k+1)=Ax(k)+Bu(k)+V(k) (4)

y(k)=Hx(k)+W(k) (5)

Where: V(k) is the system noise; W(k) is the measurement noise.

Further, the steps of the extended Kalman filter algorithm include:

Among them, M and N are the covariance matrices of V and W respectively, K(k+1) is the gain matrix, the superscript ~ is the predicted value, and the superscript ∧ is the check value.

Further, in the second step, using the extended Kalman filter EKF to construct the vector control means: the dq axis is the αβ axis model, the EKF observer is designed under the αβ axis, the EKF is used to construct the vector control, and the rotor flux linkage ψ _α , ψ _β , the rotational speed ω and the rotor position angle θ are the state variables, and the state equation and measurement equation of the motor with the stator voltage as the input variable, if the sampling frequency of the closed-loop speed control is sufficiently large compared to the mechanical time constant or moment of inertia of the motor, then The speed is constant during the sampling period, so that the speed estimation error is attributed to the system noise, and the accuracy of the motor model is not affected.

Among them, the flux linkage equation of PMSM is:

The stator voltage equation is:

Substituting the flux linkage equation into the voltage equation yields:

Setting ω to be constant in each sampling period, we get:

and

Selecting x(t)=[ψ _α ψ _β ωθ] ^T as the state variable, the constructed state equation and output equation are:

in,

v is the system noise; w is the measurement noise.

Further, in the described step 3, the step of realizing PMSM with DMC algorithm is as follows:

It is known that the motion equation of PMSM is Equation (3). When id = 0 control strategy is adopted, the electromagnetic torque _formula of the motor is:

Let the load torque T _L be 0, and take the Laplace transform of both sides of Equation (3) to obtain the frequency domain model as:

Among them, K=1.5P _n ψ _f , and then starting from the step response of the controlled object of PMSM in formula (16), its dynamic characteristics are represented by dynamic coefficients a ₁ , a ₂ , ..., a _p , and p is the model Length of time domain; a _p is a coefficient close enough to the steady-state value. At time k, the set control action remains unchanged, and there is an initial predicted value for the speed output in the future. Taking the quadrature current i _q of the PMSM in the dq coordinate system as the control quantity, under the continuous control increment action Δi _q (k), ..., Δi _q (k+ji), the output value of the motor speed at each moment in the future is:

in,

The specific control increment of the dynamic matrix algorithm is determined by the optimization criterion formula, and the optimization criterion formula is:

Among them, q and r are the error weight coefficient and the control weight coefficient respectively, ω(k+j|k) is the expected output, and ω(k+j|k) is set as the reference trajectory of the speed of the permanent magnet synchronous motor, then

W=[ω(k+1|k),ω(k+2|k),L,ω(k+p|k)] ^T (20)

The optimization criterion formula (19) is expressed as:

In formula (21), the control vector is derived, and the result is set to 0. When the specific rolling is implemented, only the immediate control increment is taken, and the immediate control increment is obtained by formula (22):

in,

Q and R respectively represent the diagonal matrix composed of the error weight coefficient and the control weight coefficient, c ^T =[1 0 L 0], d is the control vector, d ^T =c ^T (A ^T QA+RE) ^-1 A ^T Q, thus constituting the actual control u(k), which is:

After the control function is implemented, the motor output speed y ^* (k+1) at the next moment is collected,

Use the estimated rotational speed of the oil drilling rig system PMSM to correct the prediction and carry out a new optimization. After the real-time control of the PMSM is implemented at time k, the predicted output at this time is:

the predicted value at this time Compared with the detected PMSM rotational speed estimation output value y ^* (k+1), the output error is obtained as:

By weighting the error e ^* (k+1), the prediction of the PMSM rotation speed at the future time is corrected, that is:

in,

After updating the state, the revised PMSM speed is predicted As the initial prediction value at the next moment, the rotation speed prediction of the PMSM at the next moment is finally obtained according to formula (27) for:

Further, in the step 4, an EKF-based permanent magnet motor DMC vector control structure is formed, and the entire motor system of the control structure is a double closed-loop speed control system composed of an outer speed loop and an inner current loop, and four of the EKF speed estimation module. The input is the stator current and stator voltage in the static coordinate system, and the output is the estimated rotor speed, and the output is used as the feedback information of the speed loop. The error obtained after comparing with the predicted output is further corrected by the DMC algorithm, and the entire system is finally completed. sensorless speed control.

The beneficial technical effects of the present invention are: because the EKF needs to perform matrix operations including addition, multiplication, inversion and transposition in practical applications, the entire calculation and control process is very complicated, and the present invention first converts the highly nonlinear through variable element conversion. The permanent magnet synchronous motor model is linearly processed. The existence of the rotor position angle θ parameter in the process of variable element replacement makes the model after variable substitution appreciably controllable. On the basis of EKF-based control, the output speed predicted by EKF replaces the original speed The sensor in the dynamic matrix control of the permanent magnet synchronous motor measures the rotational speed, so that the entire control process is completed by the computer, which improves the controllability of the system and is more convenient for application in more occasions.

Description of drawings

The present invention will be further elaborated below in conjunction with the accompanying drawings and implementation examples.

Fig. 1 is the dynamic matrix calculation flow chart of the present invention;

FIG. 2 is a structural block diagram of the motor DMC vector control based on the EKF of the present invention.

Detailed ways

Example 1

A dynamic matrix control method for a permanent magnet synchronous motor, the steps are as follows:

1. Establish the dq-axis mathematical model of PMSM, use the extended Kalman filter EKF as a random observer, and correct the predicted variables through the observation variables of the extended Kalman filter algorithm, so as to obtain the optimal predicted value;

2. Use extended Kalman filter EKF to construct vector control, set rotor flux linkage, speed and rotor position angle as state variables, and set stator voltage as input variable. If the moment of inertia is large enough, the speed is constant in the sampling period, so that the speed estimation error is attributed to the system noise, and the accuracy of the motor model is not affected;

3. Realize PMSM with DMC algorithm. DMC algorithm uses the step response of the object, and the realization steps go through model prediction, rolling optimization and feedback correction;

Fourth, constitute the DMC vector control structure of permanent magnet motor based on EKF.

Example 2

As a preference to Embodiment 1, the PMSM is a surface-mounted PMSM. When the PMSM is used as the driving device of the oil drilling rig system, the surface-mounted PMSM is taken as the research object because the permanent magnet poles of the surface-mounted PMSM facilitate the realization of the optimal design and improve the control performance of the motor.

The dq-axis mathematical model of PMSM is established as follows:

Voltage equation (1)

Electromagnetic torque equation (2)

Mechanical equation of motion(3)

In the formula, id , i _q and _ud , u _q are the _dq components of the stator current and voltage, respectively; L _d , L _q and ψ _d , ψ _q are the dq components of the stator inductance and flux linkage, respectively; R _S is the stator resistance; ω is the mechanical angular velocity of the rotor; _{n p} is the number of pole pairs; ψ _f is the permanent magnet flux linkage; Te and T _L are the electromagnetic torque and load torque of the motor, respectively; J is the moment of inertia; P is the viscous friction coefficient.

Further, the extended Kalman filter algorithm is:

x(k+1)=Ax(k)+Bu(k)+V(k) (4)

y(k)=Hx(k)+W(k) (5)

Where: V(k) is the system noise; W(k) is the measurement noise.

Example 3

As a preference to Embodiment 2, the steps of the extended Kalman filter algorithm include:

Among them, M and N are the covariance matrices of V and W respectively, K(k+1) is the gain matrix, the superscript ~ is the predicted value, and the superscript ∧ is the check value.

In the second step, using the extended Kalman filter EKF to construct the vector control means: the dq axis is the αβ axis model, the EKF observer is designed under the αβ axis, the EKF is used to construct the vector control, and the rotor flux linkage ψ _α , ψ _β is set, The rotational speed ω and the rotor position angle θ are the state variables, and the state equation and measurement equation of the motor with the stator voltage as the input variable, if the sampling frequency of the closed-loop control of the rotational speed is sufficiently large compared to the mechanical time constant or the moment of inertia of the motor, the rotational speed is in the sampling frequency. It is a constant in the period, so that the speed estimation error is attributed to the system noise, and the accuracy of the motor model is not affected.

Among them, the flux linkage equation of PMSM is:

The stator voltage equation is:

Substituting the flux linkage equation into the voltage equation yields:

Since the sampling period in the digital system is very short, ω can be assumed to be constant in each sampling period, then:

and

Selecting x(t)=[ψ _α ψ _β ωθ] ^T as the state variable, the constructed state equation and output equation are:

in,

v is the system noise; w is the measurement noise.

Example 4

As a preference of Embodiment 1, as shown in Figure 1, in the third step, the steps of implementing PMSM with the DMC algorithm are as follows:

It is known that the motion equation of PMSM is Equation (3). When id = 0 control strategy is adopted, the electromagnetic torque _formula of the motor is:

Let the load torque T _L be 0, and take the Laplace transform of both sides of Equation (3) to obtain the frequency domain model as:

Among them, K=1.5P _n ψ _f , and then starting from the step response of the controlled object of PMSM in formula (16), its dynamic characteristics are represented by dynamic coefficients a ₁ , a ₂ , ..., a _p , and p is the model Length of time domain; a _p is a coefficient close enough to the steady-state value. At time k, the set control action remains unchanged, and there is an initial predicted value for the speed output in the future. Taking the quadrature current i _q of the PMSM in the dq coordinate system as the control quantity, under the continuous control increment action Δi _q (k), ..., Δi _q (k+ji), the output value of the motor speed at each moment in the future is:

in,

The specific control increment of the dynamic matrix algorithm is determined by the optimization criterion formula, and the optimization criterion formula is:

Among them, q and r are the error weight coefficient and the control weight coefficient respectively, ω(k+j|k) is the expected output, and ω(k+j|k) is set as the reference trajectory of the speed of the permanent magnet synchronous motor, then

W=[ω(k+1|k),ω(k+2|k),L,ω(k+p|k)] ^T (20)

The optimization criterion formula (19) is expressed as:

In formula (21), the control vector is derived, and the result is set to 0. When the specific rolling is implemented, only the immediate control increment is taken, and the immediate control increment is obtained by formula (22):

in,

Q and R respectively represent the diagonal matrix composed of the error weight coefficient and the control weight coefficient, c ^T =[1 0 L 0], d is the control vector, d ^T =c ^T (A ^T QA+RE) ^-1 A ^T Q, thus constituting the actual control u(k), which is:

After the control function is implemented, the motor output speed y ^* (k+1) at the next moment is collected,

Use the estimated rotational speed of the oil drilling rig system PMSM to correct the prediction and carry out a new optimization. After the real-time control of the PMSM is implemented at time k, the predicted output at this time is:

the predicted value at this time Compared with the detected PMSM rotational speed estimation output value y ^* (k+1), the output error is obtained as:

By weighting the error e ^* (k+1), the prediction of the PMSM rotation speed at the future time is corrected, that is:

in,

After updating the state, the revised PMSM speed is predicted As the initial prediction value at the next moment, the rotation speed prediction of the PMSM at the next moment is finally obtained according to formula (27) for:

As shown in Figure 2, in the fourth step, the EKF-based permanent magnet motor DMC vector control structure is formed. The entire motor system of the control structure is a double closed-loop speed control system composed of an outer speed loop and an inner current loop. The EKF speed estimation module The four inputs are the stator current and stator voltage in the static coordinate system, the output is the estimated rotor speed, and the output is used as the feedback information of the speed loop, and the error obtained after comparing with the predicted output is further corrected by the DMC algorithm. Complete the sensorless speed control of the entire system.

The use of traditional position sensors will increase the mechanical load of the drilling rig system, which is not conducive to the installation and movement of the drilling rig, and the work of the sensor will also be disturbed in harsh environments, which will affect the control effect of the PMSM and the normal operation of the drilling rig. Therefore, EKF ( The extended Kalman filter) is used to design PMSM without position sensor, and the closed-loop control of the motor is carried out by observing the position and speed information of the motor, which simplifies the mechanical equipment of the drilling rig, so that the use of the drilling rig system is more flexible and the reliability is improved.

By detecting some electrical signals such as voltage and current in the PMSM, and adding appropriate algorithm programs to estimate the PMSM's rotational speed and position information, that is, no mechanical sensor is required, thus forming the PMSM sensorless control technology. Using the excellent ability of the Kalman filter algorithm to weaken random interference and measurement noise, it is developed from the field of linear systems to the field of nonlinearity. The Kalman filter gain of the designed filter can be adaptively adjusted with the environment, and then the system state can be estimated online. , to achieve real-time control of the system state. Due to the excellent ability of the Kalman filter algorithm to weaken random interference and measurement noise, and its characteristics of adaptive adjustment with the environment, the EKF algorithm is selected for the PMSM positionless sensor design. On the basis of the PMSM speed loop DMC control of the oil drilling rig system, the sensorless technology of EKF is applied to reduce the installation of mechanical equipment, reduce the cost, and increase the reliability of the drilling rig system, which can further improve the working efficiency of the drilling rig, and is more conducive to complex run in the environment.

Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above-mentioned specific embodiments, and those skilled in the art can make various variations or modifications within the scope of the claims, which do not affect the essential content of the present invention.

Claims (7)

1. a permanent magnet synchronous motor dynamic matrix control method, is characterized in that, step is as follows: 1. Establish the dq-axis mathematical model of PMSM, use the extended Kalman filter EKF as a random observer, and correct the predicted variables through the observation variables of the extended Kalman filter algorithm, so as to obtain the optimal predicted value; 2. Use extended Kalman filter EKF to construct vector control, set rotor flux linkage, speed and rotor position angle as state variables, and set stator voltage as input variable. If the moment of inertia is large enough, the speed is constant in the sampling period, so that the speed estimation error is attributed to the system noise, and the accuracy of the motor model is not affected; 3. Realize PMSM with DMC algorithm. DMC algorithm uses the step response of the object, and the realization steps go through model prediction, rolling optimization and feedback correction; Fourth, constitute the DMC vector control structure of permanent magnet motor based on EKF. 2 . The dynamic matrix control method of a permanent magnet synchronous motor according to claim 1 , wherein the PMSM adopts a surface-mounted PMSM. 3 . 3. permanent magnet synchronous motor dynamic matrix control method according to claim 1, is characterized in that: the dq axis mathematical model of described establishment PMSM refers to: Voltage equation (1) Electromagnetic torque equation (2) Mechanical equation of motion(3) In the formula, id , i _q and _ud , u _q are the _dq components of the stator current and voltage, respectively; L _d , L _q and ψ _d , ψ _q are the dq components of the stator inductance and flux linkage, respectively; R _S is the stator resistance; ω is the mechanical angular velocity of the rotor; _{n p} is the number of pole pairs; ψ _f is the permanent magnet flux linkage; Te and T _L are the electromagnetic torque and load torque of the motor, respectively; J is the moment of inertia; P is the viscous friction coefficient. 4. the dynamic matrix control method of permanent magnet synchronous motor according to claim 1, is characterized in that: described extended Kalman filter algorithm is: x(k+1)=Ax(k)+Bu(k)+V(k) (4) y(k)=Hx(k)+W(k) (5) Where: V(k) is the system noise; W(k) is the measurement noise. Further, the steps of the extended Kalman filter algorithm include: Among them, M and N are the covariance matrices of V and W respectively, K(k+1) is the gain matrix, the superscript ~ is the predicted value, and the superscript ∧ is the check value. 5. The dynamic matrix control method of permanent magnet synchronous motor according to claim 1, is characterized in that: in described step 2, constructing vector control with extended Kalman filter EKF means: dq axis is αβ axis model, and in αβ axis The EKF observer is designed below, the vector control is constructed with EKF, the rotor flux linkage ψ _α , ψ _β , the rotational speed ω and the rotor position angle θ are set as state variables, and the motor state equation and measurement equation with the stator voltage as the input variable, if the rotational speed is closed-loop If the sampling frequency of the control is sufficiently large compared to the mechanical time constant or moment of inertia of the motor, the speed is constant during the sampling period, so that the speed estimation error is attributed to the system noise, and the accuracy of the motor model is not affected. Among them, the flux linkage equation of PMSM is: The stator voltage equation is: Substituting the flux linkage equation into the voltage equation yields: Setting ω to be constant in each sampling period, we get: and Select x(t)=[ψ _α ψ _β ω θ] ^T as the state variable, and the constructed state equation and output equation are: in, v is the system noise; w is the measurement noise. 6. permanent magnet synchronous motor dynamic matrix control method according to claim 1, is characterized in that: in described step 3, the step that realizes PMSM with DMC algorithm is as follows: It is known that the motion equation of PMSM is Equation (3). When id = 0 control strategy is adopted, the electromagnetic torque _formula of the motor is: Let the load torque T _L be 0, and take the Laplace transform of both sides of Equation (3) to obtain the frequency domain model as: Among them, K=1.5P _n ψ _f , and then starting from the step response of the controlled object of PMSM in formula (16), its dynamic characteristics are represented by dynamic coefficients a ₁ , a ₂ , ..., a _p , and p is the model Length of time domain; a _p is a coefficient close enough to the steady-state value. At time k, the set control action remains unchanged, and there is an initial predicted value for the speed output in the future. Taking the quadrature current i _q of the PMSM in the dq coordinate system as the control quantity, under the continuous control increment action Δi _q (k), ..., Δi _q (k+ji), the output value of the motor speed at each moment in the future is: in, The specific control increment of the dynamic matrix algorithm is determined by the optimization criterion formula, and the optimization criterion formula is: Among them, q and r are the error weight coefficient and the control weight coefficient respectively, ω(k+j|k) is the expected output, and ω(k+j|k) is set as the reference trajectory of the speed of the permanent magnet synchronous motor, then W=[ω(k+1|k),ω(k+2|k),…,ω(k+p|k)] ^T (20) The optimization criterion formula (19) is expressed as: In formula (21), the control vector is derived, and the result is set to 0. When the specific rolling is implemented, only the immediate control increment is taken, and the immediate control increment is obtained by formula (22): in, Q and R represent diagonal matrices composed of error weight coefficients and control weight coefficients, respectively, c ^T =[1 0 ... 0], d is the control vector, d ^T =c ^T (A ^T QA+RE) ^-1 A ^T Q, thus constituting the actual control u(k), which is: After the control function is implemented, the motor output speed y ^* (k+1) at the next moment is collected, Use the estimated rotational speed of the oil drilling rig system PMSM to correct the prediction and make new optimizations. After the real-time control of the PMSM is implemented at time k, the predicted output at this time is: the predicted value at this time Compared with the detected PMSM rotational speed estimation output value y ^* (k+1), the output error is obtained as: By weighting the error e ^* (k+1), the prediction of the PMSM rotation speed at the future time is corrected, that is: in, After updating the state, the revised PMSM speed is predicted As the initial prediction value at the next moment, the rotation speed prediction of the PMSM at the next moment is finally obtained according to the formula (27). for: 7. permanent magnet synchronous motor dynamic matrix control method according to claim 1, is characterized in that: in described step 4, constitute the permanent magnet motor DMC vector control structure based on EKF, and the whole motor system of control structure is speed outer loop The double closed-loop speed control system composed of the inner loop and the current loop, the four inputs of the EKF speed estimation module are the stator current and stator voltage in the static coordinate system, and the output is the estimated rotor speed, and the output is used as the feedback information of the speed loop, and the prediction The error obtained after the comparison is output, and the predicted value is further corrected by the DMC algorithm, and the sensorless speed control of the entire system is finally completed.