CN117914204A - Permanent magnet synchronous motor active disturbance rejection control method based on improved extended state observer - Google Patents
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Abstract
The invention discloses a permanent magnet synchronous motor active disturbance rejection control method based on an improved extended state observer, which belongs to the field of permanent magnet synchronous motor control and comprises the following steps: modeling the total disturbance of the rotating speed ring, constructing a state equation with the rotating speed and the total disturbance as state variables, and expanding disturbance differential terms into a brand new state variable; constructing an improved third-order extended state observer, and carrying out multiple observation on disturbance and disturbance differential terms through the observer according to errors of the actual measurement value and the estimated value of the rotating speed to obtain a more accurate disturbance estimated value for compensating the total disturbance; according to the error of the rotation speed actual measurement value and the command value, calculating an initial current command value through an error feedback control rate, and obtaining a reference current command value through disturbance compensation; and controlling the output of the inverter through a current controller and a space vector modulation module. Compared with the traditional control method, the invention speeds up the dynamic response speed of the system without overshoot and static difference of the motor rotation speed, and greatly improves the disturbance suppression capability of the system under the condition of ensuring the unchanged noise suppression capability of the system.
Description
Technical Field
The invention discloses a permanent magnet synchronous motor active disturbance rejection control method based on an improved extended state observer, and belongs to the field of permanent magnet synchronous motor control.
Background
The permanent magnet synchronous motor (PERMANENT MAGNET synchronous motor, PMSM) has the advantages of small volume, high power density, high efficiency, simple structure, low noise, quick dynamic response and the like, and is widely applied to various fields in recent years, particularly in occasions with higher requirements on motor performance and higher requirements on operation reliability, such as all-electric airplanes, electric automobiles and the like. The topology of the typical permanent magnet synchronous motor control system consists of an outer ring rotating speed ring and an inner ring current ring, and the rotating speed ring calculates a current instruction of the current inner ring according to a rotating speed instruction and a rotating speed feedback value, so that the quality of the control performance of the rotating speed ring directly determines the speed regulation performance of the motor.
At present, various advanced control strategies mostly have different degrees of dependence on motor parameters, and in order to achieve good dynamic and static performance, the traditional proportional integral control (proportional integral, PI) also needs to calculate proportional and integral gains by means of the motor parameters. Under the complex operation condition, the permanent magnet synchronous motor driving system is difficult to avoid the problem of frequent parameter change, the comprehensive operation performance of the system is influenced, and the high performance requirement is difficult to meet.
With the application of modern control theory and the rapid development of digital controllers, active disturbance rejection control (active disturbance reiection control, ADRC) has been widely studied in the field of motor control by virtue of its advantages of fast dynamic response, high disturbance rejection, good reliability, no dependence on models, etc. The extended state observer (extended state observer, ESO) is the core of the active disturbance rejection control, the bandwidth of the observer influences the performance of the system, when the bandwidth of the observer is increased, the disturbance rejection capability of the system in a low frequency band can be improved, but a series of problems such as the noise rejection capability of the system in a high frequency band can be brought.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a permanent magnet synchronous motor active disturbance rejection control method based on an improved extended state observer, which expands disturbance differential terms into brand-new state variables, carries out multiple observation on disturbance and disturbance differential terms to obtain more accurate disturbance estimation values, greatly improves the disturbance rejection capability of a system while not weakening the noise rejection capability of the system, and realizes faster and more stable permanent magnet synchronous motor rotating speed ring control.
The invention adopts the following technical scheme for realizing the purposes:
the permanent magnet synchronous motor active disturbance rejection control method based on the improved extended state observer is characterized by comprising the following steps of:
Step 1), modeling the total disturbance of the permanent magnet synchronous motor by taking the motor rotor rotating speed omega as a state variable x 1 according to a torque equation and a mechanical motion equation of the permanent magnet synchronous motor, taking the internal disturbance and the external disturbance as a whole, defining the total disturbance f as a state variable x 2, and taking the differential term of the disturbance on the basis Expanding the model into a new state variable x 3, and establishing a third-order state equation;
Step 2), an improved three-order expansion state observer is built according to a three-order state equation, z 1 is an observed value of a state variable x 1, z 2 is an observed value of a state variable x 2, z 3 is an observed value of a state variable x 3, multiple observations are carried out on disturbance and differential terms of the disturbance, the total disturbance quantity is estimated more accurately, and a disturbance compensation value z 2 is output through disturbance calculation;
Step 3), designing a linear error feedback control law, and inputting an error between the actual rotating speed omega and the given rotating speed omega * of the motor into the linear error feedback control law to obtain an initial current command value And then, carrying out feedback compensation on the total disturbance quantity estimated by the improved linear expansion state observer to obtain a reference current command value/>
Step 4), according to the reference current command valueBinding/>And controlling, namely outputting voltages u d and u q through a current controller, generating six paths of switching signals of the inverter to control the inverter after the processing of the coordinate change and space vector pulse width modulation algorithm SVPWM, and further driving the permanent magnet synchronous motor to normally work through the inverter to realize closed loop feedback control of the permanent magnet synchronous motor.
Compared with the prior art, the technical scheme provided by the invention has the following technical effects:
(1) The transient performance of the permanent magnet synchronous motor is optimized, and the permanent magnet synchronous motor has faster response speed and smaller overshoot;
(2) The improved linear expansion state observer expands the state equation into a third order, and can resist disturbance in a more complex form;
(3) The disturbance suppression capability of the system is greatly improved while the noise suppression capability of the system is ensured to be certain;
(4) The system has the advantages of strong robustness, less required model parameters, little influence by motor parameter change, simple parameter configuration and flexible control.
Drawings
Fig. 1 is a block diagram of a permanent magnet synchronous motor active disturbance rejection control system based on an improved extended state observer.
Fig. 2 is a specific structural block diagram of the improved active disturbance rejection control.
FIG. 3 is a comparison of the transfer function bird plot of the low frequency band versus the disturbance for a conventional ESO and the improved ESO proposed by the present invention.
FIG. 4 is a comparison of the transfer function bode plot of the conventional ESO versus the improved ESO proposed by the present invention versus noise at the high frequency band.
Fig. 5 is a comparison of waveform simulation graphs of rotational speeds of a motor under step-type load disturbance using conventional PI control, conventional ADRC control, and ADRC control based on MESO according to the present invention.
Fig. 6 is a comparison of waveform simulation graphs of rotational speeds of a motor under ramp-type load disturbance using conventional PI control, conventional ADRC control, and ADRC control based on MESO according to the present invention.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings and examples.
The invention discloses a permanent magnet synchronous motor active disturbance rejection control method based on an improved extended state observer, which is shown in figure 1. The method is implemented according to the following steps:
Step 1), modeling the total disturbance of the permanent magnet synchronous motor by taking the motor rotor rotating speed omega as a state variable x 1 according to a torque equation and a mechanical motion equation of the permanent magnet synchronous motor, taking the internal disturbance and the external disturbance as a whole, defining the total disturbance f as a state variable x 2, and taking the differential term of the disturbance on the basis Expanding to a new state variable x 3 and establishing a third-order state equation.
Specifically, the torque equation and the mechanical motion equation of the surface-mounted permanent magnet synchronous motor are as follows:
Wherein P is the pole pair number; omega is the mechanical angular velocity; phi f is flux linkage; i q is q-axis current; t e is electromagnetic torque; t L is the load torque; j is moment of inertia; b a is a damping coefficient; f 0 is other disturbances in the system.
A first-order state equation with the rotating speed omega as a state variable is constructed according to the equation:
the internal disturbance and the external disturbance in the system are defined as total disturbance f, and the expression is:
The motor rotor speed omega is taken as a state variable x 1, the total disturbance f is defined as a state variable x 2, and the differential term of the disturbance is defined Expanding to a new state variable x 3, and establishing a third-order state equation:
wherein y is the system output, namely the rotating speed omega; u is the control quantity, i.e. given current B is a state equation parameter and satisfies/>
Step 2), an improved three-order expansion state observer is built according to a three-order state equation, z 1 is an observed value of a state variable x 1, z 2 is an observed value of a state variable x 2, z 3 is an observed value of a state variable x 3, multiple observations are carried out on disturbance and differential terms of the disturbance, the total disturbance quantity is estimated more accurately, and a disturbance compensation value z 2 is output through disturbance calculation.
Specifically, the conventional second-order Extended State Observer (ESO) structure is:
Wherein e is the state observation error of ESO; z 1 is the observation of the state variable x 1, i.e. the rotation speed ω; z 2 is the observation of state variable x 2, i.e., the disturbance f observation; b 0 is an estimate of parameter b; h 1、h2 is the gain factor of the ESO.
The observer gain coefficients are configured according to the bandwidth method: h 1＝2ω0 of the total number of the components,Omega 0 is the observer bandwidth, the larger the observer omega 0, the stronger the disturbance rejection capability of the system, but at the same time the noise of the system will become larger.
Further, the improved three-order extended state observer (MESO) provided by the invention is built, and the structure is as follows:
Wherein e is the state observation error of MESO; z 1 is the observation of the state variable x 1, i.e. the rotation speed ω; z 2 is the observation of state variable x 2, i.e., the disturbance f observation; z 3 is the observed value of state variable x 3; b 0 is an estimate of parameter b; h 1、h2、h3 is the gain factor of the MESO, and the improved observer gain factor is configured according to the bandwidth method: h 1＝3ω0 of the total number of the components, Omega 0 is the observer bandwidth.
The characteristic equation of MESO is λ(s) =s 3+h1s2+h2s+h3, when h 1＝3ω0 is satisfied,When ω 0 > 0, the root of the feature equation is to the left of the complex plane and the system is stable.
According to the observer disturbance calculation method, the total disturbance estimated value z 2 is output, and a specific structure diagram is shown in fig. 2.
Step 3), designing a linear error feedback control law, and inputting an error between the actual rotating speed omega and the given rotating speed omega * of the motor into the linear error feedback control law to obtain an initial current command valueAnd then, carrying out feedback compensation on the total disturbance quantity estimated by the improved linear expansion state observer to obtain a reference current command value/>
Specifically, the actual measured value of the rotating speed and a given value are subjected to error feedback, and an initial current given value is obtained through linear error feedback control law calculation
Where k p is the controller gain factor.
Then compensating the disturbance compensation value z 2 obtained in the step 2) to an initial current command valueObtain the reference current command value/>
Step 4), according to the reference current command valueBinding/>And controlling, namely outputting voltages u d and u q through a current controller, generating six paths of switching signals of the inverter to control the inverter after the processing of the coordinate change and space vector pulse width modulation algorithm SVPWM, and further driving the permanent magnet synchronous motor to normally work through the inverter to realize closed loop feedback control of the permanent magnet synchronous motor.
Further, in order to show the superior performance of the MESO proposed by the present invention, a frequency domain analysis method is adopted to compare and analyze the performance of the MESO and the ESO:
First, noise and disturbance rejection capabilities are analyzed:
aiming at the traditional ESO structure, the transfer function of the observer to disturbance and noise is obtained by combining an automatic control principle:
Similarly, for the MESO structure of the expansion disturbance differential term provided by the invention, the transfer function of the observer to disturbance and noise is written as follows:
Respectively carrying out bird diagram drawing on disturbance and noise, and comparing the traditional ESO with the transfer function bird diagram of the MESO provided by the invention on the disturbance in the low frequency band, it can be seen that the suppression capability of the MESO on the disturbance in the low frequency band is greatly improved; FIG. 4 is a graph showing the transfer function of MESO versus noise at high frequency, where it can be seen that there is little impairment of noise suppression capability.
Analyzing disturbance estimation errors of the observer:
Considering the step disturbance and the ramp disturbance, the following can be written:
Wherein U(s) is a step disturbance; k u is the step disturbance gain; r(s) is a ramp disturbance; k r is the ramp perturbation gain.
The disturbance estimation error of the observer is expressed as:
e(s)＝z2(s)-f(s)
writing a disturbance estimation expression of the traditional ESO, and analyzing estimation errors under the conditions of step disturbance and slope disturbance:
it can be seen that the conventional ESO can perform better estimation on the step disturbance, but there is always a certain error on the slope disturbance estimation.
The same analysis is carried out on the MESO provided by the invention, and the method can obtain:
Therefore, the MESO can well estimate the step disturbance and the slope disturbance, and the anti-interference performance is enhanced.
Furthermore, in order to verify the superior performance of the ADRC control method based on the MESO, simulation verification is performed, and the given rotating speed 1000 r.min -1,kp＝0.2,ki＝80,ω0 =1000 of the motor is set.
As shown in FIG. 5, which is a graph comparing the rotational speed results of the ADRC control based on MESO with the rotational speed results of the conventional ADRC control and the conventional PI control, it can be seen that the ADRC control based on MESO and the conventional ADRC control provided by the invention have no overshoot and the conventional PI control has 2.7% overshoot in the rotational speed starting stage of the motor; when loading, the fluctuation amount of the rotating speed and the adjustment time are superior to the traditional ADRC control and the traditional PI control based on the MESO.
As shown in FIG. 6, the comparison of the ADRC control based on MESO and the rotation speed results of the conventional ADRC control and the conventional PI control is shown, and it can be seen from the graph that the ADRC control based on MESO can accurately track the given rotation speed during loading, but the conventional ADRC control and the conventional PI control cannot inhibit disturbance and cannot track the given rotation speed.
It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein, including technical and scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
While the foregoing is directed to embodiments of the present invention, other and further details of the invention may be had by the present invention, it should be understood that the foregoing description is merely illustrative of the present invention and that no limitations are intended to the scope of the invention, except insofar as modifications, equivalents, improvements or modifications are within the spirit and principles of the invention.
Claims (4)
1. The permanent magnet synchronous motor active disturbance rejection control method based on the improved extended state observer is characterized by comprising the following steps of:
Step 1), modeling the total disturbance of the permanent magnet synchronous motor by taking the motor rotor rotating speed omega as a state variable x 1 according to a torque equation and a mechanical motion equation of the permanent magnet synchronous motor, taking the internal disturbance and the external disturbance as a whole, defining the total disturbance f as a state variable x 2, and taking the differential term of the disturbance on the basis Expanding the model into a new state variable x 3, and establishing a third-order state equation;
Step 2), an improved three-order expansion state observer is built according to a three-order state equation, z 1 is an observed value of a state variable x 1, z 2 is an observed value of a state variable x 2, z 3 is an observed value of a state variable x 3, multiple observations are carried out on disturbance and differential terms of the disturbance, the total disturbance quantity is estimated more accurately, and a disturbance compensation value z 2 is output through disturbance calculation;
Step 3), designing a linear error feedback control law, and inputting an error between the actual rotating speed omega and the given rotating speed omega * of the motor into the linear error feedback control law to obtain an initial current command value And then, carrying out feedback compensation on the total disturbance quantity estimated by the improved linear expansion state observer to obtain a reference current command value/>
Step 4), according to the reference current command valueBinding/>And controlling, namely outputting voltages u d and u q through a current controller, generating six paths of switching signals of the inverter to control the inverter after the processing of the coordinate change and space vector pulse width modulation algorithm SVPWM, and further driving the permanent magnet synchronous motor to normally work through the inverter to realize closed loop feedback control of the permanent magnet synchronous motor.
2. The improved active disturbance rejection control method of the permanent magnet synchronous motor according to claim 1, wherein the torque equation and the mechanical motion equation of the surface-mounted permanent magnet synchronous motor in the step 1 are as follows:
Wherein P is the pole pair number; omega is the mechanical angular velocity; phi f is flux linkage; i q is q-axis current; t e is electromagnetic torque; t L is the load torque; j is moment of inertia; b a is a damping coefficient; f 0 is other disturbances in the system.
The motor rotor speed omega is taken as a state variable x 1, the total disturbance f is defined as a state variable x 2, and the differential term of the disturbance is definedExpanding to a new state variable x 3, and establishing a third-order state equation:
wherein y is the system output, namely the rotating speed omega; u is the control quantity, i.e. given current B is a state equation parameter, satisfies
3. The improved active-disturbance-rejection control method of permanent magnet synchronous motor according to claim 1, wherein the improved third-order extended state observer (MESO) in step 2 has the structure:
Wherein e is the state observation error of MESO; z 1 is the observation of the state variable x 1, i.e. the rotation speed ω; z 2 is the observation of state variable x 2, i.e., the disturbance f observation; z 3 is the observed value of state variable x 3; b 0 is an estimate of parameter b; h 1、h2、h3 is the gain factor of the MESO, and the improved observer gain factor is configured according to the bandwidth method: h 1＝3ω0 of the total number of the components, Omega 0 is the observer bandwidth.
4. The improved active-disturbance-rejection control method of permanent magnet synchronous motor according to claim 1, wherein in step 3, error feedback is performed on the rotation speed actual measurement value and the given value, and the initial current given value is obtained through calculation of a linear error feedback control law
Where k p is the controller gain factor
Then the obtained disturbance compensation value z 2 is compensated to the initial current command valueObtain the reference current command value/> 。
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