CN104779873B - A kind of predictive functional control algorithm for PMSM servo-drive systems - Google Patents

Abstract

The invention discloses a predictive function control method for a PMSM servo system. The method first collects the rotor position signal θ and the motor current signal i _q of the PMSM servo system, uses a Kalman filter to observe the rotor load disturbance, and obtains the rotor load torque and rotor speed Then the rotor load torque and optimal control Feedback to the speed prediction unit of the predictive function control (PFC) to obtain the predicted value ω _m of the rotor speed, and the rotor speed and the predicted value ω _m of the rotor speed are input to the error prediction unit controlled by the prediction function to obtain the error value e of the rotor speed; finally, e, ω _m and Input to the optimization control unit of predictive function control to obtain the optimal control amount Realize high-precision control of PMSM servo system under the influence of disturbance. This method organically combines Kalman filter and predictive function control, and the two complement each other, which can optimize the control amount of the servo system and improve the control accuracy and anti-disturbance ability of the PMSM servo system.

Description

A Predictive Function Control Method for PMSM Servo System

technical field

The invention relates to a predictive function control method for a permanent magnet synchronous motor (PMSM) servo system, belonging to the technical field of high-precision servo control systems.

Background technique

With the improvement of the control precision of the servo system, the disturbance has become an important problem that cannot be ignored. Disturbances often come from uncertain factors neglected in the modeling process, sudden load changes and parameter changes during system operation. The existence of these factors makes the performance of the closed-loop system worse or even unstable. Therefore, in order to improve the control performance of the servo system, its controller must overcome the influence of external disturbance on the system.

In the PMSM servo control system, as a multivariable, nonlinear and strongly coupled controlled object, PMSM has the characteristics of nonlinearity and uncertainty. In order to achieve high-precision servo control, it is necessary to overcome the influence of the uncertain factors of the controlled object including PMSM and load and external disturbance on system performance. Traditional feedback control strategies, such as high-gain PID control methods, have the advantages of simple structure and easy implementation. Usually, better performance can be obtained under the condition of parameter matching, but in actual engineering, too high gain will lead to system oscillation. Unsteady.

In practical industrial applications, there will always be more or less disturbances, including friction and load disturbances. In order to eliminate the influence of disturbances and improve the control performance of servo systems, domestic and foreign scholars have conducted a lot of research. Predictive Functional Control (PFC) is a kind of computer control algorithm developed in recent years. Because it adopts control strategies such as multi-step testing and feedback correction, it has the advantages of online optimization, constraint processing, and less online calculation. It is easy to use, can realize simple and intuitive design criteria, and has good control effects. Precise digital models of complex industrial production processes. Literature (Xia Zezhong, Zhang Guangming. Predictive function control and its simulation research in servo system [J]. Chinese Journal of Electrical Engineering, 2005, 25(14): 130-134.) proposed a predictive function control method for a typical servo control system , the simulation results show that this method can improve the tracking performance in the servo system, however, in practical industrial applications, the predictive function control method cannot suppress the rotor load disturbance of the servo system, because the method does not consider the sudden change of the rotor load disturbance, when the PMSM When the servo system is faced with the rotor load disturbance, it cannot eliminate the sudden effect of the rotor load disturbance, which makes the control performance of the servo system worse.

Contents of the invention

Aiming at the deficiencies of the prior art, the present invention provides a predictive function control method for a PMSM servo system, which organically combines Kalman filter and predictive function control (PFC) technology, the two complement each other, and can optimize the control amount of the servo system , and then improve the control accuracy and anti-disturbance ability of PMSM servo system.

For realizing above technical purpose, the present invention will take following technical scheme:

A kind of predictive function control method that is used for PMSM servo system, it is characterized in that, at first, gather the rotor position signal θ of PMSM servo system and motor current signal i _q , use rotor position signal θ and motor current signal i _q as Kalman filter The input signal of the rotor, according to the rotor position signal θ and the motor current signal i _q , use the Kalman filter to observe the rotor load disturbance, and obtain the rotor load torque and rotor speed Then, it is assumed that the predictive function control (PFC) includes an optimization control unit, an error prediction unit and a speed prediction unit, and the rotor load torque and the optimal control quantity output by the optimized control unit Input to the speed prediction unit to obtain the predicted value ω _m of the rotor speed, and at the same time, the rotor speed and the predicted value ω _m of the rotor speed are input to the error prediction unit to obtain the rotor speed error value e; finally, the rotor speed error value e, the rotor speed predicted value ω _m and the rotor speed Input to the optimization control unit of predictive function control (PFC) to obtain the optimal control amount Realize the high-precision control of the PMSM servo system under the influence of disturbance; among them,

The Kalman filter is established based on the following formula:

In formula (4), is the estimated value of the rotor load disturbance by the Kalman filter of the servo system at time k, and the superscript "∧" represents the meaning of estimation; F is the coefficient of the rotor load disturbance estimated value, and G is the coefficient of the rotor load disturbance coefficient matrix; is the left inverse matrix of the rotor load disturbance coefficient matrix at time k-1, and its expression is:

in, is the transpose of the input matrix D _k-1 of the servo system at time k-1, and its superscript "T" is the symbol of matrix transposition; D _k-1 is the discrete input matrix at time k-1, and its expression for:

Among them, T _s is the sampling cycle time of the servo system, and J is the moment of inertia of the motor load;

In formula (4), A _k-1 is the discrete matrix of the servo system at time k-1, and its expression is:

Among them, B is the viscous friction coefficient;

In formula (4), x _k|k is the prior prediction value of the Kalman filter for the discrete prediction value x _k at the k-th moment, x _k is the discrete prediction value of the motor state variable x at the k-th moment, and the expression of x is: x＝[ω θ T _L ] ^T , where ω is the rotor speed, θ is the rotor position, T _L is the rotor load torque; Kalman filter for the discrete estimated value of the k-1th moment The posterior estimate of , is the motor state variable The discrete estimated value of the k-1th moment, The expression is: The superscript "∧" represents the meaning of estimation; u _k-1 is the discrete output of the system to the motor state variable u at k-1 time, and the expression of u is: u=[T _e ], where T _e is the motor Electromagnetic torque;

The predicted value ω _m of the rotor speed is established based on the following formula:

In the formula, ω _m (k+i) is the predicted value of the rotor speed of the servo system at k+i time, i=1, 2,...P, P is the length of the time domain for prediction optimization, and K _m is the prediction function control (PFC ), its expression is: K _m =(1-α _m )K _t /B, and α _m is the second coefficient of the rotational speed prediction unit of predictive function control (PFC), and its expression is: is the i-th power of the second coefficient of the speed prediction unit of predictive function control (PFC), K _t is the rotor load torque constant, is the optimal control quantity of the servo system at time k, T _L (k) is the rotor load torque value of the servo system at time k;

The rotational speed error value e of the rotor is established based on the following formula:

In the formula, e(k+i) is the error value of the rotor speed at time k+i, i=1,2,...P, P is the length of the prediction optimization time domain, is the rotor speed value observed by the Kalman filter at time k, and ω _m (k) is the predicted value of the rotor speed of the servo system at time k;

The optimal control amount Based on the following formula:

In formula (14), W ₁ is the first coefficient matrix of the optimal control unit of predictive function control (PFC), and its expression is:

Q is the input quantity weighting coefficient matrix of the optimization control unit, and its expression is: in, is the square of the weighted coefficient of the input quantity of the optimized control unit; R is the weighted coefficient matrix of the controlled quantity of the optimized control unit, and its expression is: R=[r ² ], where r ² is the weighted coefficient of the controlled quantity of the optimized control unit square; W ₂ (k) is the second coefficient matrix of the optimal control unit of predictive function control (PFC) at time k, and its expression is: W ₂ (k)=[ω _r (k+1)…ω _r (k+ P)] ^T , where ω _r (k+1) is the rotor speed reference value of the servo system at k+1 time; W ₃ (k) is the third coefficient matrix of the optimal control unit of the predictive function control (PFC) at k time , whose expression is: E(k) is the rotational speed error matrix of the rotor, and its expression is: E(k)=[e(k+1)...e(k+P)] ^T .

According to the above technical scheme, the following beneficial effects can be achieved:

This method organically combines the Kalman filter and predictive function control (PFC) technology, the motor rotor speed error value e, the rotor speed prediction value ω _m and the rotor speed Input to the optimization control unit of predictive function control (PFC) to obtain the optimal control amount of the rotor The high-precision control of the PMSM servo system under the influence of disturbance is realized, and the anti-disturbance ability of the servo system is improved.

Description of drawings

Fig. 1 is PMSM servo system block diagram of the present invention;

Fig. 2 is a kind of flowchart that is used for the predictive function control method of PMSM servo system that the present invention proposes;

Fig. 3 is the velocity response experiment result figure of the PMSM servo system adopting the inventive method;

Figure 4 is a diagram of the speed response experiment results of the PMSM servo system using the traditional predictive function control method.

detailed description

The accompanying drawing discloses a non-restrictive structural schematic diagram of a preferred embodiment involved in the present invention, and the technical solution of the present invention will be described in detail below in conjunction with the accompanying drawings.

As shown in Figure 1, it discloses a system block diagram of a predictive function control method for a PMSM servo system according to the present invention, which adopts a photoelectric encoder to collect the position signal θ of the PMSM servo motor, and the photoelectric encoder is installed on the motor Internally, the Hall current sensor is used to collect the current signals i _u and _iv of the motor at the same time, and the Clarke transformation and Park transformation are performed on them to obtain i _d and i _q , and the motor position signal θ and the motor current signal i _q are fed back to the Kalman filter The Kalman filter is used to observe the rotor load torque, rotor speed and rotor position, and the observation results are fed back to the predictive function control (PFC). After the adjustment of the predictive function control (PFC), the optimal control amount is obtained. obtained through the PI regulator with Then with the position signal observed by the Kalman filter, after Park inverse transformation, the reference value of the stator phase voltage in the α-β coordinate system is obtained with The PWM control signal is generated by using the space vector pulse width debugging technology, and then the three-phase inverter is controlled by the PWM control signal, and the required three-phase AC power is converted to drive the motor to run.

Specifically: described a kind of predictive function control method for PMSM servo system comprises following four steps:

Step 1: Build the Kalman filter

Collect the rotor position signal θ and current signal i _q of the PMSM servo system, then use the rotor position signal θ and current signal i _q as the input signal of the Kalman filter, use the Kalman filter to observe the rotor load disturbance, and obtain the rotor load torque and rotor speed The steps to construct a Kalman filter are as follows:

Step 1: Collect rotor position signal θ and current signal i _q

Use the photoelectric encoder to collect the position signal θ of the PMSM servo motor, use the current sensor to collect the PMSM stator current i _u and _iv , and obtain the d-axis current i _d and q-axis current i in the two-phase rotating coordinate system through Clarke transformation and Park transformation _q ;

Step 2: Construct the Rotor Discrete Load Disturbance Observer

Substituting the rotor load disturbance and measurement error in the servo system into the state equation of the motor, the discrete equations of the servo system are obtained as follows:

In the formula, x _k is the discrete predicted value of the motor state variable x at the kth moment, and the expression of x is: x=[ω θ T _L ] ^T , where ω is the rotor speed, θ is the rotor position, and T _L is the rotor Load torque; y _k is the discrete predicted value of the system input variable y at the kth moment; u _k is the discrete output of the system to the motor state variable u at k-1 time, and the expression of u is: u=[T _e ] , where T _e is the electromagnetic torque of the motor; w _k is the rotor load disturbance, v _k is the measurement error, A _k is the discrete system matrix corresponding to the servo system at time k, and its expression is: D _k is the input matrix corresponding to the k moment of the servo system, and its expression is: C _k is the output matrix corresponding to the k moment of the servo system, and its expression is: C _k = [01 0], where T _s is the sampling cycle time of the servo system, B is the viscous friction coefficient, and J is the moment of inertia of the motor load ;

In order to estimate the rotor load disturbance value of the servo system at time k+1, formula (1) is:

In the formula, is the estimated value of the rotor load disturbance by the Kalman filter of the servo system at time k, Γ ⁺ is the load disturbance coefficient matrix to estimate the load disturbance w _k of the servo system, and the rotor discrete load disturbance observer is:

In the formula, is the left inverse matrix of the rotor load disturbance coefficient matrix at time k-1, and its expression is:

in, is the transposition of the input matrix D _k-1 of the servo system at k-1 moment; Φ(z) is a low-pass filter, and its expression is: Φ(z)=H(zI-F) ^-1 G; F is the coefficient of the rotor load disturbance value of the system, G is the coefficient of the rotor load disturbance coefficient matrix of the system; H is the constant coefficient matrix;

Step 3: Construction of the Kalman filter

According to the principle algorithm of the Kalman filter and the discrete load disturbance observer, the required Kalman filter is established based on the following formula:

Step 2: Calculate the rotor speed prediction value

Fig. 2 is the flow chart of a kind of predictive function control method for PMSM servo system that the present invention proposes, has shown Kalman filter and predictive function control (PFC), and predictive function control (PFC) comprises optimization control unit, error prediction unit and the speed prediction unit, the observed rotor load disturbance and the optimal control quantity output by the optimized control unit As the input signal of the speed prediction unit of predictive function control (PFC), the predicted value of rotor speed ω _m is obtained. In the permanent magnet synchronous motor servo system, in order to decouple the speed and current, use (The set value of the d-axis current is always 0) vector control, according to the Laplace transform, the mechanical equation model of the motor dynamics is:

In formula (5), ω(s) is the mechanical angular velocity of the motor, K _t is the system torque constant, is the rotor control quantity, formula (5) is written as a differential equation:

In formula (6), ω _m (k+1) is the predicted value of the rotor speed of the servo system at time k+1, K _m is the first coefficient of the speed prediction unit of predictive function control (PFC), and its expression is: K _m = (1-α _m )K _t /B, α _m is the second coefficient of the speed prediction unit of predictive function control (PFC), and its expression is: is the optimal control quantity of the servo system at time k, T _L (k) is the rotor load torque value of the servo system at time k;

At the next sampling time k+2 of the system, we have

Assuming the value of the control variable of the servo system in the future, the optimal control variable of the servo system is:

Substitute formula (6) into formula (7) to get:

The above formula (6), formula (7) and formula (8) are superimposed in sequence to get:

In formula (9), ω _m (k+i) is the predicted value of the rotor speed of the system at time k+i, i=1,2,...P, P is the length of the predicted time domain, It is the i power of the second coefficient α _m of the speed prediction unit of predictive function control (PFC);

Step 3: Calculate the rotor speed error e, the calculation formula is:

In the formula (10), e(k+i) is the error value of the rotor speed at k+i moment, i=1,2,...P, P is the length of the prediction optimization time domain, is the rotor speed value observed by the Kalman filter at time k, and ω _m (k) is the predicted value of the rotor speed of the servo at time k;

The fourth step: the rotor speed error value e, the rotor speed prediction value ω _m and the rotor speed Input to the optimization control unit of predictive function control (PFC) to obtain the optimal control amount Realize the high-precision control of the PMSM servo system under the influence of disturbance, including the following steps:

Step 1: Set the output control quantity basic function of predictive function control (PFC), its expression is:

In formula (11), is the optimal control quantity of the system at time k+i, f _j (i) is the step value of the basis function at time t=iT _s , T _s is the system sampling cycle time; i=1,2,...P, P is Predict the length of optimization time domain, j=1,2,...N, N is a natural number; μ _j is the coefficient of basis function, adopts step function as basis function, N=1, f ₁ (i)=1, its basis The function is:

Step 2: Set the rotor speed reference trajectory, its expression is:

In formula (12), ω _r (k+i) is the rotor speed reference trajectory of the system at time k+i, ω ^* is the given rotor speed of the system at time k, is the rotor speed value observed by the Kalman filter at time k, is the coefficient of the difference between the given rotor speed and the subtraction of the rotor speed, and its expression is: T _r is the expected response time of the PMSM servo system.

Step 3: The rotor speed error e, the rotor speed prediction value ω _m and the rotor speed Input to the optimization control unit of predictive function control (PFC) to obtain the optimal control amount

The cost function for the PMSM servo system is denoted as Its calculation formula is:

In formula (13), is the cost function; let, Determining the cost function for the above PMSM servo system The minimum value of , the coefficients of the coefficient matrix of the optimized control unit are updated in real time at each sampling time, and the optimal control quantity of the servo system is obtained as:

In formula (14), W ₁ is the first coefficient matrix of the optimal control unit of predictive function control (PFC), and its expression is: Q is the input quantity weighting coefficient matrix of the optimization control unit, and its expression is: in, is the square of the weighted coefficient of the input quantity of the optimized control unit; R is the weighted coefficient matrix of the controlled quantity of the optimized control unit, and its expression is: R=[r ² ], where r ² is the weighted coefficient of the controlled quantity of the optimized control unit square; W ₂ (k) is the second coefficient matrix of the optimal control unit of predictive function control (PFC) at time k, and its expression is: W ₂ (k)=[ω _r (k+1)…ω _r (k+ P)] ^T , where ω _r (k+1) is the rotor speed reference value of the servo system at k+1 time; W ₃ (k) is the third coefficient matrix of the optimal control unit of the predictive function control (PFC) at k time , whose expression is: E(k) is the rotational speed error matrix of the rotor, and its expression is: E(k)=[e(k+1)...e(k+P)] ^T .

With reference to Fig. 3, have shown to adopt a kind of predictive function control method that is used for PMSM servo system of the present invention, PMSM servo system is in the face of load sudden change, and rotor speed recovery time is 0.21s, and rotor rotational speed maximum drops 24rpm; Refer to Fig. 4. It shows that when the PMSM servo system using the traditional predictive function control method faces a sudden load change, the rotor speed recovery time is 0.51s, and the maximum rotor speed drop is 68rpm. The rotor speed recovery time and the maximum rotor speed drop of the two methods are compared From the comparison of the data in Fig. 3 and Fig. 4, it can be concluded that a predictive function control method for PMSM servo system of the present invention has better performance in terms of anti-disturbance.

The experimental platform of the specific embodiment of the present invention adopts an ARM-based full digital control implementation mode, and the programming language is C language. The system uses the XMC4500 chip of Infineon as the core to form the control circuit part; the hall current sensor is used to collect two current signals i _u and _iv ; the rotor position detection component is a 2500-line incremental photoelectric encoder used to collect The rotor position signal of the motor; the inverter circuit takes the intelligent power device as the core, it converts the power input into the corresponding three-phase AC voltage according to the space vector pulse width modulation control signal generated by the XMC4500 chip, and is used to drive the motor; the load The rated power of the motor is 3kW, and the rotor position sensor is a 24-bit multi-turn absolute encoder.

Claims (1)

1. a predictive function control method for PMSM servo system, it is characterized in that, at first, gather the rotor position signal θ of PMSM servo system and the motor current signal i _q , with rotor position signal θ and motor current signal i _q as Kalman The input signal of the filter, according to the rotor position signal θ and the motor current signal i _q , use the Kalman filter to observe the rotor load disturbance, and obtain the rotor load torque and rotor speed Then, it is assumed that the predictive function control (PFC) includes an optimization control unit, an error prediction unit and a speed prediction unit, and the rotor load torque and the optimal control quantity output by the optimized control unit Input to the speed prediction unit to obtain the predicted value ω _m of the rotor speed, and at the same time, the rotor speed and the predicted value ω _m of the rotor speed are input to the error prediction unit to obtain the rotor speed error value e; finally, the rotor speed error value e, the rotor speed predicted value ω _m and the rotor speed Input to the optimization control unit of predictive function control (PFC) to obtain the optimal control amount Realize the high-precision control of the PMSM servo system under the influence of disturbance; among them, The Kalman filter is established based on the following formula: In formula (4), is the estimated value of the rotor load disturbance by the Kalman filter of the servo system at time k, and the superscript "∧" represents the meaning of estimation; F is the coefficient of the rotor load disturbance estimated value, and G is the coefficient of the rotor load disturbance coefficient matrix; is the left inverse matrix of the rotor load disturbance coefficient matrix at time k-1, and its expression is: in, is the transpose of the input matrix D _k-1 of the servo system at time k-1, and its superscript "T" is the symbol of matrix transposition; D _k-1 is the discrete input matrix at time k-1, and its expression for: Among them, T _s is the sampling cycle time of the servo system, and J is the moment of inertia of the motor load; In formula (4), A _k-1 is the discrete matrix of the servo system at time k-1, and its expression is: Among them, B is the viscous friction coefficient; In formula (4), x _k|k is the prior prediction value of the Kalman filter for the discrete prediction value x _k at the k-th moment, x _k is the discrete prediction value of the motor state variable x at the k-th moment, and the expression of x is: x＝[ω θ T _L ] ^T , where ω is the rotor speed, θ is the rotor position, T _L is the rotor load torque; Kalman filter for the discrete estimated value of the k-1th moment The posterior estimate of , is the motor state variable The discrete estimated value of the k-1th moment, The expression is: The superscript "∧" represents the meaning of estimation; u _k-1 is the discrete output of the system to the motor state variable u at k-1 time, and the expression of u is: u=[T _e ], where T _e is the motor Electromagnetic torque; The predicted value ω _m of the rotor speed is established based on the following formula: In the formula, ω _m (k+i) is the predicted value of the rotor speed of the servo system at time k+i, i=1, 2,...P, P is the length of the predicted time domain, and K _m is the predictive function control (PFC) The first coefficient of the rotational speed prediction unit, its expression is: K _m =(1-α _m )K _t /B, α _m is the second coefficient of the rotational speed prediction unit of predictive function control (PFC), its expression is: is the i-th power of the second coefficient of the speed prediction unit of predictive function control (PFC), K _t is the rotor load torque constant, is the optimal control quantity of the servo system at time k, T _L (k) is the rotor load torque value of the servo system at time k; The rotational speed error value e of the rotor is established based on the following formula: In the formula, e(k+i) is the error value of the rotor speed at time k+i, i=1,2,...P, P is the length of the prediction optimization time domain, is the rotor speed value observed by the Kalman filter at time k, and ω _m (k) is the predicted value of the rotor speed of the servo system at time k; The optimal control amount Based on the following formula: In formula (14), W ₁ is the first coefficient matrix of the optimal control unit of predictive function control (PFC), and its expression is: Q is the input quantity weighting coefficient matrix of the optimization control unit, and its expression is: in, is the square of the weighted coefficient of the input quantity of the optimized control unit; R is the weighted coefficient matrix of the controlled quantity of the optimized control unit, and its expression is: R=[r ² ], where r ² is the weighted coefficient of the controlled quantity of the optimized control unit square; W ₂ (k) is the second coefficient matrix of the optimal control unit of predictive function control (PFC) at time k, and its expression is: W ₂ (k)=[ω _r (k+1)…ω _r (k+ P)] ^T , where ω _r (k+1) is the rotor speed reference value of the servo system at k+1 time; W ₃ (k) is the third coefficient matrix of the optimal control unit of the predictive function control (PFC) at k time , whose expression is: E(k) is the rotational speed error matrix of the rotor, and its expression is: E(k)=[e(k+1)...e(k+P)] ^T .