CN113411026A - Design method of self-adaptive sliding film disturbance observer for permanent magnet synchronous linear motor - Google Patents

Design method of self-adaptive sliding film disturbance observer for permanent magnet synchronous linear motor Download PDF

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CN113411026A
CN113411026A CN202110830936.7A CN202110830936A CN113411026A CN 113411026 A CN113411026 A CN 113411026A CN 202110830936 A CN202110830936 A CN 202110830936A CN 113411026 A CN113411026 A CN 113411026A
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disturbance
sliding film
observer
parameter
adaptive sliding
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宋宝
钟靖龙
陈天航
唐小琦
周向东
杨承博
李虎
余文韬
吉文博
张泽之
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Huazhong University of Science and 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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0017—Model reference adaptation, e.g. MRAS or MRAC, useful for control or parameter estimation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/22—Current control, e.g. using a current control loop
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/06—Linear motors
    • H02P25/064—Linear motors of the synchronous type
    • 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 provides a design method of a self-adaptive sliding film disturbance observer for a permanent magnet synchronous linear motor, which comprises the following steps: constructing a PMLSM electrical subsystem dynamic model based on motor parameter mismatch and disturbance caused by part unmodeled dynamics; representing dynamic lumped disturbance according to an electrical subsystem dynamic model of PMLSM; analyzing the dynamic lumped disturbance to obtain an analysis conclusion; and designing an adaptive sliding film disturbance observer based on the analysis conclusion, designing sliding film parameters of the adaptive sliding film disturbance observer, and designing a sliding film control function of the adaptive sliding film disturbance observer based on an exponential approximation law. The invention designs a synovial membrane disturbance observer (SDO), introduces a new synovial membrane index approach law, designs an adaptive synovial membrane disturbance observer (ASDO), and finally uses the observer for observing model lumped disturbance to realize real-time compensation of parameter disturbance.

Description

Design method of self-adaptive sliding film disturbance observer for permanent magnet synchronous linear motor
Technical Field
The invention relates to the field of motor observation control, in particular to a design method of a self-adaptive sliding film disturbance observer for a permanent magnet synchronous linear motor.
Background
With the demand for high-speed/high-precision linear motion systems, PMLSM (Permanent magnet synchronous linear motor) has been applied in a variety of industrial scenes, such as semiconductor manufacturing, numerical control machines, and the like. In an actual PMLSM control system, the performance of current control is a critical factor in determining the performance of the control system. Therefore, to achieve high-precision position location and high dynamic current response performance, a variety of current control methods have been proposed. Among them, hysteresis control, PI (proportional-integral) control, and predictive control are the most widely used control methods.
Hysteresis control, also known as bang-bang control, has the advantages of simple and easy-to-implement algorithm, small tracking error, fast current response, strong robustness and the like. However, this method also has some significant problems, such as large current ripple, variable switching frequency, etc., and these problems are difficult to avoid in practical applications. The PI control has the advantages of small steady-state error, fixed switching frequency and the like. However, the PMLSM control system is a non-linear system with uncertainty, complex disturbances, and mismatch of motor parameters, which makes it difficult for PI control to have satisfactory dynamic performance throughout the entire operation of such non-linear system.
Compared with hysteresis control and PI control, the steady-state and dynamic performance of predictive control is better. It is mainly divided into two categories: model predictive control and deadbeat predictive control. Among them, the model predictive control has a drawback in application because of its high computational complexity, especially for multi-step prediction or multi-level converter applications, which is more exponentially increased. In contrast, dead-beat predictive control can achieve similar dynamic tracking performance and better static tracking performance with less computation. However, deadbeat predictive control relies entirely on accurate motor models, meaning that mismatches in model parameters can cause the calculated voltage reference to deviate from its expected value. In addition, control delays, such as sampling delays, duty cycle refresh delays, etc., of a digitally controlled system can significantly degrade the control performance of the system.
Disclosure of Invention
The invention provides a design method of a self-adaptive sliding film disturbance observer for a permanent magnet synchronous linear motor, aiming at the technical problems in the prior art, and the method comprises the following steps: constructing a PMLSM electrical subsystem dynamic model based on motor parameter mismatch and disturbance caused by part unmodeled dynamics; representing dynamic lumped disturbance according to an electrical subsystem dynamic model of PMLSM; analyzing the dynamic lumped disturbance to obtain an analysis conclusion; and designing an adaptive sliding film disturbance observer based on the analysis conclusion, designing sliding film parameters of the adaptive sliding film disturbance observer, and designing a sliding film control function of the adaptive sliding film disturbance observer based on an exponential approximation law.
The design method of the self-adaptive sliding film disturbance observer for the permanent magnet synchronous linear motor has the advantages that a Permanent Magnet Synchronous Linear Motor (PMSLM) driving system based on dead beat current predictive control (DPCC) has good dynamic performance and high steady-state precision, but the method has high dependence on the accuracy of motor model parameters, actual parameters and nominal parameters have deviation in practical application, and the parameter disturbance problem caused by the deviation influences the current control quality. A slip film disturbance observer (SDO) is designed for the purpose, a new slip film index approximation law is introduced, an adaptive slip film disturbance observer (ASDO) is designed, and the observer is finally used for observing model lumped disturbance to realize real-time compensation of parameter disturbance.
Drawings
FIG. 1 is a flow chart of a design method of an adaptive sliding film disturbance observer for a permanent magnet synchronous linear motor according to the present invention;
FIG. 2 is a timing diagram of a discrete-time current controller;
FIGS. 3(a) -3 (f) are schematic diagrams of DPCC simulation results under parameter mismatch;
FIGS. 4(a) -4 (f) are schematic diagrams of simulation results of DPCC + ASDO under parameter mismatch;
FIGS. 5(a) -5 (d) are schematic diagrams illustrating SDO disturbance estimation results under parameter mismatch;
6(a) -6 (d) are schematic diagrams illustrating the results of ASDO perturbation estimation under parameter mismatch;
fig. 7(a) to fig. 7(c) are schematic diagrams comparing the three control methods when R is 5 Rso;
fig. 8(a) to 8(c) are schematic diagrams comparing the three control methods when L is 2 Lso;
FIG. 9(a) to FIG. 9(c) are
Figure BDA0003175525440000031
Comparing the schematic diagrams of the three control methods;
fig. 10(a) -10 (c) are schematic diagrams comparing three control methods under multi-parameter mismatch.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
For current control of PMLSM, ideally, full tracking of the reference current can be achieved by a two-step delay of DPCC. However, in an actual control system, due to measurement errors and time-varying characteristics of motor parameters under different operating conditions such as temperature rise and magnetic saturation, it is difficult to accurately obtain the motor parameters. Therefore, parameter mismatch between the controller and the actual device will inevitably exist, thereby seriously affecting the system performance and even stability. Based on this consideration, much work has been done to improve the robustness of DPCC to parameter mismatches.
Due to the rank deficient character of the d-axis and q-axis dynamic equations, a simultaneous accurate estimation of all parameters of the synchronous machine (i.e. resistance, d-axis and q-axis inductance and permanent magnet flux) is not possible. Therefore, many indirect identification or estimation methods are applied to improve the performance of DPCC. Among them, there are proposed adaptive parameter estimation schemes to iteratively estimate three parameters, and also proposed integral on-line adjustment parameters with d-axis and q-axis current errors, thereby eliminating static error current in a steady state. But the method neglects the influence of resistance and does not analyze transient performance temporarily.
Indirectly, the effects of parameter mismatch and unmodeled dynamics can be treated as a concentrated disturbance, and then the transient response is improved by using a disturbance estimation/observation method in combination with feedforward compensation, thereby eliminating the quiescent current error. Some of these schemes add a simple integral compensation to the PCC in parallel with the error between the reference current and the sample current. However, the selection of the integral gain should be carefully balanced between the current response speed and overshoot. With the development of modern control theory, various methods have been expanded in order to improve the robustness of the control. A linear Luenberger observer was designed to observe the effects of model uncertainty and observer gain can be easily adjusted by pole placement techniques. A higher order SMO was designed to estimate the lumped disturbance with jitter reduction based on the principle of invariance of the synovial external and internal disturbances. Although better observation and compensation results can be obtained, specific gain tuning instructions remain to be studied. The current at the next sampling instant is estimated by designing an Extended Kalman Filter (EKF) for command voltage calculation of PCC. The robustness of EKF to parameter variations makes it a promising optimization method, but the large computational load limits the sampling frequency. Still other solutions use lumped disturbances as an extended state, and extended state observers have been proposed to estimate the disturbance.
Based on this, the embodiment of the present invention provides an adaptive sliding-film disturbance observer for observing lumped disturbance, and applying the observation result to DPCC, as shown in fig. 1, where the method includes: s1, constructing a PMLSM electrical subsystem dynamic model based on motor parameter mismatch and disturbance caused by part unmodeled dynamics; s2, representing dynamic lumped disturbance according to the electrical subsystem dynamic model of the PMLSM; s3, analyzing the dynamic lumped disturbance to obtain an analysis conclusion; and S4, designing an adaptive sliding film disturbance observer based on the analysis conclusion, designing the sliding film parameters of the adaptive sliding film disturbance observer, and designing the sliding film control function of the adaptive sliding film disturbance observer based on the exponential approximation law.
It can be understood that the design process of the adaptive sliding film disturbance observer provided by the embodiment of the invention mainly comprises three parts: the first part is used for modeling a dynamic equation of PMLSM and modeling PMLSM lumped disturbance based on a dynamic equation model; the second part is used for analyzing dynamic lumped disturbance in the DPCC; and in the third part, designing an adaptive sliding film disturbance observer.
The design method of the self-adaptive sliding film disturbance observer for the permanent magnet synchronous linear motor has the advantages that a Permanent Magnet Synchronous Linear Motor (PMSLM) driving system based on dead beat current predictive control (DPCC) has good dynamic performance and high steady-state precision, but the method has high dependence on the accuracy of motor model parameters, actual parameters and nominal parameters have deviation in practical application, and the parameter disturbance problem caused by the deviation influences the current control quality. A slip film disturbance observer (SDO) is designed for the purpose, a new slip film index approximation law is introduced, an adaptive slip film disturbance observer (ASDO) is designed, and the observer is finally used for observing model lumped disturbance to realize real-time compensation of parameter disturbance.
In the process of modeling the dynamic equation of the PMLSM in step S1, considering the parameter mismatch of the motor and the disturbance caused by part of unmodeled dynamics, the dynamic model of the electrical subsystem of the PMLSM can be expressed as:
Figure BDA0003175525440000051
wherein u isd/uqAnd id/iqThe d/q axis stator voltage and current, respectively. RsAnd LsRespectively winding resistance and stator inductance,. psifIs a permanent magnetic flux linkage omegaeAnd pi v/tau is the electrical angular velocity, wherein v is the linear velocity of the rotor, and tau is the polar distance. The lower corner mark "o" represents the nominal value of the parameter, fd,fqRepresenting the lumped disturbances due to parameter mismatch and unmodeled dynamics, can be calculated by:
Figure BDA0003175525440000061
wherein R iss＝Rso+ΔRs,Ls＝Lso+ΔLs,ψf＝ψfo+Δψf，εd/εqLumped unmodeled dynamics for d/q axes, respectively.
For the electrical subsystem dynamics model of PMLSM of equation (1), the dynamics equations can be rewritten as a discrete form of equation (3) in view of the zero order hold characteristic of the inverter in an actual digital control system:
Figure BDA0003175525440000062
wherein, TsK is the discrete sampling time instant for a discrete sampling period.
According to equation (3), the current equation can be expressed in the form of a matrix as follows:
I(k+1)＝G0I(k)+H0[U(k)-Φ(k)-D(k)]； (4)
wherein:
I(k)＝[id(k) iq(k)]T,U(k)＝[ud(k) uq(k)]T
Φ(k)＝[0 πv(k)ψfo/τ]T,D(k)＝[fd(k) fq(k)]T,
Figure BDA0003175525440000063
Figure BDA0003175525440000064
the above embodiment shows the dynamic model of PMLSM, and the following shows the lumped disturbance, that is, the specific implementation process of step S2 is that, since the control delay cannot be completely eliminated in the actual digital control system, when SVPWM is used, the calculated voltage command at the time k will be updated at the time (k + 1). Therefore, there is a delay of two sampling periods between the time of onset of the current command and the sampling time of the feedback current, as shown in fig. 2, which is a discrete time current controller timing diagram.
When the control command changes, the control delay causes large overshoot and oscillation. However, this delay can be eliminated by predicting the current at time (k +1) to be calculated with the known state at time k to command the current using equation (4).
Figure BDA0003175525440000071
Wherein, the superscripts "^" and "+" represent the estimated value and the instruction value, respectively.
Thus, the voltage command at time (k +1) can be calculated as:
Figure BDA0003175525440000072
on the other hand, as shown in equation (6), the lumped disturbance depends on the mismatch of the motor parameters and the system state, and the unmodeled dynamics (epsilon) is neglectedd/εq) The dynamic lumped perturbation can be calculated by equation (7):
Figure BDA0003175525440000081
from equation (7), the dynamic lumped perturbation consists of the following three parts: motor parameter mismatch, current variation, and speed variation.
Step S3 analyzes the dynamic lumped disturbance, and in order to analyze the variation trend of the lumped disturbance more intuitively, the following two assumptions are made:
assume that 1:
Figure BDA0003175525440000082
and d/q axis current is completely decoupled;
assume 2: the mismatch of the motor parameters is slowly variable and even time-invariant;
based on hypothesis 1, the conclusion is reached: i.e. id≈0,d(id)/dt≈0,d2(id)/dt 20. From hypothesis 2, one can deduce d (Δ R)s)/dt≈0,d(ΔLs)/dt≈0,d(Δψf) And/dt is approximately equal to 0. It can be seen that when the above two assumptions are satisfied, some parts of the dynamic lumped perturbation are negligible, and in this case, the dynamic lumped perturbation can be further simplified as:
Figure BDA0003175525440000091
from equation (8), the following can be inferred:
(1) when PMLSM is at high speed (ω)e) High acceleration (d (ω)e) Dt) and large inductance mismatch (Δ L)s) When the position instruction of (2) moves, the d-axis lumped disturbance change is obvious, so that the d-axis current and the q-axis current cannot be completely decoupled;
(2) when PMLSM is in high acceleration, high speed and high jump (d)2(iq)/dt2) When the position command of (2) moves, the dynamic lumped disturbance of the q axis is not negligible; in addition, the motor parameter mismatch (Δ R)s,ΔLs,Δψf) Also cannot be ignored, therefore, when f cannot be matchedqWhen sufficient compensation is made, the transient response of the q-axis current will be degraded.
The conclusion obtained by analyzing the dynamic lumped disturbance shows that some parts of the dynamic lumped disturbance are not negligible, so that a synovial disturbance observer needs to be designed to observe the disturbance of the PMLSM system.
The main process of designing the synovial membrane observer in step S4 is as follows:
according to the electrical subsystem dynamics model (1) of PMLSM, the expansion dynamics equation of PMLSM can be expressed in terms of parameter variations as:
Figure BDA0003175525440000092
Figure BDA0003175525440000101
for parameter estimation and current prediction, a synovial membrane disturbance observer was designed as follows:
Figure BDA0003175525440000102
Figure BDA0003175525440000103
where the superscript "^" indicates the estimated value, Udsmo indicates the synovial control function, and g indicates the synovial parameter.
After the synovial membrane disturbance observer is designed, the parameters and control functions of the synovial membrane are selected and designed.
From equations (9) to (12), the following error equation is obtained:
Figure BDA0003175525440000104
Figure BDA0003175525440000105
wherein the content of the first and second substances,
Figure BDA0003175525440000106
in order to estimate the error for the current,
Figure BDA0003175525440000107
Figure BDA0003175525440000111
the error is estimated for the disturbance.
According to the slip film control theory, the slip film design process can be divided into two steps, wherein the first step is slip film surface design, and the second step is slip film control function design, so that the state track is converged to the slip film surface. A linear slide surface is selected herein, expressed as:
Figure BDA0003175525440000112
the traditional design method of the synovial membrane control function only concerns whether the system meets the stability criterion, but does not concern the mode of reaching the synovial membrane surface, which has important influence on the performance of the synovial membrane system. Therefore, in order to improve the observation accuracy of the synovial membrane observer, an exponential approximation law is adopted to design a synovial membrane control function, wherein the exponential approximation law is as shown in formula (16):
Figure BDA0003175525440000113
wherein k and lambda are approach law parameters which are positive numbers, and approach time t of exponential approach law1Can be obtained from 0 to t by the pair formula (16)1And (3) integral calculation:
Figure BDA0003175525440000114
from the formula (17), it can be seen that the higher the k and λ values are, the faster the film surface can be reached. Therefore, in order to achieve performance faster, k and λ should be increased; however, this directly increases the level of buffeting due to the inherent properties of the slip film. Therefore, in practical applications, parameters need to be adjusted to average the convergence speed and buffeting level.
By bringing formula (15) into formula (16):
Figure BDA0003175525440000115
by substituting formula (13) and formula (14) into formula (18), it is possible to obtain:
Figure BDA0003175525440000121
from equation (19), with disturbance of e2 and e4 as control functions, the design of the slip film variable structure control function is:
Figure BDA0003175525440000122
to guarantee the current estimation error (e)1，e3) And disturbance estimation error (e)2，e4) The observer parameters k and g should be reasonably selecteddAnd gq. Therefore, the stability condition of the slip film observer, as shown in equation (21), must be satisfied.
The following pairs of design observer parameters k, gdAnd gqBased on satisfying the stability condition of the synovial observer, formula (21) can be obtained:
Figure BDA0003175525440000123
according to equations (13) and (20), the first inequality of the stability condition (21) can be rewritten as:
Figure BDA0003175525440000124
to ensure
Figure BDA0003175525440000125
The d-axis observer parameter k is:
k＞|e2|/Lso； (23)
similarly, the q-axis observer parameters are:
k＞|e4|/Lso； (24)
therefore, to ensure the observer to be stable, the parameter k is selected within the range of:
k＞max(|e2|,|e4|)/Lso； (25)
the proposed synovial observer with parameter k can reach and stay on the synovial surface within a limited time, implying an error e1And e3And derivatives thereof
Figure BDA0003175525440000134
And
Figure BDA0003175525440000135
may converge to zero; then, equations (13) and (14) can be simplified as:
Figure BDA0003175525440000131
e is then2And e4Respectively as follows:
Figure BDA0003175525440000132
selecting an appropriate parameter g according to equation (27)dAnd gqSo that the disturbance error e2And e4Convergence, wherein the parameter gdAnd gqThe positive value must be chosen to ensure convergence of the perturbation error. Convergence rate and gdAnd gqThere is a direct relationship.
In order to further improve the control performance, on the basis of the traditional synovial membrane index approach law, an adaptive synovial membrane approach law is provided and is realized by selecting an index item adaptive to synovial membrane change. The new approach law is as follows:
Figure BDA0003175525440000133
wherein M is k/(ε + (1+1/| x) - ε) e-δ|s|，k＞0、δ＞0、0＜ε＜1。
It can be observed in equation (28) that if the synovium | s | increases, the variable M converges in the exponential approximation law to a value where k/ε is greater than k. This means that the new approach law has a faster approach speed than the exponential approach law. On the other hand, as the synovial membrane | s | decreases, the variable M converges to k | x |/(1+ | x |), where the state | x | gradually decreases to 0 as a function of the synovial membrane control function. This means that as the system trajectory approaches the synovial face s at 0, the variable M is gradually decreased to 0 to suppress synovial chatter. Therefore, a synovial state observer using this adaptive approach law can dynamically adapt to changes in the surface of the synovial membrane by varying the variable M between 0 and k/ε.
An adaptive sliding membrane disturbance observer is designed, and the effectiveness of the method is verified by respectively adopting simulation and experiments. Under nominal conditions, the main parameters used in the simulation were the same as the prototype motor, and the specific parameters are shown in table 1.
TABLE 1 PMLSM Main parameters
Figure BDA0003175525440000141
A simulation model is built in MATLAB/Simulink, wherein the sampling frequency is 10kHZ, and the simulation parameters are as follows: k 150, λ 20, δ 1.5, e 0.1, gd＝gq＝550。
The simulation results of the current reference and current response under different parameter mismatch are shown in fig. 3, where L is 2L in fig. 3(a)soThe result of the APCC simulation is shown in fig. 3(b) as L ═ 0.5LsoThe simulation result of time-dependent DPCC is shown in FIG. 3(c) as R ═ 5Rsotime-DPCC simulationAs a result, in fig. 3(d), R is 0.2RsoThe results of time-dependent DPCC simulation are shown in FIG. 3(e)
Figure BDA0003175525440000144
The results of time-dependent DPCC simulation are shown in FIG. 3(f)
Figure BDA0003175525440000145
time-DPCC simulation results. From FIG. 3, it can be seen that at 0.05s, the speed command is from 0 to 0.5 m/s. At 0.2 and 0.35s, the load force abruptly increased from 0 to 10N, and abruptly decreased from 10 to 0N. Fig. 3 shows the simulation results of conventional DPCC under the condition of mismatch of model parameters. From the simulation results of fig. 3, it can be observed that parameter mismatch, including mismatch of permanent magnet inductance, resistance and flux linkage, has an effect on the current response of the conventional DPCC method. Fig. 4 shows simulation results of the DPCC + ASDO method under different parameter mismatch, where the parameter L in fig. 4(a) is 2LsoIn fig. 4(b), the parameter L is 0.5LsoIn fig. 4(c), the parameter is R ═ 5RsoIn fig. 4(d), the parameter is R ═ 0.2RsoThe parameters in FIG. 4(e) are
Figure BDA0003175525440000142
The parameters in FIG. 4(f) are
Figure BDA0003175525440000143
As can be seen from fig. 4, the DPCC + ASDO method can accurately and quickly track the current reference current and has good steady-state performance.
In practical experiments, the observer parameters are set to k 245, λ 40, δ 2, e 0.1, gd＝gq800. In order to evaluate the performance of the proposed synovial membrane approximation law, SDO using the conventional exponential approximation law and ASDO experiments using the proposed synovial membrane approximation law were performed, respectively. The experimental results are shown in fig. 5 and fig. 6, where fig. 5 is a schematic diagram of the estimation result of the SDO disturbance under different parameter mismatching conditions, and the parameter L in fig. 5(a) is 2L ═ LsoIn fig. 5(b), the parameter is R ═ 5RsoIn fig. 5(c), the parameter L is 2Lso、R＝5Rso、
Figure BDA0003175525440000151
Fig. 6 is a schematic diagram of the estimation result of ADSO disturbance under different parameter mismatching conditions, where the parameter L in fig. 6(a) is 2LsoIn fig. 6(b), the parameter is R ═ 5RsoThe parameters in FIG. 6(c) are
Figure BDA0003175525440000152
The parameter in fig. 6(d) is L ═ 2Lso、R＝5Rso、
Figure BDA0003175525440000153
According to fig. 5 and 6, the ripple ratio under different parameter mismatch when the load force is varied from 0 to 10N is shown in table 2.
TABLE 2 ASDO disturbance estimation ripple contrast
Figure BDA0003175525440000154
The disturbance estimation ripple of ASDO is significantly reduced compared to SDO. In the R-5 Rso state, the fd ripple of ASDO drops from 1.236V to 0.396V, with a drop of up to 68%. The fq ripple of the ASDO is reduced from 4.602V to 0.512V by as much as 89%. In the L-2 Lso state, the fd ripple of ASDO decreases from 10.356V to 1.018V, with a drop of up to 90%. The fq pulsation of ASDO was reduced from 7.004V to 0.912V with a reduction of up to 87%. In that
Figure BDA0003175525440000155
Under the condition, fd ripple of ASDO is reduced from 4.424V to 0.508V, and is reduced by 88%. The fq pulsation of ASDO was reduced from 4.975V to 0.47V with a drop of up to 90%. When R is 5Rso, L is 2Lso,
Figure BDA0003175525440000161
Under the condition, fd ripple of ASDO is reduced from 8.782V to 1.018V, and is reduced by 88%. The fq ripple of the ASDO is reduced from 8.174V to 1.172V, which is reduced by 85%. The experimental result shows that the proposed approach law can reduce the synovial membrane buffeting of the observer, and compared with the SDO of the traditional approach law, the ASDO adopting the new approach law has better observationThe performance of the detector.
FIG. 7, FIG. 8 and FIG. 9 show R-5 Rso, L-2 Lso,
Figure BDA0003175525440000162
Q-axis current response comparisons for the next three different control methods (where fig. 7(a), 8(a), and 9(a) are the DPCC control method, fig. 7(b), 8(b), and 9(b) are the DPCC + SDO control method, and fig. 7(c), 8(c), and 9(c) are the DPCC + ASDO control method). In the case of parameter mismatch, the q-axis current response of the DPCC method is clearly subject to steady state errors. Furthermore, it is clear from quantitative comparisons that the proposed DPCC + SDO and DPCC + ASDO methods can effectively suppress the effect of steady state errors. Similarly, fig. 10 is a comparison of current responses of different control methods when a multi-parameter mismatch occurs in the control system, where fig. 10(a) is the DPCC control method, fig. 10(b) is the DPCC + SDO control method, and fig. 10(c) is the DPCC + ASDO control method. Under different parameter mismatching conditions, the q-axis response current ripple ratio of the three control methods is shown in table 3.
Figure BDA0003175525440000163
Figure BDA0003175525440000171
The effectiveness of the proposed DPCC + SDO and DPCC + ASDO methods can be derived from simulation and experimental results.
The embodiment of the invention provides a method for designing a self-adaptive sliding film disturbance observer for a permanent magnet synchronous linear motor, which is characterized in that in order to predict stator current and collective disturbance in real time, a sliding film disturbance observer (SDO) is designed, a new sliding film index approximation law is introduced, a self-adaptive sliding film disturbance observer (ASDO) is designed, and finally the observer is used for observing model collective disturbance to realize real-time compensation on parameter disturbance.
Wherein, a control algorithm (DPCC + SDO) combining DPCC and a synovial membrane disturbance observer is provided, and the control performance of the permanent magnet synchronous linear motor system is improved; a new synovial membrane index approach law is introduced, and the synovial membrane buffeting is restrained. And a DPCC + ASDO method is developed, and the performance of the DPCC + SDO method is further improved.

Claims (9)

1. A design method of an adaptive sliding film disturbance observer for a permanent magnet synchronous linear motor is characterized by comprising the following steps:
constructing a PMLSM electrical subsystem dynamic model based on motor parameter mismatch and disturbance caused by part unmodeled dynamics;
representing dynamic lumped disturbance according to an electrical subsystem dynamic model of PMLSM;
analyzing the dynamic lumped disturbance to obtain an analysis conclusion;
and designing an adaptive sliding film disturbance observer based on the analysis conclusion, designing sliding film parameters of the adaptive sliding film disturbance observer, and designing a sliding film control function of the adaptive sliding film disturbance observer based on an exponential approximation law.
2. The adaptive sliding film disturbance observer design method of claim 1, wherein the electrical subsystem dynamics model of PMLSM is represented as:
Figure FDA0003175525430000011
wherein u isd/uqAnd id/iqStator voltage and current, R, of d/q axis respectivelysAnd LsRespectively winding resistance and stator inductance,. psifIs a permanent magnetic flux linkage, omegaeAnd pi v/tau is the electrical angular velocity, wherein v is the linear velocity of the rotor, and tau is the polar distance. The lower corner mark "o" represents the nominal value of the parameter, fd,fqRepresenting the lumped disturbances due to parameter mismatch and unmodeled dynamics, can be calculated by:
Figure FDA0003175525430000012
wherein R iss＝Rso+ΔRs,Ls＝Lso+ΔLs,ψf＝ψfo+Δψf，εd/εqLumped unmodeled dynamics for d/q axes, respectively.
3. The adaptive sliding film disturbance observer design method of claim 2, wherein the electrical subsystem dynamics model of PMLSM is rewritable as a discrete form, taking into account the zero order hold characteristic of the inverter in a real digital control system:
Figure FDA0003175525430000021
wherein, TsIs a discrete sampling period, and k is a discrete sampling moment;
according to the formula, the current equation can be expressed in the form of a matrix as follows:
I(k+1)＝G0I(k)+H0[U(k)-Φ(k)-D(k)]； (4)
wherein:
I(k)＝[id(k) iq(k)]T,U(k)＝[ud(k) uq(k)]T
Φ(k)＝[0 πv(k)ψfo/τ]T,D(k)＝[fd(k) fq(k)]T,
Figure FDA0003175525430000022
Figure FDA0003175525430000023
4. the adaptive sliding film disturbance observer design method of claim 3, wherein the representing dynamic lumped disturbances from the electrical subsystem dynamics model of PMLSM comprises:
the current at time (k +1) is predictively calculated from the known state at time k to command the current according to equation (4):
Figure FDA0003175525430000031
wherein, the superscripts of 'A' and 'X' represent an estimated value and an instruction value respectively;
the voltage command at time (k +1) may be calculated as:
Figure FDA0003175525430000032
the lumped disturbance depends on the mismatch of motor parameters and system state, neglecting unmodeled dynamics (epsilon)d/εq) The dynamic lumped perturbation can be calculated by equation (7):
Figure FDA0003175525430000033
5. the adaptive sliding film disturbance observer design method of claim 4, wherein analyzing the dynamic lumped disturbances to arrive at an analysis conclusion comprises:
two assumptions are made:
assume that 1:
Figure FDA0003175525430000041
assume 2: the mismatch of the motor parameters is slowly variable and even time-invariant;
based on hypothesis 1, the conclusion is reached: i.e. id≈0,d(id)/dt≈0,d2(id)/dt20. From hypothesis 2, one can deduce d (Δ R)s)/dt≈0,d(ΔLs)/dt≈0,d(Δψf) And/dt is approximately equal to 0. The dynamic lumped perturbation can be further simplified as:
Figure FDA0003175525430000042
from equation (8), the following conclusions can be drawn:
when PMLSM is at high speed (ω)e) High acceleration (d (ω)e) Dt) and large inductance mismatch (Δ L)s) When the position command of (2) moves, the lumped disturbance change of the d axis is obvious; and the number of the first and second groups,
when PMLSM is in high acceleration, high speed and high jump (d)2(iq)/dt2) When the position command of (2) moves, the dynamic lumped disturbance of the q axis is not negligible; in addition, the motor parameter mismatch (Δ R)s,ΔLs,Δψf) Also cannot be ignored, therefore, when f cannot be matchedqWhen sufficient compensation is made, the transient response of the q-axis current will be degraded.
6. The adaptive sliding film disturbance observer design method according to claim 5, wherein designing the adaptive sliding film disturbance observer based on the analysis conclusion comprises:
according to the electrical subsystem dynamics model (1) of PMLSM, the expansion dynamics equation of PMLSM can be expressed in terms of parameter variations as:
Figure FDA0003175525430000051
Figure FDA0003175525430000052
for parameter estimation and current prediction, a synovial membrane disturbance observer was designed as follows:
Figure FDA0003175525430000053
Figure FDA0003175525430000054
wherein the superscript ^ represents the estimated value, UsmoRepresents the synovial control function and g represents the synovial parameter.
7. The method according to claim 6, wherein the designing the synovial parameters of the adaptive sliding film disturbance observer and designing the synovial control function based on exponential approximation law comprises:
from equations (9) to (12), the following error equation is obtained:
Figure FDA0003175525430000061
Figure FDA0003175525430000062
wherein the content of the first and second substances,
Figure FDA0003175525430000063
in order to estimate the error for the current,
Figure FDA0003175525430000064
Figure FDA0003175525430000065
estimating an error for the disturbance;
according to the synovial membrane control theory, the synovial membrane design process is divided into design of a synovial membrane surface and design of a synovial membrane control function, so that a state locus converges to the synovial membrane surface, wherein the expression of the linear synovial membrane surface is as follows:
Figure FDA0003175525430000066
the synovial control function was designed using the exponential approach law:
Figure FDA0003175525430000067
wherein k and lambda are approach law parameters which are positive numbers, and approach time t of exponential approach law1Can be obtained from 0 to t by the pair formula (16)1And (3) integral calculation:
Figure FDA0003175525430000068
substitution of formula (15) for formula (16) can give:
Figure FDA0003175525430000071
by substituting formula (13) and formula (14) into formula (18), it is possible to obtain:
Figure FDA0003175525430000072
by the formula (19), e2And e4As disturbance of the control function, the design of the synovial variable structure control function is:
Figure FDA0003175525430000073
to guarantee the current estimation error (e)1,e3) And disturbance estimation error (e)2,e4) The synovium parameters k and g of the observer are reasonably designeddAnd gq。
8. The adaptive sliding film disturbance observer design method according to claim 7, wherein the sliding film parameters k, g of the observer are designed in the following mannerdAnd gq：
Based on satisfying the stability condition of the synovial observer, formula (21) can be obtained:
Figure FDA0003175525430000074
according to equations (13) and (20), the first inequality of the stability condition (21) can be rewritten as:
Figure FDA0003175525430000075
to ensure
Figure FDA0003175525430000076
The d-axis observer parameter k is:
k＞|e2|/Lso； (23)
similarly, the q-axis observer parameters are:
k＞|e4|/Lso； (24)
therefore, to ensure the observer to be stable, the parameter k is selected within the range of:
k＞max(|e2|,|e4|)/Lso； (25)
the proposed synovial observer with parameter k can reach and stay on the synovial surface within a limited time, implying an error e1And e3And derivatives thereof
Figure FDA0003175525430000081
And
Figure FDA0003175525430000082
may converge to zero; then, equations (13) and (14) can be simplified as:
Figure FDA0003175525430000083
then e2 and e4 are:
Figure FDA0003175525430000084
selecting an appropriate parameter g according to equation (27)dAnd gqSo that the disturbance error e2And e4And (6) converging.
9. The adaptive sliding film disturbance observer design method according to claim 7, wherein the exponential approximation law selects an exponential approximation law that adapts to changes in the sliding film:
Figure FDA0003175525430000085
wherein M ═ k/(ε + (1+1/| x |) - ε) e-δ|s|，k＞0、δ＞0、0＜ε＜1。
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