CN109687801B - Dead-beat current control method for permanent magnet synchronous linear motor - Google Patents

Dead-beat current control method for permanent magnet synchronous linear motor Download PDF

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CN109687801B
CN109687801B CN201910129447.1A CN201910129447A CN109687801B CN 109687801 B CN109687801 B CN 109687801B CN 201910129447 A CN201910129447 A CN 201910129447A CN 109687801 B CN109687801 B CN 109687801B
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CN109687801A (en
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林健
刘晗
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Nanjing Institute of Technology
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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
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/12—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
    • 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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Abstract

The invention discloses a dead-beat current control method for a permanent magnet synchronous linear motor, which comprises the following steps: obtaining a next sampleReference current command i of time motor q axisq *Reference current command i of (k +1) and d axesd *(k + 1); acquiring the actual current of the motor at the current sampling moment, and converting the actual current into d-axis current i under a dq coordinate systemd(k) And q-axis current iq(k) (ii) a I to be acquiredd(k)、iq(k) And the actual voltage u of the current sampling moment of the motord(k)、uq(k) Transmitting to an improved extended state observer to obtain an observed value of the parameter disturbance quantity at the current sampling moment
Figure DDA0001974758990000011
fq(k) (ii) a I to be acquiredd(k)、iq(k)，
Figure DDA0001974758990000012
fq(k) And iq *(k+1)、id *(k +1) is transmitted to a dead-beat prediction controller to obtain a reference command u of a control voltaged *(k)、uq *(k) (ii) a U to be acquiredd *(k)、uq *(k) Through coordinate conversion, the result obtained through conversion is output through an SVPWM control inverter, and the control of the motor is realized.

Description

Dead-beat current control method for permanent magnet synchronous linear motor
Technical Field
The invention relates to the technical field of motor control, in particular to a dead-beat current control method for a permanent magnet synchronous linear motor.
Background art:
the accurate thrust control is the basis for realizing the high tracking accuracy of the permanent magnet synchronous linear motor, and the permanent magnet synchronous linear motor system indirectly controls the output thrust by adjusting the motor current, so the quality of the motor output thrust is determined by the performance of a current control method in a current closed-loop system. The dead-beat current predictive control has good dynamic performance and decoupling capability, and is very suitable for a permanent magnet synchronous linear motor digital control system. However, dead-beat predictive control relies entirely on accurate permanent magnet synchronous linear motor models, which means that model parameter perturbations can cause the calculated voltage to deviate from its expected value. Therefore, the parameter disturbance compensation method is very necessary for the dead-beat current prediction control system of the permanent magnet synchronous linear motor, and the parameter disturbance of the motor inductance, resistance, flux linkage and the like can be well observed by applying the parameter disturbance method of the Extended State Observer (ESO), so that the dependence of the dead-beat current prediction algorithm on a precise motor model is reduced. However, the conventional Extended State Observer (ESO) controls the observer to observe the disturbance amount through the error of the current amount, does not conform to the error control principle, affects the convergence speed of the observer, and affects the dynamic response capability of the motor current. Meanwhile, an Extended State Observer (ESO) is a high-gain observer, and the high gain can cause the problem of overlarge peak value at the initial moment, so that the phenomenon of overlarge overshoot and even oscillation of the motor current occurs. Therefore, there is a need to develop an improved Extended State Observer (ESO) to overcome the above-mentioned problems, so as to provide high-quality thrust for the permanent magnet synchronous linear motor, and achieve fast dynamic response and high tracking accuracy of the motor.
Disclosure of Invention
The invention aims to provide a deadbeat current control method for a permanent magnet synchronous linear motor, which aims to solve one of the defects caused by the prior art.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme:
a dead beat current control method for a permanent magnet synchronous linear motor comprises the following steps:
step 1, adopting a linear motor control system with a speed and current double closed-loop structure and a grating as a position detector, and calculating the measured displacement to obtain the actual speed v (k) of the motor at the current sampling moment k
Step2, setting the expected speed v of the motor rotor*(k) Inputting the difference between the actual speed v (k) of the motor and the actual speed v (k) of the motor into a PI controller, and outputting a reference current command i of the next sampling time k +1 of a q axis by the PI controllerq *The reference current command of the next sampling time k +1 of the (k +1) and d axes is id *(k+1)；
Step 3, measuring the actual current i at the current sampling moment ka(k)，ib(k)，ic(k) And is converted into d-axis current i under dq coordinate system through coordinate transformationd(k) And q-axis current iq(k)；
Step 4, the current i at the current sampling time k is measuredd(k)、iq(k) And the actual voltage quantity ud(k)、uq(k) Inputting the measured values into an improved extended state observer to obtain observed values of the parameter disturbance quantity at the k moment
Figure BDA0001974758970000021
fq(k)；
Step 5, the current i at the k moment is measuredd(k)、iq(k) And disturbance amount observed value
Figure BDA0001974758970000022
fq(k) Together with the current i at the time k +1q *(k+1)、id *(k +1) are input into the dead-beat prediction controller together to obtain a reference command u of the required control voltaged *(k)、uq *(k)；
Step 6, mixing ud *(k)、uq *(k) After coordinate transformation, the output of the inverter is controlled through SVPWM, and the control of the motor is realized.
The invention has the advantages that:
1. according to the invention, the parameter disturbance quantity is observed by the improved extended state observer and is used for compensating the dead-beat prediction control system, so that the method has stronger robustness on disturbance caused by system parameter deviation, and the problems of current static error and instability caused by parameter disturbance are avoided;
2. the invention designs the improved extended state observer, and the observer is controlled to observe the disturbance quantity by using the disturbance quantity error, so that the convergence speed of the observer is improved, and the dynamic response speed of the motor current is improved. Meanwhile, the problem of overlarge peak value of an observed value of the extended state observer at the initial moment is restrained by using a variable gain mode, so that the problem of overlarge overshoot of the motor current is restrained. Therefore, the tracking speed and the anti-interference capability of the current are effectively improved.
Drawings
FIG. 1 is a system block diagram of a control method according to an embodiment of the present invention;
FIG. 2 is a comparison graph of current tracking waveforms for a given inductance of 2.5L in accordance with an embodiment of the present invention;
FIG. 3 is a waveform diagram of current tracking without ESO for a given inductance of 2.5L in accordance with an embodiment of the present invention;
FIG. 4 is a waveform diagram of current tracking under conventional ESO given an inductance of 2.5L in accordance with an embodiment of the present invention;
FIG. 5 is a waveform of current tracking at improved ESO given an inductance of 2.5L in accordance with an embodiment of the present invention;
FIG. 6 shows a given flux linkage according to an embodiment of the present invention
Figure BDA0001974758970000032
Comparing the time current tracking waveform;
FIG. 7 shows a given flux linkage according to an embodiment of the present invention
Figure BDA0001974758970000033
Current tracking oscillogram under the ESO condition is not existed;
FIG. 8 shows a given flux linkage according to an embodiment of the present invention
Figure BDA0001974758970000034
Current tracking oscillogram under the conventional ESO;
FIG. 9 shows a given flux linkage according to an embodiment of the present invention
Figure BDA0001974758970000035
Improving a current tracking waveform diagram under ESO;
FIG. 10 is a comparison graph of current tracking waveforms for a given resistance of 0.2R in accordance with an embodiment of the present invention;
FIG. 11 is a graph of current tracking waveforms without ESO given a resistance of 0.2R in accordance with an embodiment of the present invention;
FIG. 12 is a graph of current tracking waveforms for conventional ESO given a resistance of 0.2R in accordance with an embodiment of the present invention;
FIG. 13 is a graph of current tracking waveforms for improved ESO given a resistance of 0.2R in accordance with an embodiment of the present invention;
FIG. 14 is a velocity waveform tracking comparison graph with difference deviation according to an embodiment of the present invention.
In the figure: v. of*(k) Is the desired velocity at the previous sampling instant k, v is the actual velocity at the previous sampling instant k, iq *(k +1) is a reference current command at the next sampling time of the q-axis, id *(k +1) is a reference current command for the next sampling instant of the d-axisa(k),ib(k),ic(k) For measured actual three-phase currents, id(k)、iq(k) Is the actual current of the dq axis,
Figure BDA0001974758970000031
fq(k) observed value of disturbance amount of dq axis, ud *(k)、uq *(k) The voltage reference command is controlled for the dq axis.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further described with the specific embodiments.
The invention provides a dead-beat current control method for a permanent magnet synchronous linear motor, which is characterized in that an improved extended state observer is designed as shown in figures 1-14, the information of disturbance quantity errors is extracted from current quantity errors, the disturbance quantity errors are used for adjusting disturbance quantity observed values according to an error control principle, the tracking speed of the observer is accelerated, and time-varying gains are designed for restraining the problem of overlarge current peak values. The disturbance quantity observed value is observed at the current sampling moment k
Figure BDA0001974758970000041
fq(k) And sampling the obtained actual current i at the current sampling moment kd(k)、iq(k) Together with the reference current command i at the time k +1q *(k+1)、id *(k +1) are input into the dead-beat prediction controller together to obtain a reference command u of the required control voltaged *(k)、uq *(k) In that respect The dead-beat predictive controller obtained by the method of the invention is used for system parameterThe disturbance caused by the number deviation has stronger robustness, the current tracking speed is improved, and the current peak value at the initial moment is effectively restrained.
A dead beat current control method for a permanent magnet synchronous linear motor comprises the following steps:
step 1, calculating the measured displacement by adopting a linear motor control system with a speed and current double closed-loop structure and a grating as a position detector to obtain the actual speed v (k) of a motor at the current sampling moment k;
step2, setting the expected speed v of the motor rotor*(k) Inputting the difference between the actual speed v (k) of the motor and the actual speed v (k) of the motor into a PI controller, and outputting a reference current command i of the next sampling time k +1 of a q axis by the PI controllerq *The reference current command of the next sampling time k +1 of the (k +1) and d axes is id *(k+1)；
Step 3, measuring the actual current i at the current sampling moment ka(k)，ib(k)，ic(k) And is converted into d-axis current i under dq coordinate system through coordinate transformationd(k) And q-axis current iq(k)；
Step 4, the current i at the current sampling time k is measuredd(k)、iq(k) And the actual voltage quantity ud(k)、uq(k) Inputting the measured values into an improved extended state observer to obtain observed values of the parameter disturbance quantity at the k moment
Figure BDA0001974758970000042
fq(k)；
Step 5, the current i at the k moment is measuredd(k)、iq(k) And disturbance amount observed value
Figure BDA0001974758970000043
fq(k) Together with the current i at the time k +1q *(k+1)、id *(k +1) are input into the dead-beat prediction controller together to obtain a reference command u of the required control voltaged *(k)、uq *(k)；
Step 6, mixing ud *(k)、uq *(k) Warp beamAfter coordinate transformation, the output of the inverter is controlled through SVPWM, and the control of the motor is realized.
In the present embodiment, the PI controller functions as a speed controller; actual voltage value u at current sampling time kd(k)、uq(k) Control voltage reference command u equal to the last sampling instant k-1 respectivelyd *(k-1)、uq *(k-1). In this embodiment, the improved extended state observer comprises the following design steps:
step 1, establishing a voltage equation of the permanent magnet synchronous linear motor under a dq coordinate system:
Figure BDA0001974758970000051
in formula (1): r is the primary resistance, tau is the secondary pole distance,
Figure BDA0001974758970000059
is a secondary permanent magnet flux linkage, Ld、LqD-axis and q-axis inductance components respectively, and can be L-shaped due to the surface-mounted structured＝Lq＝L。ud、uqPrimary d and q axis voltages, id、iqPrimary d-axis current and q-axis current respectively, and v is primary motion speed.
Step2, taking the current equation when the actual parameter and the nominal parameter have deviation into consideration, and modeling the disturbance quantity of the system parameter;
the current equation can be obtained by equation (1) with parameter deviations taken into account:
Figure BDA0001974758970000052
in formula (2): r0、L0、
Figure BDA0001974758970000053
-nominal parameters of motor resistance, inductance, flux linkage;
ΔR、ΔL、
Figure BDA0001974758970000054
-parameter deviations of the motor resistance, inductance, flux linkage, Δ R ═ R-R0，ΔL＝L-L0，
Figure BDA0001974758970000055
Let fd、fqF can be obtained as d and q axis parameter disturbances respectivelyd、fqThe expression is as follows:
Figure BDA0001974758970000056
step 3, let the disturbance change rate
Figure BDA0001974758970000057
Describing a state space of the q-axis current and the parameter disturbance quantity thereof, and constructing a traditional extended state observer according to a current error;
3.1, describing a state space of the q-axis current and a parameter disturbance quantity thereof:
Figure BDA0001974758970000058
in formula (4): x ═ x1 x2]T＝[iq fq]TIs a state variable matrix; u is the input quantity uq；
Figure BDA0001974758970000061
Is a state transition matrix; b ═ 1/L0 0]TIs a control matrix; e ═ 01]TIs an interference matrix;
Figure BDA0001974758970000062
3.2, constructing a traditional extended state observer according to the current error:
Figure BDA0001974758970000063
in the formula:
Figure BDA0001974758970000064
is a matrix of the observations of which,
Figure BDA0001974758970000065
is to iqThe observed value is obtained by observing the measured value,
Figure BDA0001974758970000066
is to fqObserving the value; e ═ e1 e2]T＝[z1-x1 z2-x2]TIs the error value of the observer; e.g. of the type1Is the error between the observed and actual values of the current, e2Is q-axis parameter disturbance quantity error, namely the error between the observed value and the actual value of the parameter disturbance quantity,
Figure BDA0001974758970000067
for observer gain matrix,/1、l2Is the gain of the observer, and1、l2the performance of the observer is controlled by adjusting the gain as a constant; x is the number of1Is the actual value x of the current detected by the current detection2Is a disturbance value; z is a radical of1、z2Is the observed value of the observer.
And Step 4, extracting the disturbance quantity error from the current quantity error information, and observing the disturbance quantity by using the disturbance quantity error, so that the convergence speed of the observer is increased. Meanwhile, aiming at the problem that the current peak value of the motor at the initial moment is too large due to high gain of the traditional extended state observer, the gain of the observer is set to be a proportional function, a smaller gain is set at the initial moment to inhibit the problem that the current peak value is too large, and the current peak value is gradually increased to a constant value. Finally forming an improved extended state observer;
4.1, subtracting the equation (5) and the equation (4) to obtain a system parameter disturbance quantity error:
Figure BDA0001974758970000068
wherein:
Figure BDA0001974758970000069
4.2, the disturbance quantity error is used for realizing the observation of the disturbance quantity, the observer gain is set to be a proportional function, and the traditional extended state observer with the formula (5) is changed into an improved extended state observer:
Figure BDA00019747589700000610
in formula (7):
Figure BDA00019747589700000611
for observer gain matrix,/1(t)、l2(t) is the observer gain value; l1(t) and l2(t) is a scaling function that increases with time, gradually increasing from a constant value that is smaller at an initial instant to another constant value with a fixed scaling factor and remaining constant. The problem that the peak value of the observer is too large can be restrained because the gain is small at the initial moment, and the convergence performance of the observer can be guaranteed to be good because the gain is gradually increased to another constant value. Let l1(t) and l2(t) a proportional function of
Figure BDA0001974758970000071
Wherein: gamma rayiIs a constant value at the initial moment; etaiConstant value which is finally kept unchanged; k is a radical ofiIs a proportionality coefficient; t is tiIs time, i ═ 1, 2; k is a radical ofitiRepresenting a gain that increases in direct proportion to time.
Step 5, carrying out forward Euler discretization on a state space equation of the current and the disturbance quantity thereof and the improved extended state observer, subtracting the discretized state space equation from the extended state observer to obtain an error state equation, and finally carrying out stability analysis on the improved extended state observer through the error state equation;
the discretized state space equation and the modified extended state observer are:
x(k+1)＝A1x(k)+B1u(k)+E1h(k) (8)
z(k+1)＝A1z(k)+B1u(k)-L2(k)e(k) (9)
in formulae (8) and (9): the state transition matrix becomes A1TA + I; control matrix becomes B1TB; interference matrix becomes E1TE; observer gain matrix becomes L2＝TL1(ii) a T is a sampling period; and I is an identity matrix.
Subtracting the equation (8) and the equation (9) to obtain an error state equation, assuming that the sampling period T is small enough and the perturbation is almost constant in two sampling periods, h (k) in the error state equation can be ignored:
Figure BDA0001974758970000072
and (3) performing linear transformation on the error state equation to obtain an equation (11), thereby calculating a characteristic equation of the error state of the observer:
Figure BDA0001974758970000081
|λI-M|＝λ2+[T(l2(k)+l1(k))+2]λ+T(l2(k)+l1(k))+T2l1(k)l2(k)+1＝0
(12)
in formula (11):
Figure BDA0001974758970000086
is e1(k+1)、e2(k +1) error state variables after linear transformation.
In formula (12): because the gains of the extended state observers are all larger than 0, the characteristic roots are all negative real parts, namely the observer error finally tends to 0, and the observer is stable.
Step 6, obtaining a d-axis improved extended state observer in the same way, and performing stability analysis;
the improved extended state observer of the d axis is as follows:
c(k+1)＝A1z(k)+B1ud(k)-L2(k)(k) (13)
in the formula:
Figure BDA0001974758970000082
is an observed value matrix of a d-axis modified extended observer;
Figure BDA0001974758970000083
is for d-axis current idIs detected by the measured values of (a) and (b),
Figure BDA0001974758970000084
is a disturbance of d-axis fdThe observed value of (a);
Figure BDA0001974758970000085
is the error between the observed and actual values of the d-axis current,2is the error between the observed value and the actual value of the disturbance quantity of the d-axis parameter.
The d-axis modified extended state observer can be calculated to have the same characteristic equation of error state as the q-axis modified extended state observer:
|λI-M|＝λ2+[T(l2(k)+l1(k))+2]λ+T(l2(k)+l1(k))+T2l1(k)l2(k)+1＝0 (14)
in formula (14): because the gains of the extended state observers are all larger than 0, the characteristic roots are all negative real parts, namely the observer error finally tends to 0, and the observer is stable.
In this embodiment, the dead-beat prediction controller includes the following design steps:
step 1, carrying out forward Euler discretization on a permanent magnet synchronous linear motor voltage equation under the dq coordinate system, and calculating a dq axis voltage reference instruction u according to the discretized equationd *(k)、uq *(k)：
Figure BDA0001974758970000091
Equation (15) is a conventional dead-beat predictive control algorithm, where: f. ofd(k)、fq(k) Can not be directly measured and calculated, so the calculated ud *(k)、uq *(k) It will be inaccurate.
Step2, obtaining the parameter disturbance quantity f which can not be directly measured and calculated in the traditional dead beat prediction control algorithmd(k)、fq(k) Observed value of disturbance quantity at current sampling moment k observed by improved extended state observer
Figure BDA0001974758970000092
fq(k) Instead, a dq-axis voltage reference command u is obtained by calculationd *(k)、uq *(k) Namely, the dead beat prediction control algorithm after parameter disturbance compensation:
Figure BDA0001974758970000093
in the present embodiment, the inverter is a three-phase two-level voltage inverter.
In order to verify the effectiveness of the designed current prediction control algorithm, a traditional extended state observer and an improved extended state observer are respectively utilized to carry out a motor current tracking test and a speed tracking test. The parameters of the motor are as follows: inductance L is 0.0134H, resistance R is 1.3 Ω, pole pitch τ is 0.032m, flux linkage Ψ is 0.11Wb, damping coefficient is 0.2N · s/m, and sampling period is 100 μ s. The gain and time parameters of the modified extended state observer are set to: gamma ray1＝3，η1＝6，t1＝4ms，γ2＝400，η2＝600，t24 ms. The traditional extended state observer gain parameters are: l1＝4，l2600. Firstly, the given parameters of inductance, flux linkage and resistance in the controller are respectively set2.5L of,
Figure BDA0001974758970000094
0.2R, using idControl strategy of 0 and given current iq2A. As shown in fig. 2-5, when the given value of the inductance is 2.5L, the harmonic content of the dead-beat predictive control system without the extended state observer gradually increases, instability occurs, and the current response speed is slow; 6-9, when the flux linkage given value is 0.5 psi, the system without extended state observer, iqDeviation exists and gradually increases; as shown in FIGS. 10 to 13, when the given value of the resistance is 0.2R, iqThere is a constant deviation; the control method of the traditional extended state observer and the control method of the improved extended state observer can inhibit the problems caused by parameter disturbance, but the improved extended state observer can better inhibit the current peak value, and the current tracking speed is higher.
When comparing the speed tracking performance, the given motor speed is 100mm/s, the applied load force is 300N, and the given values of the parameters of inductance, flux linkage, resistance and the like in the controller are set as 2.5L,
Figure BDA0001974758970000101
0.2R, fig. 14 shows that the corresponding speed tracking waveform comparison, the dead beat prediction control of the improved extended state observer is applied, the motor speed fluctuation is smaller during starting, the speed is more stable after starting, and the peak value is higher and oscillation occurs at the initial time under the compensation of the traditional extended state observer. The experimental result shows that the current control algorithm provided by the invention has a low peak value at the initial moment and a high response speed, and avoids the problems of current static error and instability caused by parameter disturbance.
It will be appreciated by those skilled in the art that the invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The embodiments disclosed above are therefore to be considered in all respects as illustrative and not restrictive. All changes which come within the scope of or equivalence to the invention are intended to be embraced therein.

Claims (6)

1. A dead beat current control method for a permanent magnet synchronous linear motor is characterized by comprising the following steps:
acquiring the actual speed v (k) of the motor at the current sampling moment;
obtaining a reference current instruction i of a motor q axis at the next sampling momentq *(k +1) and reference current command i of motor d shaft at next sampling momentd *(k+1)；
Obtaining the actual current i of the motor at the current sampling momenta(k)，ib(k)，ic(k) And converting it into d-axis current i in dq coordinate systemd(k) And q-axis current i in dq coordinate systemq(k)；
I to be acquiredd(k)、iq(k) And the actual voltage u of the current sampling moment of the motord(k)、uq(k) Transmitting to an improved extended state observer to obtain an observed value of the parameter disturbance quantity at the current sampling moment
Figure FDA0002662424570000011
I to be acquiredd(k)、iq(k)，
Figure FDA0002662424570000012
And iq *(k+1)、id *(k +1) is transmitted to a dead-beat prediction controller to obtain a reference command u of a control voltaged *(k)、uq *(k)；
U to be acquiredd *(k)、uq *(k) After coordinate conversion, the result obtained by conversion is output through an SVPWM control inverter to control a motor;
the improved extended state observer comprises the following design steps:
step 1, establishing a voltage equation of the permanent magnet synchronous linear motor under a dq coordinate system, wherein the equation is as follows:
Figure FDA0002662424570000013
wherein R is the primary resistance, tau is the secondary pole distance,
Figure FDA0002662424570000014
is a secondary permanent magnet flux linkage, Ld、LqD and q axis inductance components, Ld＝Lq＝L，ud、uqPrimary d and q axis voltages, id、iqPrimary d-axis current and q-axis current respectively, and v is a primary motion speed;
step2, constructing a current equation, and modeling the disturbance quantity of system parameters;
the current equation can be obtained by adding the parameter deviation to the equation (1), and the current equation is:
Figure FDA0002662424570000021
wherein: r0、L0、
Figure FDA0002662424570000022
Respectively are the nominal parameters of the motor resistance, the inductance and the flux linkage;
ΔR、ΔL、
Figure FDA0002662424570000023
parameter deviations of motor resistance, inductance and flux linkage respectively, wherein Delta R is R-R0，ΔL＝L-L0，
Figure FDA0002662424570000024
Let fd、fqAs d and q axis parameter disturbance respectively to obtain fd、fqThe expression is as follows:
Figure FDA0002662424570000025
step 3, constructing a traditional extended state observer;
3.1, describing a state space of the q-axis current and a parameter disturbance quantity thereof:
Figure FDA0002662424570000026
wherein: x ═ x1 x2]T＝[iq fq]TIs a state variable matrix; u is the input quantity uq；
Figure FDA0002662424570000027
Is a state transition matrix; b ═ 1/L0 0]TIs a control matrix; e ═ 01]TIs an interference matrix;
Figure FDA0002662424570000028
Figure FDA0002662424570000029
3.2, constructing the traditional extended state observer according to the error between the current observed value and the actual value:
Figure FDA00026624245700000210
wherein:
Figure FDA00026624245700000211
in order to be a matrix of the observations,
Figure FDA00026624245700000212
is to iqThe observed value is obtained by observing the measured value,
Figure FDA00026624245700000213
is to fqObserving the value; e ═ e1e2]T＝[z1-x1 z2-x2]TIs the error value of the observer; e.g. of the type1Is the error between the observed and actual values of the current, e2Is the error of the disturbance quantity of the parameter,
Figure FDA00026624245700000214
for observer gain matrix,/1、l2Is the gain of the observer, and1、l2is a constant;
Figure FDA00026624245700000215
step 4, obtaining an improved extended state observer;
4.1, acquiring system parameter disturbance quantity error e2：
Figure FDA0002662424570000031
Wherein:
Figure FDA0002662424570000032
4.2, obtaining an improved extended state observer:
Figure FDA0002662424570000033
wherein:
Figure FDA0002662424570000034
for observer gain matrix,/1(t)、l2(t) is the observer gain value;
step 5, forward Euler discretization is carried out on a state space equation of the current and the disturbance quantity of the current and the improved extended state observer, the discretized state space equation is subtracted from the extended state observer to obtain an error state equation, and stability analysis is carried out on the improved extended state observer through the error state equation;
and 6, acquiring the d-axis improved extended state observer in the modes of the steps 1 to 5, and analyzing the stability of the extended state observer.
2. The deadbeat current control method of a permanent magnet synchronous linear motor according to claim 1, wherein said deadbeat predictive controller comprises the design steps of:
step 1, carrying out forward Euler discretization on a permanent magnet synchronous linear motor voltage equation under a dq coordinate system, and calculating a dq axis voltage reference instruction u according to the discretized equationd *(k)、uq *(k) Namely, the traditional dead beat prediction control algorithm;
step2, observing the parameter disturbance amount of the current sampling moment
Figure FDA0002662424570000035
Substitution of fd(k)、fq(k) Obtaining a dq-axis voltage reference command ud *(k)、uq *(k) Namely a dead beat predictive control algorithm after parameter disturbance compensation.
3. The deadbeat current control method for a permanent magnet synchronous linear motor of claim 1 wherein desired speed v of motor mover is adjusted*(k) The difference between the actual speed v (k) of the motor and the actual speed v (k) of the motor is input into a PI controller, and the PI controller outputs iq *(k +1) and id *(k+1)。
4. The deadbeat current control method of a permanent magnet synchronous linear motor according to claim 3, wherein said PI controller is a speed controller.
5. The deadbeat current control method of claim 1 wherein said actual voltage magnitude u at said current sample time k isd(k)、uq(k) Equal to the last sampling instant k-1, respectivelyControl voltage reference command ud *(k-1)、uq *(k-1)。
6. The deadbeat current control method for a permanent magnet synchronous linear motor of claim 1 wherein said inverter is a three-phase two-level voltage inverter.
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