CN112019116B - Speed tracking control method for permanent magnet linear synchronous motor - Google Patents
Speed tracking control method for permanent magnet linear synchronous motor Download PDFInfo
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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
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/18—Estimation of position or speed
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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
- H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
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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
- 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
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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
- 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
- H02P25/06—Linear motors
- H02P25/064—Linear motors of the synchronous type
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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
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/34—Modelling or simulation for control purposes
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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
- 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 discloses a speed tracking control method of a permanent magnet linear synchronous motor, which comprises the following steps: s100, constructing a dq coordinate system permanent magnet linear synchronous motor model; s200, converting a dq coordinate system permanent magnet linear synchronous motor model into three subsystems of a speed loop, a q-axis current loop and a d-axis current loop; s300, designing an improved extended state observer by utilizing a speed loop, a q-axis current loop and a d-axis current loop; s400, designing a speed tracking controller and a current loop controller based on the improved extended state observer, and realizing speed tracking control according to speed tracking error feedback. The invention takes a permanent magnet linear synchronous motor as a control object, designs a new improved extended state controller, designs a feedback controller based on the extended state observer, ensures the convergence and stability of the controller by selecting proper observer and controller parameters, achieves the expected control performance and realizes the speed tracking control.
Description
Technical Field
The invention belongs to the technical field of motor servo and control, and particularly relates to a speed tracking control method for a permanent magnet linear synchronous motor.
Background
The linear motor system generally needs to accurately control the speed of the system, so that higher requirements are provided for acquiring a speed signal and controlling the speed, certain accuracy is ensured on one hand, and higher requirements are provided for real-time performance. The speed is a differential signal of the distance, the dynamic characteristic of a reaction system is reflected, the differential signal of a general system is difficult to directly measure, the differential signal is obtained by adopting a classical differentiator, the system noise is amplified, and the effect of a filter is combined, but the noise suppression capability of the filter is limited and the signal phase information is lost, so that the control based on the differential signal is difficult to really realize physically.
The extended state observer is an observer firstly proposed by the institute of mathematics of the academy of sciences of China, Han Jing Qing researchers, and accurately estimates other system state signals and unknown disturbances according to input and output signals of a controlled object, wherein the other system state signals and the unknown disturbances include unknown and uncertain parts of a system and all disturbances applied to the controlled object. The controller is designed by combining the extended state observer, unknown disturbance can be observed and compensated, and a controlled object is transformed into a standard form of an integrator series linear system, so that feedback linearization of a dynamic nonlinear system is realized, and active disturbance rejection control of the controlled object is realized by utilizing efficient state error feedback. The extended state observer does not need an accurate mathematical model of a controlled object, and has strong robustness and engineering practical value. The active disturbance rejection control is widely researched and applied due to excellent disturbance rejection and robustness and independent of a system model, and the rule of selecting some parameters is summarized. However, theoretical studies on extended state observers and active disturbance rejection control are relatively rare. In particular, strict analysis on the extended state observer convergence and the active disturbance rejection control stability proves that the influence of the parameters on the extended state observer convergence and the active disturbance rejection control stability is also rarely involved.
Disclosure of Invention
The invention aims to avoid the defects in the prior art and provides a speed tracking control method of a permanent magnet linear synchronous motor, which takes the permanent magnet linear synchronous motor as a control object, designs a new improved extended state controller, designs a feedback controller based on an extended state observer, ensures the convergence and stability of the controller by selecting proper observer and controller parameters, achieves the expected control performance and realizes the speed tracking control.
The purpose of the invention is realized by the following technical scheme: the speed tracking control method of the permanent magnet linear synchronous motor comprises the following steps:
s100, constructing a dq coordinate system permanent magnet linear synchronous motor model;
s200, converting a dq coordinate system permanent magnet linear synchronous motor model into three subsystems of a speed loop, a q-axis current loop and a d-axis current loop;
s300, designing an improved extended state observer by utilizing a speed loop, a q-axis current loop and a d-axis current loop;
s400, designing a speed tracking controller and a current loop controller based on the improved extended state observer, and realizing speed tracking control according to speed tracking error feedback.
As a further improvement, in step S100, an expression of the dq coordinate system permanent magnet linear synchronous motor model is as follows:
in the formula idIs d-axis stator current, iqIs the q-axis stator current, v is the permanent magnet linear synchronous motor speed,
are respectively id、iqFirst differential of v, udIs d-axis stator voltage, uqIs q-axis stator voltage, R is permanent magnet linear synchronous motor stator winding resistance, tau is permanent magnet linear synchronous motor pole pitch, LdIs d-axis stator inductance, LqFor q-axis stator inductance,. psifIs a magnetic flux linkage, m is the weight of the mover, B is the viscosity coefficient, FwFor other resistances and disturbances, npIs the number of pole pairs.
As a further improvement, the speed loop in step S200 is defined as sigmavQ-axis current loop is defined as ∑qD-axis current loop is defined as ∑dLet system state x ═ x1 x2 z1 w1]T＝[s v iq iq]TThe system input u ═ uq ud]The system output y ═ y1 y2 y3]T＝[x1 z1 w1]Then speed loop ΣvQ-axis current loop ΣqD-axis current loop ΣdAre respectively:
in the formula, x1、x2、z1、w1Respectively represent s, v, iq、idWhere s is the speed loop ΣvThe distance that can be measured is,
are respectively x1、x2、z1、w1First order differential of (y)1、y2、y3Respectively representing the speed loop sigmavQ-axis current loop ΣqD-axis current loop ΣdOutput signals s, i measurable by three subsystemsq、id。
As a further improvement, the step S300 is embodied as:
s301, setting the system input u and the derivative thereof to be bounded;
s302, under the bounded system input u, setting the system state x to be bounded; (ii) a
S303, setting the system disturbance and the derivative thereof to be bounded;
s304, if the speed ring sigmavThe system is a second-order system, and an improved third-order extended state observer is designed as follows:
in the formula (I), the compound is shown in the specification,
an observer of the velocity loop, which can be measured by means of a measurable position signal x1Accurately observing the velocity and disturbance signals, x3To indicate the unknown disturbance,
are respectively x1、x2Is detected by the measured values of (a) and (b),
are respectively as
The first order differential of the first order of the,
are respectively the actual signal x1、x2、x3And observed signal
Observation error between, C1、C2And C3Are all positive design parameters, and are,
if q axis current loop ΣqD-axis current loop ΣdAnd if the two-order extended state observers are first-order systems, the improved second-order extended state observer is designed as follows:
wherein, C4、C5、C6、C7Are all positive design parameters, and are,
z2、w2both represent unknown perturbations.
As a further improvement, the step S400 is embodied as:
s401, selecting proper extended state observer design parameters C1、C2、C3、C4、C5、C6、C7To make the state observed
Can quickly and accurately converge to a system state x, wherein
Wherein the content of the first and second substances,
are each z1、w1The observed value of (a);
s402, according to the improved extended state observer, a system state x and an extended state representing total disturbance are obtained, and an active disturbance rejection controller is designed through state feedback to achieve speed tracking of the electromagnetic propulsion system.
As a further improvement, if the modified extended state observer is a three-order extended state observer modified in step S304, the extended state of the total disturbance is x3；
If the modified extended state observer is the modified second-order extended state observer in step S304, the extended state of the total disturbance is z2And w2Is superimposed on the unknown disturbance.
As a further improvement, the speed tracking error in step S400 is defined as:
in the formula, evIndicating velocity tracking error, vrAt the desired speed.
As a further improvement, the active disturbance rejection controller designed in step S402 comprises a speed tracking controller ADRCvADRC (advanced digital control loop) of current loop controllerqAnd ADRCdWherein, ADRCv、ADRCqAnd ADRCdAre respectively:
wherein the content of the first and second substances,
are each ud、uq、zeFirst order differential of o1、o2、o3Respectively represent ADRCv、ADRCqAnd ADRCdFeedback control output of (2), zeDenotes ADRCvThe amount of control required, and also ADRCqDesired input of k1、k2For positive feedback control parameters, τ1、τ2、τ3Respectively the cut-off frequency of the low-pass filter.
The invention provides a speed tracking control method of a permanent magnet linear synchronous motor, which comprises the following steps of firstly constructing a dq coordinate system permanent magnet linear synchronous motor model; then, converting the dq coordinate system permanent magnet linear synchronous motor model into three subsystems of a speed loop, a q-axis current loop and a d-axis current loop; then, designing an improved extended state observer by utilizing a speed loop, a q-axis current loop and a d-axis current loop; and finally, designing a speed tracking controller and a current loop controller based on the improved extended state observer, and realizing speed tracking control according to speed tracking error feedback. Through the process, the permanent magnet linear synchronous motor is used as a control object, a new improved extended state controller is designed, a feedback controller is designed based on the extended state observer, the convergence and stability of the controller are guaranteed by selecting proper observer and controller parameters, the expected control performance is achieved, and speed tracking control is achieved.
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The invention is further illustrated by means of the attached drawings, but the embodiments in the drawings do not constitute any limitation to the invention, and for a person skilled in the art, other drawings can be obtained on the basis of the following drawings without inventive effort.
Fig. 1 is a flow chart of a permanent magnet linear synchronous motor speed tracking control method.
Fig. 2 is a schematic diagram of stationary and rotating coordinate systems in a permanent magnet linear synchronous motor.
FIG. 3 is a block diagram of a third order extended state observer according to an embodiment of the present invention.
Fig. 4 is a block diagram of the speed tracking controller and current loop controller architecture.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the following detailed description of the present invention is provided with reference to the accompanying drawings and specific embodiments, and it is to be noted that the embodiments and features of the embodiments of the present application can be combined with each other without conflict.
As shown in fig. 1, the present invention provides a method for tracking and controlling a speed of a permanent magnet linear synchronous motor, comprising the following steps:
s100, constructing a dq coordinate system permanent magnet linear synchronous motor model; it should be noted that, if the influence of the edge effect is ignored, the model of the permanent magnet linear synchronous motor is the same as that of the permanent magnet rotary synchronous motor, the rotary motor is cut along the radial direction, and then the rotary motor can be regarded as the permanent magnet linear synchronous motor after being expanded along the circumferential direction, the three-phase static ABC coordinate system is converted into the dq synchronous rotary coordinate system through coordinate transformation, as shown in fig. 2, the ABC three-phase static coordinate system is converted into the α β two-phase static coordinate system through Clarke transformation (Clarke transformation), and the α β two-phase static coordinate system is converted into the two-phase dq synchronous rotary coordinate system through Park transformation (Park transformation), wherein the magnetic pole axis of the mover is the d-axis, the forward 90 ° electric angle along the d-axis direction is the q-axis, the α -phase winding axis is the reference axis, and the electric angle between the d-axis and the reference axis is θ. And a dq coordinate system permanent magnet linear synchronous motor model is established, and d-axis and q-axis currents are independently controlled respectively, so that better motor control performance can be obtained.
The synchronous motor stator three-phase current is:
the stator side voltage equation is:
wherein R isa、RbAnd RcIs ABC three-phase resistor psia、ψbAnd psicABC three-phase flux linkage;
the Clarke transformation equation is:
the Park transformation equation is:
under the three-phase symmetric condition, the voltage equation of the permanent magnet linear synchronous motor under the dq coordinate system can be obtained through conversion:
in the formula: u. ofd、uq-d-axis, q-axis stator voltages;
id、iq-d-axis, q-axis stator currents;
ψd、ψq-d-axis, q-axis flux linkage;
r is the stator winding resistance of the permanent magnet linear synchronous motor;
v-synchronous speed of permanent magnet linear synchronous motor;
tau is the pole pitch of the permanent magnet linear synchronous motor;
wherein, the d-axis and q-axis magnetic linkage can be expressed as
In the formula, LdIs d-axis stator inductance, LqFor q-axis stator inductance,. psifIs a magnetic flux linkage of the magnet;
the thrust equation of the permanent magnet linear synchronous motor can be expressed as follows:
wherein n ispIs the number of pole pairs.
The dq coordinate system model of the permanent magnet linear synchronous motor can be expressed as follows:
wherein m is the weight of the mover, B is the viscosity coefficient, FwOther drag and turbulence.
In order to obtain maximum thrust, a permanent magnet linear synchronous motor system usually adopts vector control, idRotor field orientation 0, armature current equal to q-axis current iqThe included angle between the armature magnetic field and the rotor magnetic pole is 90 degrees, the motor thrust is the largest at the moment, the normal force is 0, and meanwhile, the interference of the motor normal force on the suspension guide system is effectively avoided.
The motor stator adopts a hollow structure and is three-phase symmetrical, and the dq axis inductance components are equal, so that a thrust equation can be simplified as follows:
it can be seen that the electromagnetic force of the permanent magnet linear synchronous motor is in linear relation with the q-axis current, and i is enabled to be controlled through the vectordWhen the q-axis current is adjusted to be 0, the electromagnetic force of the motor can be accurately controlled.
Accordingly, the process proceeds to step S200.
S200, converting a dq coordinate system permanent magnet linear synchronous motor model into three subsystems of a speed loop, a q-axis current loop and a d-axis current loop; wherein the speed loop is defined as ∑vQ-axis current loop is defined as ∑qD-axis current loop is defined as ∑dLet system state x ═ x1 x2 z1 w1]T＝[s v iq iq]TThe system input u ═ uq ud]The system output y ═ y1 y2 y3]T＝[x1 z1w1]Then speed loop ΣvQ-axis current loop ΣqD-axis current loop ΣdAre respectively:
in the formula, x1、x2、z1、w1Respectively represent s, v, iq、idWhere s is the speed loop ΣvThe distance that can be measured is,
are respectively x1、x2、z1、w1First order differential of (y)1、y2、y3Respectively representing the speed loop sigmavQ-axis current loop ΣqD-axis current loop ΣdOutput signals s, i measurable by three subsystemsq、id。
S300, designing an improved extended state observer by utilizing a speed loop, a q-axis current loop and a d-axis current loop; preferably, this step is embodied as:
s301, setting the system input u and the derivative thereof to be bounded;
s302, under the bounded system input u, setting the system state x to be bounded; (ii) a
S303, setting the system disturbance and the derivative thereof to be bounded;
s304, if the speed ring sigmavThe system is a second-order system, and an improved third-order extended state observer is designed as follows:
in the formula (I), the compound is shown in the specification,
an observer of the velocity loop, which can be measured by means of a measurable position signal x1Accurately observing the velocity and disturbance signals, x3To indicate the unknown disturbance,
are respectively x1、x2Is detected by the measured values of (a) and (b),
are respectively as
First order differential, x &1、x～2、x～3Respectively, the actual signal x1、x2、x3And observed signal
Observation error between, C1、C2And C3Are all positive design parameters, and are,
the structural block diagram of the third-order extended state observer is shown in fig. 3;
if q axis current loop ΣqD-axis current loop ΣdAnd if the two-order extended state observers are first-order systems, the improved second-order extended state observer is designed as follows:
wherein, C4、C5、C6、C7Are all positive design parameters, and are,
z2、w2both represent unknown perturbations.
The new extended state observer designed by the process can be suitable for nonlinear, time-varying, coupled, uncertain and disturbance complex systems. The observation error of each state is calculated through iteration, the improved extended state observer is designed in a feedback mode, the observer is simple and clear in structure, the set condition requirement is low and easy to judge, the convergence condition is clear, and theoretical analysis proves that only the parameter C is required1＞0、C2＞0、C4＞0、C6> 0 and C3、C5、C7And if the size is large enough, the observer can be ensured to be converged, the parameter debugging is simpler, and the engineering application is easy to realize. It should be noted that, the specific embodiment of the present invention takes a very general nonlinear time-varying second-order system and first-order system as an example to perform design and analysis, which can represent a large class of systems, and can be extended to n-order at the same time, and can be applied to a large number of actual systems.
S400, designing a speed tracking controller and a current loop controller based on the improved extended state observer, and realizing speed tracking control according to speed tracking error feedback; in particular, by selecting the appropriate extended state observer parameters C1、C2、C3、C4、C5、C6、C7To make the state observed
Can quickly and accurately converge to a system state x, wherein
Wherein the content of the first and second substances,
are each z1、w1The observed value of (a); and then, according to the improved extended state observer, obtaining a system state x and an extended state representing total disturbance, and designing an active disturbance rejection controller through state feedback to realize the speed tracking of the electromagnetic propulsion system. It should be noted that, if the modified extended state observer is the third-order extended state observer modified in step S304, the extended state of the total disturbance is x3(ii) a If the modified extended state observer is the modified second-order extended state observer in step S304, the extended state of the total disturbance is z2And w2Is superimposed on the unknown disturbance. The invention can accurately observe the system state and the total disturbance based on the new extended state observer, and adopts the active disturbance rejection control technology to design the controller on the basis, thereby eliminating the total disturbance of the system and ensuring the safe, reliable and stable operation of the system.
As a further preferred embodiment, the present invention defines the velocity tracking error as:
in the formula, evIndicating velocity tracking error, vrAt the desired speed.
Designing a speed tracking controller ADRCvADRC (advanced digital control loop) of current loop controllerqAnd ADRCdRespectively as follows:
wherein the content of the first and second substances,
are each ud、uq、zeFirst order differential of o1、o2、o3Respectively represent ADRCv、ADRCqAnd ADRCdFeedback control output of (2), zeDenotes ADRCvThe amount of control required, and also ADRCqDesired input of k1、k2For positive feedback control parameters, τ1、τ2、τ3Respectively the cut-off frequency of the low-pass filter.
By selecting appropriate extended state observer parameters and feedback control parameters k1And k2The observation state can be quickly and accurately converged to the system state, and the system state stability and stable tracking are ensured. The speed tracking controller and the current loop controller are configured in block diagram form with particular reference to fig. 4.
The speed tracking control method of the permanent magnet linear synchronous motor can select MATLAB for simulation analysis after relevant parameter values are set.
In a word, the permanent magnet linear synchronous motor is used as a control object, the position information of the permanent magnet linear synchronous motor measured by the system is utilized to observe a speed signal by using the improved extended state observer, so that more accurate and real-time speed information is obtained, the observed speed information and other disturbances are used for a speed control system, and the speed tracking control is realized by combining a method of cascade control of a speed loop and a current loop, so that the speed observation and speed tracking control effects are good.
In the description above, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore should not be construed as limiting the scope of the present invention.
In conclusion, although the present invention has been described with reference to the preferred embodiments, it should be noted that, although various changes and modifications may be made by those skilled in the art, they should be included in the scope of the present invention unless they depart from the scope of the present invention.
Claims (4)
1. A speed tracking control method for a permanent magnet linear synchronous motor is characterized by comprising the following steps:
s100, constructing a dq coordinate system permanent magnet linear synchronous motor model: under the influence of neglecting the edge effect, the model of the permanent magnet linear synchronous motor is the same as the permanent magnet rotary synchronous motor, the permanent magnet rotary synchronous motor is cut along the radius direction and then can be regarded as the permanent magnet linear synchronous motor after being expanded along the circumferential direction, an ABC three-phase static coordinate system is converted into an alpha beta two-phase static coordinate system through Clarke conversion, the alpha beta two-phase static coordinate system is converted into a two-phase dq synchronous rotary coordinate system through Park conversion, wherein the magnetic pole axis of a rotor is a d axis, the forward rotation along the d axis direction is a q axis by 90 degrees of electric angle, the alpha phase winding axis is a reference axis, the electric angle between the d axis and the reference axis is theta, a dq coordinate system permanent magnet linear synchronous motor model is established based on the two-phase dq synchronous rotary coordinate system, meanwhile, a vector control permanent magnet linear synchronous motor system is adopted, the included angle between the armature magnetic field and the magnetic pole of the rotor is set as 90 degrees, the interference of the normal force of the motor on the suspension guide system is avoided, the motor stator adopts a hollow structure and is three-phase symmetrical, the inductance components of the dq axes are equal, and the d-axis current i is controlled by a vectordWhen the q-axis current is adjusted to be 0, the electromagnetic force of the motor can be accurately controlled;
s200, converting a dq coordinate system permanent magnet linear synchronous motor model into three subsystems of a speed loop, a q-axis current loop and a d-axis current loop; the speed loop is defined as ∑vQ-axis current loop is defined as ∑qD-axis current loop is defined as ∑dLet system state x ═ x1 x2 z1 w1]T＝[s v iq iq]TIs a system ofThe input u ═ uq ud]The system output y ═ y1 y2 y3]T＝[x1 z1 w1]Then speed loop ΣvQ-axis current loop ΣqD-axis current loop ΣdAre respectively:
∑v:
∑q:
∑d:
in the formula, x1、x2、z1、w1Respectively represent s, v, iq、idWhere s is the speed loop ΣvMeasurable distance, v is the permanent magnet linear synchronous motor speed, udIs d-axis stator voltage, uqIs q-axis stator voltage, R is permanent magnet linear synchronous motor stator winding resistance, tau is permanent magnet linear synchronous motor pole pitch, LdIs d-axis stator inductance, LqFor q-axis stator inductance,. psifIs a magnetic flux linkage, m is the weight of the mover, B is the viscosity coefficient, FwFor other resistances and disturbances, npThe number of the pole pairs is the number of the pole pairs,
are respectively x1、x2、z1、w1First order differential of (y)1、y2、y3Respectively representing the speed loop sigmavQ-axis current loop ΣqD-axis current loop ΣdOutput signals s, i measurable by three subsystemsq、id，idIs d-axis stator current, iqIs the q-axis stator current;
s300, designing an improved extended state observer by utilizing a speed loop, a q-axis current loop and a d-axis current loop, and specifically:
s301, setting the system input u and the derivative thereof to be bounded;
s302, under the bounded system input u, setting the system state x to be bounded;
s303, setting the system disturbance and the derivative thereof to be bounded;
s304, if the speed ring sigmavThe system is a second-order system, and an improved third-order extended state observer is designed as follows:
in the formula (I), the compound is shown in the specification,
an observer of the velocity loop, which can be measured by means of a measurable position signal x1Accurately observing the velocity and disturbance signals, x3To indicate the unknown disturbance,
are respectively x1、x2、x3Is detected by the measured values of (a) and (b),
are respectively as
The first order differential of the first order of the,
respectively, the actual signal x1、x2、x3And observed signal
Observation error between, C1、C2And C3Are all positiveThe design parameters of (a) are set,
if q axis current loop ΣqD-axis current loop ΣdAnd if the two-order extended state observers are first-order systems, the improved second-order extended state observer is designed as follows:
wherein, C4、C5、C6、C7Are all positive design parameters, and are,
z2、w2are all indicative of an unknown disturbance,
are each z1、z2、w1、w2Is detected by the measured values of (a) and (b),
are respectively as
The first order differential of the first order of the,
respectively the actual signal z1、z2、w1、w2And observed signal
The observation error between;
s400, designing a speed tracking controller and a current loop controller based on the above improved extended state observer, and implementing speed tracking control according to speed tracking error feedback, specifically,
s401, selecting proper extended state observer design parameters C1、C2、C3、C4、C5、C6、C7To make the state observed
Can quickly and accurately converge to a system state x, wherein
S402, obtaining a system state x and an extended state representing total disturbance according to the improved extended state observer, designing an active disturbance rejection controller through state feedback, and realizing the speed tracking of the electromagnetic propulsion system, wherein the active disturbance rejection controller comprises a speed tracking controller ADRCvADRC (advanced digital control loop) of current loop controllerqAnd ADRCdWherein, ADRCv、ADRCqAnd ADRCdAre respectively:
ADRCv:
ADRCq:
ADRCd:
wherein e isvWhich is indicative of a velocity tracking error,
are respectively asud、uq、zeFirst order differential of o1、o2、o3Respectively represent ADRCv、ADRCqAnd ADRCdFeedback control output of (2), zeDenotes ADRCvThe amount of control required, and also ADRCqDesired input of k1、k2、k2For positive feedback control parameters, τ1、τ2、τ3Respectively the cut-off frequency of the low-pass filter.
2. The method for tracking and controlling the speed of the permanent magnet linear synchronous motor according to claim 1, wherein the expression of the model of the permanent magnet linear synchronous motor in the dq coordinate system in the step S100 is as follows:
in the formula idIs d-axis stator current, iqIs the q-axis stator current, v is the permanent magnet linear synchronous motor speed,
are respectively id、iqFirst differential of v, udIs d-axis stator voltage, uqIs q-axis stator voltage, R is permanent magnet linear synchronous motor stator winding resistance, tau is permanent magnet linear synchronous motor pole pitch, LdIs d-axis stator inductance, LqFor q-axis stator inductance,. psifIs a magnetic flux linkage, m is the weight of the mover, B is the viscosity coefficient, FwFor other resistances and disturbances, npIs the number of pole pairs.
3. The method according to claim 2, wherein if the modified extended state observer is a third-order extended state observer modified in step S304, the extended state of the total disturbance is x3；
If the modified extended state observer is the stepIn the case of the modified second-order extended state observer in S304, the extended state of the total disturbance is z2And w2Is superimposed on the unknown disturbance.
4. The method for controlling tracking of the speed of the permanent magnet linear synchronous motor according to claim 3, wherein the speed tracking error in the step S400 is defined as:
in the formula, evIndicating velocity tracking error, vrAt the desired speed.
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