CN108390597A - Permanent magnet synchronous motor nonlinear predictive controller design with disturbance observer - Google Patents

Abstract

The invention discloses the design of a nonlinear predictive controller of a permanent magnet synchronous motor with a disturbance observer, and belongs to the technical field of high-performance motor drive control systems. First, considering all model errors and external disturbances in the dq coordinate system, a nonlinear mathematical model of PMSM is constructed; secondly, on the basis of this model, the predictive controllers of the outer loop speed loop and the inner loop current loop are designed separately, and in the presence of The design of the disturbance observer is carried out when the control device is limited. The present invention overcomes the limitation of the processed variables and the limitation of current in the system by designing the nonlinear model predictive controller of the cascaded structure and the disturbance observer with anti-saturation, which is very dependent on the electrical parameters of the motor, and The disturbance will be considered and compensated in the predictive controller, thus enhancing the robustness of the permanent magnet synchronous motor control system. The invention verifies through experiments that the method can make the system output track the reference track more accurately, and at the same time, considering that the current limit can maintain strong robustness when the model parameter error and load change.

Description

Design of Nonlinear Predictive Controller for Permanent Magnet Synchronous Motor with Disturbance Observer

technical field

The invention relates to a design of a nonlinear predictive controller for a permanent magnet synchronous motor with a disturbance observer, and belongs to the technical field of high-performance motor drive control.

Background technique

The characteristics of high efficiency and high power density of permanent magnet synchronous motor make it occupy a very important position in practical industrial applications; however, the multivariable, nonlinear, time-varying parameters of its model and its fast dynamics make its control very difficult. complex; although a variety of advanced control methods for permanent magnet synchronous motor drive systems have been proposed based on modern control theories, such as adaptive control, self-tuning control, intelligent control, etc. The dynamics of modeling and the adaptability to disturbance are poor, and the robustness of the system needs to be further solved, so the application range is limited.

The main challenge of our research task is to conceive a control method for permanent magnet synchronous motors, which can have better continuous trajectory tracking performance, disturbance rejection performance, stability and robustness, and when parameters are uncertain, considering physical constraints While calculating the time, the strong nonlinear characteristics of the system should be preserved at the same time.

Under this framework, model predictive control is proposed as an ideal solution; however, the conceived discrete-time model-based nonlinear predictive controller requires long computation time, which limits nonlinear systems to dynamic processes with slower In the process of industrial application, such as metallurgy, oil refining, chemical industry and paper making, etc., this is due to the long calculation time required for the optimization of nonlinear problems, especially when considering the influence of constraints; it is for this reason that in In most cases, researchers linearize the predicted behavior of the nonlinear system at a working point to avoid solving nonlinear constrained optimization problems and reduce the amount of online calculations, but they do not fully consider the resulting approximation and constraints Nonlinear problems; with the development of new technologies of nonlinear predictive control based on continuous time models, the calculation time of the system is greatly reduced; in these new technologies, Taylor series expansion is used to design predictive models based on continuous time models, and then in the digital The analysis and modeling of the obtained controller on the signal processor has achieved good results; however, we know that the robustness of the system is poor when this control strategy considers external disturbances and the built model is inaccurate; for Therefore, we propose the addition of a disturbance observer capable of estimating all disturbances affecting output regulation. Combining nonlinear predictive control and disturbance observation, the system can still maintain high robustness under the influence of motor parameter changes and external disturbances. On the other hand, usually the variables we deal with are limited by the saturation module. In practical applications, an anti-saturation module is usually added to the control loop when designing a disturbance observer.

Contents of the invention

The invention provides a non-linear predictive control of a permanent magnet synchronous motor with a disturbance observer for high-performance motor drive control applications that require a permanent magnet synchronous motor to have a fast dynamic response process, high precision and stable speed tracking performance, and strong robustness The design method of the controller is based on the nonlinear model of permanent magnet synchronous motor considering all model errors and external disturbances. Based on the generalized predictive control theory, the nonlinear model predictive control and disturbance observer design are closely combined. A rolling time-domain optimization control strategy is established; this control strategy can make the system output more accurately track the reference trajectory, while taking into account the influence of the current limit, it can maintain strong robustness when the model parameter error and load change .

Method of the present invention comprises the following steps:

Step 1: Consider all model errors and external disturbances in the dq coordinate system, and construct a nonlinear mathematical model of PMSM

(25)

In the formula, , and Indicates model errors and external load disturbances.

Step 2: On the basis of the established disturbance model, design the predictive controllers of the outer loop speed loop and the inner loop current loop respectively. According to the generalized predictive control theory, select the cost function, and find it by minimizing it in the rolling time domain. Optimal control rate, so that the output of the system within the prediction time can track the given reference trajectory, so as to achieve the purpose of predictive control; at the same time, consider the design of the disturbance observer when there is a control device limitation, so that the system can be controlled when the model parameter error It can maintain strong robustness when the load changes.

Firstly, the design of the predictive controller of the outer loop speed loop is carried out;

State space model of speed loop of permanent magnet synchronous motor is the state variable, the quadrature axis current component is the input, the speed for output. The purpose of nonlinear model predictive control is to find the appropriate quadrature axis current component , so that the chosen cost function minimum.

Applying a Taylor series expansion expresses the prediction of the output and the prediction of the output reference value such that: is established, the minimum value of the quadrature axis current component that minimizes the cost function is finally obtained as:

(26)

in, (27).

The disturbance signal is usually an unknown variable that must be estimated and replaced in the controller to ensure the accuracy of disturbance suppression and reference signal continuity; therefore, the control rate (26) can be rewritten as:

(28)

in, represents the estimated perturbation.

Secondly, the velocity loop disturbance observer is designed when the quadrature axis current component is limited;

In order to limit the quadrature axis current component, a saturation block is introduced in the outer loop of the control loop; the disturbance observer can be written as:

(29)

in, , ,and is the parameter adjusted by the observer,

Considering (25), we get:

(30)

Will and Expand, and substitute (28) into (29), get:

(31)

in, .

Now, if we substitute (31) into the controller (28), the quadrature axis current reference that ensures speed regulation is written as the following relation:

(32)

in,

(33)

(34).

Thirdly, design the inner loop current loop controller;

The goal of the inner loop current loop design is to design a robust predictive regulator when the motor parameters change; the dynamic equations in the nonlinear form of the current loop are given by and is a state variable, and for input, and is the output; the goal of generalized predictive control is to find the controller variables that minimize the following cost function:

(35)

The output and future reference values are predicted by Taylor series expansion, and the cost function is differentiated from the control rate. The optimal control rate minimizes the cost function, that is, satisfies , and end up with:

(36)

in, ; ; ;

;

In the actual system, the disturbance is observed and compensated, so equation (36) can be rewritten as:

(37).

Finally, the inner-loop disturbance observer is designed when there are control device constraints

As with perturbation observer design in the outer loop, the initial observer that allows perturbation estimation is of the form:

(38)

in, , ,and is a constant coefficient matrix;

The error between the regulator output and the saturation block output can be integrated for observer design:

(39)

therefore:

(40)

In the end, we get the disturbance observer of the presence restriction device module as:

(41)

As before, the observer in the controller is replaced by the one defined in (37), yielding

(42)

in,

(43)

(44).

Advantages of the present invention: first, compared with the traditional control mode, the main disadvantage of the controller is the lack of robustness to model errors and load disturbance changes; the present invention fully considers model errors and loads when establishing the nonlinear model of the motor changing effects, considering them as unknown and unmeasurable disturbances in a finite time, so a new design based on the function Disturbance observer, the disturbance will be considered and compensated in the predictive controller; secondly, compared with the model predictive control of the direct structure, the limitation of the processed variables and the current limitation of the direct structure mode are very dependent on the electrical parameters of the motor ; The present invention constructs a control strategy of a cascaded structure, the outer loop of the system uses predictive control to ensure speed regulation, and the inner loop constitutes a multivariable predictive control for current regulation; the current is directly limited by the saturation module, because the outer loop contains integral and Saturation module, the speed response will inevitably overshoot every time the limiting device works; in order to eliminate the influence of the limiting device, an anti-saturation module is introduced in the control loop; through the control strategy implemented by the present invention, it can make The output more accurately tracks the reference trajectory while remaining robust to model parameter errors and load variations.

Description of drawings

Fig. 1 is a structural diagram of a cascaded nonlinear model predictive control system for a permanent magnet synchronous motor of the present invention.

Figure 2 is the speed and speed error curves of the cascade structure system of the present invention: without anti-saturation and with fast dynamics for a given signal.

Figure 3 is the speed and speed error curves of the cascade structure system of the present invention: with anti-saturation and fast dynamics for a given signal.

Fig. 4 is the speed and speed error curve of the cascade structure system of the present invention: the change of electrical parameters at T = 0.5s.

Fig. 5 is the arc-direct axis current curve of the cascade structure system of the present invention: the change of electrical parameters at T = 0.5s.

Fig. 6 is the speed and speed error curve of the cascaded structure system of the present invention: the load changes suddenly at T=0.5s.

Fig. 7 is the arc-direction axis current curve of the cascade structure system of the present invention: the load changes suddenly at T = 0.5s.

Detailed ways

Below in conjunction with accompanying drawing and specific embodiment the present invention is described in further detail;

Fig. 1 is the general block diagram of the required motor control system of the present invention, as shown in Fig. 1, the rotor position signal of permanent magnet synchronous motor control system Obtained by photoelectric encoder.

In the first step, the stator three-phase current of the permanent magnet synchronous motor is obtained by sampling the current sensor , and , and then converted to the d -axis current in the two-phase rotating coordinate system through Clark transformation (3s/2s) and Park transformation (2s/2r) and q- axis current ;exist Considering all model errors and external disturbances in the coordinate system, the nonlinear mathematical model of PMSM is constructed as follows:

(45)

In the formula, , and represents the model error and external load disturbance, and defines:

(46)

When the dynamics of various uncertainties are unknown, we assume that they change slowly compared to the dynamics of the system time constants, so, there are:

; ; (47).

In the second step, on the basis of the nonlinear disturbance model of the permanent magnet synchronous motor, the predictive controllers of the outer loop speed loop and the inner loop current loop are designed respectively, and the disturbance observer is designed when there are control device constraints , so that the system can maintain strong robustness when the model parameter error and load change.

(1) Design of outer loop speed loop controller

The state space model of permanent magnet synchronous motor is:

(48)

in, ; ; ;

therefore: (49)

The output is controllable:

(50)

The processed variable is represented by the quadrature axis current component; therefore, the saturation is directly applied to limit; the purpose of generalized predictive control is to find the appropriate quadrature axis current component to minimize the selected cost function; here, the cost function is selected:

(51)

Apply a Taylor series expansion to express the prediction of the output and the prediction of the output reference value:

; (52)

Substitute (52) into (51) to get:

(53)

This equation is equivalent to:

(54)

in,

(55)

On the other hand, the differential of velocity is:

(56)

Thus, the differential of the cost function to the quadrature axis current component can be obtained as:

(57)

The necessary condition is to make:

(58)

From equation (57), we can derive the minimum value of the quadrature axis current that minimizes the cost function, namely:

(59)

in,

(60)

Substituting (59) into (56), the dynamic error is:

(61)

Since the prediction time is positive, the dynamics of the continuous system are stable;

The disturbance is considered as an unknown variable, therefore, it must be estimated and substituted in the controller to ensure disturbance rejection and a continuous accurate magnitude of the reference signal; therefore, the control rate is rewritten as:

(62)

in, represents the estimated perturbation.

(2) The design of the disturbance observer when there is a limitation of the quadrature axis current component

To limit the quadrature axis current component, a saturation block is introduced in the outer loop of the control loop; the disturbance observer can be estimated as follows:

(63)

in,

(64)

(65)

in, is the parameter adjusted by the observer

Expand (64) and (65) to get:

(66)

Considering (48), we get:

(67)

Substituting (67) into (63) and taking into account that the differential of the disturbance is zero, we obtain the error equation for the disturbance observer:

(68)

This equation is stable when:

(69)

Note that the initial observation defined in (63) can be written in the following form:

(70)

in,

(71)

Substituting (62) and (66) into (70), we get:

(72)

in,

(73).

Now, if we substitute (72) into the controller (62), the quadrature axis current reference that ensures speed regulation is written as the following relationship:

(74)

in,

(75)

(76)

The limit value of the phase current amplitude can be transformed into the limit value of the axial current component amplitude as follows:

(77)

in, The term acts as an anti-saturation compensation, which can compensate for the adverse effects of the current limiting device.

(3) Design of the inner loop current loop controller

The goal of the inner current loop design is to design a robust predictive regulator when the motor parameters change. The dynamic equation in nonlinear form is:

(78)

in, ; ; ; ; ; ;

The controlled output is the direct-axis component of the current:

(79)

The goal of generalized predictive control is to find the controller variables that minimize the following cost function:

(80)

in,

(81)

The reference value of the quadrature axis current is calculated by formula (74); in order to calculate the control rate, we use the same steps as the outer loop;

(82)

The output is expanded by Taylor series:

(83)

In the same way, future reference values are predicted by Taylor series expansion:

(84)

Substituting (83) and (84) into (80), we get:

(85)

in, (86)

in, is a two-dimensional identity matrix;

Combining (82) and (85), the differential of the cost function with respect to the control rate can be written as:

(87)

The optimal control rate minimizes the cost function,

(88)

Solve equation (88) to get

(89)

in, ; ; ;

;

In the actual system, the disturbance is observed and compensated, so equation (4.52) can be rewritten as:

(90).

(4) Design of disturbance observer when there are control device constraints

As with perturbation observer design in the outer loop, the initial observer that allows perturbation estimation is of the form:

(91)

in,

(92)

(93)

in, is a constant coefficient matrix;

Equation (78) is written as: (94)

Substituting this relationship into the expression (91) for the initial observer yields:

(95)

We notice that when the matrix When the eigenvalue of has a negative real part, the dynamic error of the observer is stable;

However, we know that:

(96)

Therefore, to simplify the study of observer stability, the choice matrix for:

(97)

Combining these equations, we can conclude that the stability of the observer is ensured by the following conditions:

; (98)

We have noticed:

(99)

The error between the regulator output and the saturation block output can be integrated for observer design:

(100)

therefore:

(101)

Substituting (90), (96) and (99) into (101), we get the perturbation observer for the presence-limited device module as:

(102)

in,

(103)

As before, the observer in the controller is replaced by the one defined in (90), giving

(104)

in,

(105)

(106)

The restriction on the variables handled is given by:

(107).

The method of the present invention has been experimentally verified. In order to verify the performance of the nonlinear predictive control system for permanent magnet synchronous motors with disturbance observers, an experimental platform for motor drive systems with Infineon's XMC4500 chip as the core is built, which mainly includes the motor to be tested. There are two parts of the control system and the load system.

Beneficial effects: In order to verify the speed tracking performance of the system, the experimental parameters of the nonlinear predictive controller of the cascaded structure: model discrete time , the controller sampling time , the prediction time of the inner loop is T = 1.85ms, and the prediction time of the outer loop is T = 18.5ms. Fig. 2 is the speed and speed error curves of the cascaded structure system of the present invention when there is no anti-saturation and the given signal has fast dynamics. Fig. 3 is the speed and speed error curves of the cascaded structure system when the present invention has anti-saturation and the given signal has fast dynamics. It can be seen from Figure 2 and Figure 3 that the predictive control system with cascaded structure reduces the static error due to the introduction of the disturbance observer. However, due to the integration action included in the estimator, the saturation module overshoots the velocity response by about 50%. An anti-saturation module is introduced in the control strategy, which enables the system to eliminate overshoot and improve the speed response time. Fig. 4 is the speed and speed error curve of the cascaded structure system when the electrical parameters change at T = 0.5s according to the present invention. Fig. 5 is the arc-direct axis current curve of the cascade structure system when the electrical parameters change at T = 0.5s according to the present invention. It can be seen from Figure 4 and Figure 5 that the change of motor parameters has an impact on the robustness of the controller. When a disturbance observer is added to the controller, the speed error will be quickly reduced to zero, even if the parameters of the motor are not Sure. This is due to the fact that the estimator compensates for all parameter uncertainties and the effects of load disturbances. And we notice that, although all the parameters of the motor are changing, the direct axis current component remains equal to the reference value. Fig. 6 is that the present invention is at T=0.5s ( ) When the load changes suddenly, the speed and speed error curve of the cascaded structure system. Fig. 7 is that the present invention is at T=0.5s ( ) when the load changes suddenly, the arc-direct axis current curve of the cascaded structure system. It can be seen from Figure 6 and Figure 7 that when the load changes, the maximum speed error depends on the design of the disturbance observer, and the error will be completely eliminated in a short time, and the system has a good disturbance suppression ability.

The present invention proposes a method for designing a nonlinear predictive controller with a permanent magnet synchronous motor cascaded structure with a disturbance observer, which combines the rolling time-domain optimization control strategy of the nonlinear model predictive control with the design of the disturbance observer, And considering the influence of the saturation limit, not only the tracking accuracy of the system is improved, but also the robustness of the system is enhanced. The experimental results show that the control strategy effectively enhances the dynamic control performance of the system when the model parameter error and load change.

Claims (3)

1. The design of the nonlinear predictive controller of the permanent magnet synchronous motor with the disturbance observer is characterized by comprising the following two steps:

the method comprises the following steps: considering all model errors and external disturbance under a dq coordinate system, and constructing a nonlinear mathematical model of the PMSM;

step two: on the basis of the model, respectively designing a prediction controller of an outer ring speed ring and an inner ring current ring, selecting a cost function according to a generalized prediction control theory, and searching for an optimal control rate in a rolling time domain by minimizing the cost function, so that the output of the system in the prediction time can track a given reference track to achieve the purpose of prediction control; meanwhile, the design of a disturbance observer is considered when the limitation of a control device exists, so that the system can keep high robustness when the model parameter error and the load change exist.

2. The design of the nonlinear predictive controller of the permanent magnet synchronous motor with the disturbance observer according to claim 1, wherein the step one of considering all model errors and external disturbances in the dq coordinate system and constructing the nonlinear mathematical model of the PMSM comprises the following steps:

（1）

in the formula,、andrepresenting model errors and external load disturbances.

3. The design of the nonlinear predictive controller of the permanent magnet synchronous motor with the disturbance observer according to claim 1, wherein in the second step, on the basis of the constructed PMSM nonlinear disturbance model, the design of the predictive controller of an outer ring speed ring and an inner ring current ring is respectively carried out, and meanwhile, the design of the disturbance observer is considered when the limitation of a control device exists, so that the system can keep high robustness when the model parameter error and the load change exist, and the process is as follows:

(1) design of outer ring speed ring controller

The state space model of the permanent magnet synchronous motor speed ring is as follows:

（2）

wherein,；；；；；；；

the purpose of the nonlinear model predictive control is to find a suitable quadrature-axis current componentSo that the selected cost functionMinimum;

applying a taylor series expansion to represent the prediction of the output and the prediction of the output reference value, and such that:and if so, obtaining the minimum value of the quadrature axis current component which minimizes the cost function as follows:

（3）

wherein,

（4）

the disturbance signal, usually as an unknown variable, must be estimated and replaced in the controller to ensure the accuracy of disturbance rejection and reference signal continuity, so the control rate (3) can be rewritten as:

（5）

wherein,representing the estimated perturbation;

(2) design of disturbance observer when quadrature axis current component limitation is present

In order to limit the quadrature axis current component, a saturation module is introduced in the outer loop of the control loop, and the disturbance observer can estimate as follows:

（6）

wherein,，and is andis a parameter adjusted by the observer;

in view of (2), we obtain:

（7）

will be provided withAndexpanding, and jointly substituting into (6) with (5), obtaining:

（8）

wherein,；

now, if we substitute (8) into the controller (5), the quadrature axis current reference value that ensures speed regulation is written in the following relation:

（9）

wherein,

（10）

（11）

(3) design of inner loop current loop controller

The design of the inner loop current loop aims at designing a robust prediction type regulator when the parameters of the motor are changed; the nonlinear form of the dynamic equation is:

（12）

wherein,；；；；；；；

the goal of generalized predictive control is to find the controller variables that minimize the cost function:

（13）

the output and future reference values are predicted by taylor series expansion, and the derivative of the final cost function to the control rate can be written as:

（14）

the optimal control rate minimizes the cost function, i.e. satisfiesObtaining:

（15）

wherein；；；；

In a real system, the disturbance is observed and compensated for, so equation (15) can be rewritten as:

（16）

(4) design of disturbance observer when there is a control device limitation

As with the disturbance observer design in the outer loop, the initial observer allowing for disturbance estimation is of the form:

（17）

wherein,，and is andis a constant coefficient matrix;

the error between the regulator output and the saturation block output can be integrated when the observer is designed:

（18）

thus:

（19）

finally, we get the disturbance observer with the limiting device module as:

（20）

wherein,（21）

as before, the observer in the controller is replaced by that defined by (16) to obtain

（22）

Wherein,

（23）

（24）。