CN115514270A - Permanent magnet synchronous motor sliding mode active disturbance rejection control method for improving extended observer - Google Patents

Permanent magnet synchronous motor sliding mode active disturbance rejection control method for improving extended observer Download PDF

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CN115514270A
CN115514270A CN202211294468.7A CN202211294468A CN115514270A CN 115514270 A CN115514270 A CN 115514270A CN 202211294468 A CN202211294468 A CN 202211294468A CN 115514270 A CN115514270 A CN 115514270A
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permanent magnet
magnet synchronous
synchronous motor
sliding mode
equation
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朱其新
黄旭
周莉
刘红俐
张金胜
谢鸥
牛雪梅
张德义
沈晔湖
蒋全胜
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Suzhou University of Science and Technology
Jiangsu Etern Co Ltd
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Suzhou University of Science and Technology
Jiangsu Etern Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/18—Estimation of position or speed
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/20—Estimation of torque
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/22—Current control, e.g. using a current control loop
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

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Abstract

The invention belongs to the field of active disturbance rejection of permanent magnet synchronous motors, and particularly discloses a permanent magnet synchronous motor sliding mode active disturbance rejection control method for an improved extended observer, which comprises the following steps: s1: listing a mathematical equation of the actual electromagnetic torque according to a mathematical model of the permanent magnet synchronous motor; s2: discretizing the differential structure of the input signal to obtain an equation of a most tracking differentiator; s3: establishing a three-order ESO structure to obtain an expanded state observer function; s4: linearly combining the errors to obtain a nonlinear state error feedback control law; s5: and obtaining a function form of the sliding mode controller to realize the control of the sliding mode active disturbance rejection of the permanent magnet synchronous motor. The method overcomes the defect that the traditional fal function is discontinuous and not smooth, and improves the convergence speed and the observation capability of the extended state observer; the robustness and the anti-interference capability of the system are improved simultaneously.

Description

Permanent magnet synchronous motor sliding mode active disturbance rejection control method for improving extended observer
Technical Field
The invention belongs to the technical field of permanent magnet synchronous motor active disturbance rejection, and particularly relates to a permanent magnet synchronous motor sliding mode active disturbance rejection control method for an improved extended observer.
Background
The permanent magnet synchronous motor is widely applied to a high-performance position/speed servo system due to the advantages of high power density, simple and reliable structure and the like. However, due to the strong nonlinearity of the PMSM and the existence of unknown disturbance, the conventional PID control is no longer applicable. In the prior art, based on the limitation of PID, on the basis of the idea of eliminating errors by using errors, active Disturbance Rejection Control (ADRC) is proposed. The method does not depend on an accurate mathematical model of an object, can directly complete the estimation of disturbance according to input and output signals, carries out feedforward compensation in input, and has the characteristics of high interference resistance and high robustness. The active disturbance rejection control is improved from two levels of transverse direction and longitudinal direction: other control methods are introduced to form a fusion algorithm and self-algorithm improvement respectively.
The fusion algorithm aims at the problem that ADRC has limited estimation capacity, and the neural network active disturbance rejection control method is provided in the prior art to improve the problem, has the advantages of reducing the error range of an object and higher active disturbance rejection control, but the neural network takes a local minimum value as a global minimum value to increase the error. In order to solve the above problems, two schemes are adopted in the prior art, one of which introduces reverse step control, and although the scheme reduces the number of adjustment parameters, the differential operation increases the calculation difficulty; and secondly, fuzzy control is utilized, variable discourse domains are introduced, the estimation capability of active disturbance rejection is improved by the scheme, and the accuracy of the system is influenced due to the limitation of the fuzzy control. In summary, the fusion algorithm has contradiction between accuracy and estimation capability.
In the prior art, optimization of the fal function is adopted to improve the algorithm of the self. In the automatic landing flight control law design based on the active disturbance rejection control method, the new Ifal is more smooth and continuous in order to overcome the discontinuity of the fal function, but the overall control effect is not changed greatly. The novel fal function provided by the improvement of the active disturbance rejection fal function and the application of the fal function in the attitude control of the four rotors has smaller system gain and better disturbance rejection performance when the error is larger, but the continuity near the zero point of the function is not improved. Therefore, there is a great contradiction between the improvement of the fal function, and the noise immunity and continuity of the fal function cannot be kept in a better state at the same time.
Therefore, it is desirable to develop a sliding mode active disturbance rejection control method for a permanent magnet synchronous motor that can solve the above problems.
Disclosure of Invention
The invention provides a permanent magnet synchronous motor sliding mode active disturbance rejection control method for an improved extended observer, which is used for solving the problem that the disturbance rejection and continuity of the existing permanent magnet synchronous motor cannot be kept in a better state at the same time.
In order to solve the technical problems, the technical scheme of the invention is as follows: the sliding mode active disturbance rejection control method for the permanent magnet synchronous motor of the improved extended observer comprises the following steps:
s1: according to a mathematical model of the permanent magnet synchronous motor, electromagnetic torque in the mathematical model is simplified, and then a mathematical equation of actual electromagnetic torque is listed by combining disturbance of motor operation, wherein the mathematical equation is as follows:
Figure BDA0003902119200000021
wherein, T e Is an electromagnetic torque, n p Is the number of pole pairs, L md Is the mutual inductance of the d-axis, i q Is a stator current q-axis component, i df D-axis equivalent magnetizing current, μ is total perturbation;
s2: discretizing the differential structure of the input signal to obtain an equation of a most tracking differentiator;
s3: establishing a three-order ESO structure, and combining the electromagnetic torque mathematical equation of the formula 1 and the state equation of the permanent magnet synchronous motor to obtain an expanded state observer function, wherein the form is formula 2:
Figure BDA0003902119200000022
wherein z1 represents a velocity estimate; z2 represents the integrated disturbance estimate; and z3 is real-time estimation and online compensation of unknown disturbance in the total disturbance. Beta is a 1 ，β 2 ，β 3 Galn is a novel function proposed herein for the ESO observer filter coefficients;
s4: adopting a nonsingular terminal sliding mode surface function and an approach law, linearly combining errors to obtain a nonlinear state error feedback control law;
s5: and applying the equation of the most-tracking differentiator in the S2, the form function of the extended state observer in the S3 and the nonlinear state error feedback control law in the S4 to the sliding mode controller to obtain a function form of the sliding mode controller to realize the control of the sliding mode active disturbance rejection of the permanent magnet synchronous motor.
In a preferred embodiment of the present invention, the mathematical model of the permanent magnet synchronous motor in step S1 is set based on the ideal state assumption and the control mode of id =0, and is in the form of formula 3-formula 6 in the d-q coordinate system:
Figure BDA0003902119200000031
λ q ＝L q i q (4)
λ d ＝L d i d +L md i df (5)
ω e ＝n p ω r (6)
in the formula i d 、i q The stator current d and q axis components are respectively; u shape d 、U q Stator voltage d and q axis components respectively; r is s Is a stator resistor; l is a radical of an alcohol d 、L q The inductors of the d axis and the q axis of the stator are respectively; omega e Is the rotor electrical angular velocity; omega r Is the rotor mechanical angular velocity; lambda [ alpha ] d 、λ q Is a stator flux linkage of d and q axes; l is md Is the d-axis mutual inductance; i.e. i df Is d-axis equivalent magnetizing current; n is a radical of an alkyl radical p Is the number of pole pairs.
In a preferred embodiment of the present invention, the motor torque in step S1 is simplified based on the stator flux linkage equality of the d and q axes, and the simplified electromagnetic torque equation is as shown in formula 7:
Figure BDA0003902119200000032
in a preferred embodiment of the present invention, in step S2, the equation of the most tracking differentiator is equation 8:
Figure BDA0003902119200000041
wherein h is an integration step length; r is a velocity factor, the value of which determines the magnitude of the tracking velocity; h0 is a filter factor, function fhan (x) 1 ,x 2 R, h) is the fastest control synthesis function;
f ishan(x 1 ,x 2 The algorithm of r, h) is formula 9:
Figure BDA0003902119200000042
wherein h is an integration step length; r is the velocity factor.
In a preferred embodiment of the present invention, the state equation of the permanent magnet synchronous motor in step S3 is given by equation 10:
Figure BDA0003902119200000043
wherein, ω is * For a given rotational speed, ω is the actual rotational speed;
the permanent magnet synchronous motor state equation 10 is combined with the mathematical equation 1 of the actual electromagnetic torque to obtain the equation 11:
Figure BDA0003902119200000044
wherein
Figure BDA0003902119200000045
ω (t) is interference;
f (x) 1 ,x 2 ω (t), t) as state variables x 3 Then x 3 Is expressed by equation 12:
Figure BDA0003902119200000046
in a preferred embodiment of the present invention, the galn function in step S3 is expressed by formula 13,
Figure BDA0003902119200000051
in a preferred embodiment of the present invention, the nonsingular terminal sliding mode surface function in step S4 is represented by formula 14:
Figure BDA0003902119200000052
wherein h > g >0, α >0;
the approach law is formula 15:
Figure BDA0003902119200000053
wherein the content of the first and second substances,
Figure BDA0003902119200000054
k 1 >0,k 2 >0,a>1，0<b<1，h>g>0。
in a preferred embodiment of the present invention, the function form of the sliding mode controller in step S5 is formula 16:
Figure BDA0003902119200000055
wherein k is 1 、k 2 And k 3 Is a variable approximation law coefficient, n p Is the number of pole pairs, J is the moment of inertia,
Figure BDA0003902119200000056
is a permanent magnetic linkage, beta>0，h>g>0。
In a preferred embodiment of the present invention, a disturbance compensation z3 of the system is introduced in equation 16, and finally, a new active disturbance rejection control law is designed in the form of equation 17:
Figure BDA0003902119200000057
wherein k is 1 、k 2 And k 3 Is a variable approximation law coefficient, n p Is the number of pole pairs, J is the moment of inertia,
Figure BDA0003902119200000058
is a permanent magnetic linkage, beta>0，h>g>0。
Compared with the prior art, the technical scheme provided by the invention has the following advantages: aiming at the problems of load and uncertain disturbance of a permanent magnet synchronous motor control system, the invention designs a sliding mode active disturbance rejection control method based on an improved extended state observer. The discontinuous and unfinished characteristic of the traditional fal function is replaced by a novel galn function, so that the convergence speed and the observation capability of the extended state observer are improved. Sliding mode control is introduced into the nonlinear control law to form active disturbance rejection sliding mode control, and the robustness and the anti-interference capability of the system are improved simultaneously. The applicability of the sliding mode active disturbance rejection control method based on the improved extended state observer is obtained through simulation comparison of the traditional active disturbance rejection control and the novel composite active disturbance rejection control.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings of the embodiments can be obtained according to the drawings without creative efforts.
Fig. 1 is a design flowchart of a sliding mode active disturbance rejection control method of a permanent magnet synchronous motor for improving an extended observer according to an embodiment of the present invention;
fig. 2 is a structure diagram of active disturbance rejection control of a sliding mode active disturbance rejection control method of a permanent magnet synchronous motor for improving an extended observer according to an embodiment of the present invention;
fig. 3 is a structural diagram of a second-order tracking differentiator of a sliding mode active disturbance rejection control method for a permanent magnet synchronous motor of an improved extended observer according to an embodiment of the present invention;
fig. 4 is a structural diagram of an extended state observer of a sliding mode active disturbance rejection control method of a permanent magnet synchronous motor for improving the extended observer according to an embodiment of the present invention;
fig. 5 is a comparison graph of function curves of a fal function and a galn function of a sliding mode active disturbance rejection control method of a permanent magnet synchronous motor for improving an extended observer according to an embodiment of the present invention;
fig. 6 is a partially enlarged comparative graph of a function curve of a fal function and a galn function of a permanent magnet synchronous motor sliding mode active disturbance rejection control method for improving an extended observer at a point 0 according to an embodiment of the present invention;
fig. 7 is a comparison graph of the rotation speed of the sliding mode control of the novel auto-disturbance rejection of the sliding mode auto-disturbance rejection control method of the permanent magnet synchronous motor with the improved extended observer according to an embodiment of the present invention.
Detailed Description
For the convenience of understanding, the sliding mode active disturbance rejection control method of the permanent magnet synchronous motor for improving the extended observer is described in the following with reference to the embodiments, and it should be understood that these embodiments are only used for illustrating the present invention and are not used to limit the scope of the present invention.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations and positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected" and "connected" are to be construed broadly, and may be, for example, a fixed connection, a detachable connection or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
To facilitate an understanding of the invention, the invention will now be described more fully hereinafter with reference to the accompanying drawings. Preferred embodiments of the present invention are shown in the drawings. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.
1. Establishing mathematical model of permanent magnet synchronous motor
Assuming that the PMSM is ideal, the invention selects i d The control method of =0, and therefore, the study was performed with the d-q coordinate system selected. The model of the permanent magnet synchronous motor under the d-q coordinate system is as follows:
Figure BDA0003902119200000071
λ q ＝L q i q (1-2)
λ d ＝L d i d +L md i df (1-3)
ω e ＝n p ω r (1-4)
in the formula i d 、i q The stator current d and q axis components are respectively; u shape d 、U q The stator voltage d and q axis components are respectively; r s Is a stator resistor; l is a radical of an alcohol d 、L q The inductors of the d axis and the q axis of the stator are respectively; omega e Is the rotor electrical angular velocity; omega r Is the rotor mechanical angular velocity; lambda [ alpha ] d 、λ q Is a stator flux linkage of d and q axes; l is a radical of an alcohol md Mutual inductance for the d-axis; i all right angle df Is d-axis equivalent magnetizing current; n is a radical of an alkyl radical p Is a pole pair number.
The electromagnetic torque and mechanical torque equation of the permanent magnet synchronous motor is as follows:
T e ＝3n p [L md I df i q +(L d -L q )i d i q ]/2 (1-5)
T e ＝Jω r +T l (1-6)
in the formula, T e Is an electromagnetic torque; t is l Is the load torque; b is m Is the coefficient of friction; j is the moment of inertia.
Due to lambda d ＝λ q The electromagnetic torque equation of the motor can be simplified as follows:
Figure BDA0003902119200000081
where μ = T l + d, d is the external perturbation that cannot be measured and μ is the total perturbation.
2. Most tracking differentiator design
The structure of active disturbance rejection control is shown in fig. 2, a Tracking Differentiator (TD) prevents a signal from entering a jump in an input, the problem of excessive overshoot of a system is greatly reduced, so that the input signal can be quickly tracked, and the differential of the signal is obtained, and the structure is shown in fig. 3, wherein v is 0 Is an input signal of the system, v 1 Is a tracking of the input signal, v 2 Is the extraction of the input signal differential. Discretizing it yields the equation:
Figure BDA0003902119200000082
wherein h is an integration step length; r is a velocity factor, the value of which determines the magnitude of the tracking velocity; h0 is a filtering factor and plays a role in filtering. Function fhan (x) 1 ,x 2 And r, h) is the fastest control comprehensive function, and the algorithm is as follows:
Figure BDA0003902119200000091
3. observer for designing extended state
The extended state observer is a nonlinear combination mode, aims to observe the state of system output and the internal and external disturbance conditions, does not depend on a model, and can obtain an estimated value without directly measuring the disturbance, and a three-order ESO structure is shown in FIG. 4, and the state equation of a permanent magnet synchronous motor is designed as follows:
Figure BDA0003902119200000092
wherein, ω is * For a given speed, ω is the actual speed.
Can be substituted by the formula (1-8)
Figure BDA0003902119200000093
Wherein
Figure BDA0003902119200000094
ω (t) is interference.
F (x) 1 ,x 2 ω (t), t) as state variables x 3 Then, then
Figure BDA0003902119200000095
The improved extended observer is designed as follows:
Figure BDA0003902119200000096
wherein z1 represents a velocity estimate; z2 represents the integrated disturbance estimate; and z3, carrying out real-time estimation and online compensation on the unknown disturbance f in the total disturbance. Beta is a 1 ，β 2 ，β 3 Is the filter coefficient of the ESO observer. δ is the linear interval length.
The galn function has the form shown below:
Figure BDA0003902119200000101
the galn function is symmetrical about an origin and is conductive everywhere, a curve of the galn function has good continuity, convergence and smoothness, parameters to be set are few, and the rule of small error, large gain, large error and small gain is strictly followed. The function has the characteristics of symmetry, continuity, smoothness and convergence, and is suitable for the application of the normal distribution function in engineering.
In the prior art, the fal function is generally adopted to design the extended observer, and the improved extended observer is
Figure BDA0003902119200000102
Wherein z1 represents a velocity estimate; z2 represents the integrated disturbance estimate; and z3, carrying out real-time estimation and online compensation on the unknown disturbance f in the total disturbance. Beta is a 1 ，β 2 ，β 3 Is the filter coefficient of the ESO observer. δ is the linear interval length. fal (e) 1 δ) the specific form of the function is as follows:
Figure BDA0003902119200000103
by using Matlab simulation software to draw images of galn function and fal function, as shown in fig. 5, it is obvious that the following problems may exist when adopting the fal function: 1. the continuity and smoothness of the function are not good enough, and the phenomenon of high-frequency buffeting is easily caused in the neighborhood of an original point. 2. In the whole operation process, the parameters are set more, and the complexity of calculation and the difficulty of operation are increased. And the influence of high gain on the observation effect is increased due to the increase of the parameters. 3. Although the convergence speed and the observation capability can be improved, the instability of the system is aggravated by increasing the error gain.
The infinite order derivation of galn function proposed by the present invention conforms to the selection condition of nonlinear function, and it can be seen from fig. 5 that when the error is large, the gain is very small, and at this time, the function is very small
Figure BDA0003902119200000111
The error is between 0 and 1 and the gain is smaller. As can be seen from FIG. 6, inNear point 0, both functions meet the conditions of small error and large gain, but the galn function is smoother. Therefore, the galn function is more continuous and smooth, and the gain is smaller under the condition of large error.
4. Nonlinear state error feedback law
The state error feedback control law linearly combines all boundary errors of the system, and applies large gain according to the small error of the regulation principle; and applying small gain when the error is large, and reasonably and nonlinearly combining the tracking signal and the differential signal of the second-order steepest tracker with the deviation value of the output state vector of the extended state observer respectively. The sliding mode control is insensitive to the change of system internal parameters and external load disturbance due to strong robustness, has invariance to unmodeled dynamics, is a nonlinear control method which is approved by everyone at present, is introduced into the active disturbance rejection control, and is well applied.
The invention selects nonsingular terminal sliding mode surfaces:
Figure BDA0003902119200000112
wherein h > g >0, α >0.
Selecting an approach law:
Figure BDA0003902119200000113
wherein
Figure BDA0003902119200000114
k 1 >0,k 2 >0,a>1，0<b<1，h>g，p>q, and p and q are positive odd numbers.
5. Design sliding mode controller
The invention combines classical control and modern control, designs a nonlinear tracking differentiator to solve the problem of differential extraction, designs an extended observer with disturbance resistance to solve the problem of disturbance estimation, designs a novel nonlinear combined structure and finds a proper combination method in order to make up the fundamental defects of PID. The limitation of PID is broken through from the three aspects.
And applying the improved equation of the most tracking differentiator, the form function of the extended state observer and the nonlinear state error feedback rule to the sliding-mode controller to obtain a function form of the sliding-mode controller. The sliding mode controller is designed in such a way that:
Figure BDA0003902119200000121
finally, introducing disturbance compensation z3 of the system, and obtaining an auto-disturbance rejection nonlinear control law in the form of formula 5-2:
Figure BDA0003902119200000122
wherein k is 1 、k 2 And k 3 Is a variable approximation law coefficient, n p Is the number of pole pairs, J is the moment of inertia,
Figure BDA0003902119200000123
is a permanent magnetic linkage, beta>0，h>g>0。
6. Simulation and result analysis
6.1 simulation parameters and method settings
In order to verify the correctness of the active disturbance rejection sliding mode control algorithm, a permanent magnet synchronous motor simulation structure is built in the simulink. The specific parameters of the motor are that the stator resistance R =2.46 omega; d. q-axis inductance L d ＝L q =6.35mH; permanent magnetic linkage
Figure BDA0003902119200000124
Moment of inertia J =1.02g.m 2 (ii) a Viscous friction coefficient B =0.0001; pole pair number P =4; the rated rotating speed is 3000r/min, and the switching frequency of the inverter is 15kHz.
The current loop of the invention adopts PI control, and the speed loop adopts an auto-disturbance rejection sliding mode controller. And selecting nonsingular terminal sliding mode control for comparison in simulation.
6.2 analysis of simulation results
Given that the motor speed is 1000r/min, and the load is suddenly applied at 0.01s, the speed response simulation wave diagram of the PMSM is shown in the figure.
It can be seen from fig. 7 that the motor speed can both reach steady state very fast, but the motor speed overshoot under traditional ADRC control is obviously bigger, and the rotational speed overshoot under the control of novel compound ADRC controller is very little, and the load is suddenly added when 0.2s, and novel slipform auto-disturbance rejection controller compares and gets back to given rotational speed value more rapidly in traditional slipform control, and consequently novel compound control has better suppression disturbance effect.
Aiming at the problems of load and uncertain disturbance of a permanent magnet synchronous motor control system, a sliding mode active disturbance rejection control method based on an improved extended state observer is designed. The traditional fal function is discontinuous and not smooth, and is replaced by a novel galn function, so that the convergence speed and the observation capability of the extended state observer are improved. Sliding mode control is introduced into the nonlinear control law to form active disturbance rejection sliding mode control, and the robustness and the anti-interference capability of the system are improved simultaneously. And the applicability of the sliding mode active disturbance rejection control method based on the improved extended state observer is obtained through the simulation comparison of the traditional active disturbance rejection control and the novel composite active disturbance rejection control.
Finally, it should be noted that: the above examples are only for illustrating the technical solutions of the present invention, and are not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: it is to be understood that modifications may be made to the technical solutions described in the foregoing embodiments, or some or all of the technical features may be equivalently replaced, and such modifications or replacements may not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (9)

1. A permanent magnet synchronous motor sliding mode active disturbance rejection control method for improving an extended observer is characterized by comprising the following steps:
s1: according to a mathematical model of the permanent magnet synchronous motor, electromagnetic torque in the mathematical model is simplified, and then a mathematical equation of actual electromagnetic torque is listed by combining disturbance of motor operation, wherein the mathematical equation is as follows:
Figure FDA0003902119190000011
wherein, T e Is an electromagnetic torque, n p Is the number of pole pairs, L md Is the mutual inductance of the d-axis, i q Is the stator current q-axis component, i df D-axis equivalent magnetizing current, μ is total perturbation;
s2: discretizing the differential structure of the input signal to obtain an equation of a most tracking differentiator;
s3: establishing a three-order ESO structure, and using the electromagnetic torque mathematical equation of the formula 1 and the permanent magnet synchronous motor
The state equations are combined to obtain the expanded state observer function in the form of formula 2:
Figure FDA0003902119190000012
wherein z1 represents a velocity estimate; z2 represents the integrated disturbance estimate; z3, real-time estimation and online compensation are carried out on unknown disturbance in the total disturbance; beta is a 1 ，β 2 ，β 3 Galn is the nonlinear function proposed herein for the ESO observer filter coefficients;
s4: adopting a nonsingular terminal sliding mode surface function and an approach law, linearly combining errors to obtain a nonlinear state error feedback control law;
s5: and applying the equation of the most-tracking differentiator in the S2, the form function of the extended state observer in the S3 and the nonlinear state error feedback control law in the S4 to the sliding mode controller to obtain a function form of the sliding mode controller to realize the control of the sliding mode active disturbance rejection of the permanent magnet synchronous motor.
2. The sliding mode active disturbance rejection control method of the permanent magnet synchronous motor for improving the extended observer, according to claim 1, wherein the method is characterized in thatCharacterized in that the mathematical model of the permanent magnet synchronous machine in step S1 is based on an ideal state assumption and i d A control pattern setting of =0, which is in the form of formula 3 to formula 6 in the d-q coordinate system:
Figure FDA0003902119190000021
λ q ＝L q i q (4)
λ d ＝L d i d +L md i df (5)
ω e ＝n p ω r (6)
in the formula i d 、i q The stator current d and q axis components are respectively; u shape d 、U q The stator voltage d and q axis components are respectively; r s Is a stator resistor; l is d 、L q The inductors of the d axis and the q axis of the stator are respectively; omega e Is the rotor electrical angular velocity; omega r Is the rotor mechanical angular velocity; lambda d 、λ q Is a stator flux linkage of d and q axes; l is md Mutual inductance for the d-axis; i.e. i df Is d-axis equivalent magnetizing current; m is p Is the number of pole pairs.
3. The method for controlling the sliding mode active disturbance rejection of the permanent magnet synchronous motor for improving the extended observer according to claim 2, wherein in the step S1, the motor torque is simplified based on the equality of stator flux linkages of d and q axes, and an electromagnetic torque equation after the simplification is as shown in formula 7:
Figure FDA0003902119190000022
4. the sliding mode active disturbance rejection control method of the permanent magnet synchronous motor for improving the extended observer is characterized by comprising the following steps of: in step S2, the equation of the most tracking differentiator is equation 8:
Figure FDA0003902119190000023
wherein h is an integration step length; r is a velocity factor, the value of which determines the magnitude of the tracking velocity; h is 0 As a filter factor, the function fhan (x) 1 ,x 2 R, h) is the fastest control synthesis function;
the fhan (x) 1 ,x 2 The algorithm for r, h) is equation 9:
Figure FDA0003902119190000031
wherein h is an integration step length; r is a velocity factor.
5. The sliding-mode active disturbance rejection control method for the permanent magnet synchronous motor of the improved extended observer according to claim 1, wherein the state equation of the permanent magnet synchronous motor in the step S3 is as shown in formula 10:
Figure FDA0003902119190000032
wherein, ω is * For a given rotational speed, ω is the actual rotational speed;
the permanent magnet synchronous motor state equation 10 is combined with the mathematical equation 1 of the actual electromagnetic torque to obtain the equation 11:
Figure FDA0003902119190000033
wherein
Figure FDA0003902119190000034
ω (t) is interference;
f (x) 1 ,x 2 ω (t), t) as state variables x 3 Then x 3 Expression function ofIs of formula 12:
Figure FDA0003902119190000035
6. the sliding mode active disturbance rejection control method of the permanent magnet synchronous motor for improving the extended observer is characterized by comprising the following steps of: the galn function in step S3 is of the form of equation 13:
Figure FDA0003902119190000036
wherein a is a non-zero constant.
7. The sliding mode active disturbance rejection control method for the permanent magnet synchronous motor for improving the extended observer according to claim 1, wherein the nonsingular terminal sliding mode surface function in the step S4 is represented by formula 14:
Figure FDA0003902119190000041
wherein h > g >0, α >0;
the approach law is formula 15:
Figure FDA0003902119190000042
wherein the content of the first and second substances,
Figure FDA0003902119190000043
k 1 >0,k 2 >0,a>1，0<b<1，h>g>0。
8. the sliding-mode active-disturbance-rejection control method for the permanent magnet synchronous motor for improving the extended observer is characterized in that the functional form of the sliding-mode controller in the step S5 is as shown in formula 16:
Figure FDA0003902119190000044
wherein k is 1 、k 2 And k 3 Is a variable approximation law coefficient, n p Is the number of pole pairs, J is the moment of inertia,
Figure FDA0003902119190000045
is a permanent magnetic linkage, beta>0，h>g>0。
9. The sliding mode active disturbance rejection control method of the permanent magnet synchronous motor for improving the extended observer according to claim 8, characterized in that: the disturbance compensation z3 of the system is introduced in equation 16, and the form of the new active disturbance rejection control law is equation 17:
Figure FDA0003902119190000046
wherein k is 1 、k 2 And k 3 Is a variable approximation law coefficient, n p Is the number of pole pairs, J is the moment of inertia,
Figure FDA0003902119190000047
is a permanent magnetic linkage, beta>0，h>g>0。
CN202211294468.7A 2022-10-21 2022-10-21 Permanent magnet synchronous motor sliding mode active disturbance rejection control method for improving extended observer Pending CN115514270A (en)

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117040341A (en) * 2023-10-09 2023-11-10 潍柴动力股份有限公司 Disturbance estimation method, control method and related device of permanent magnet synchronous motor

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117040341A (en) * 2023-10-09 2023-11-10 潍柴动力股份有限公司 Disturbance estimation method, control method and related device of permanent magnet synchronous motor
CN117040341B (en) * 2023-10-09 2024-01-12 潍柴动力股份有限公司 Disturbance estimation method, control method and related device of permanent magnet synchronous motor

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