CN115102443A - Control method and device for permanent magnet synchronous linear motor and storage medium - Google Patents
Control method and device for permanent magnet synchronous linear motor and storage medium Download PDFInfo
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- H—ELECTRICITY
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- 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
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- 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
- H02P25/024—Synchronous motors controlled by supply frequency
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- H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
- H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
- H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
- H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation
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- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/006—Controlling linear motors
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- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
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- 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
Abstract
The invention discloses a control method, a control device and a storage medium of a permanent magnet synchronous linear motor, wherein the method comprises the following steps: acquiring d-axis and q-axis actual current values under a dq coordinate system of the PMSLM; acquiring an actual linear speed value of the PMSLM, and inputting the actual linear speed value and a q-axis actual current value into a pre-constructed state observer LESO to obtain an estimated value of generalized disturbance; acquiring a reference linear velocity value of the PMSLM, calculating a difference value between the reference linear velocity value and an actual linear velocity value, and inputting the velocity difference value and the estimated value into a pre-constructed sliding mode control SMC to obtain a q-axis expected current value; obtaining d-axis and q-axis current difference values, respectively regulating the d-axis and q-axis current difference values through a PI regulator to obtain d-axis and q-axis expected voltages, and obtaining alpha-axis and beta-axis expected voltages under an alpha beta coordinate system through conversion; after the alpha axis and beta axis expected voltages are modulated by SVPWM, the alpha axis and beta axis expected voltages are input into an inverter for driving a PMSLM to act so as to realize control; the method can improve the dynamic and static quality, the anti-interference capability and the robustness of the system, and simultaneously effectively weakens the buffeting phenomenon of sliding mode control.
Description
Technical Field
The invention relates to a control method and device of a permanent magnet synchronous linear motor and a storage medium, and belongs to the technical field of motor control.
Background
The Permanent Magnet Synchronous Linear Motor (PMSLM) has the advantages of long stroke, high thrust, high acceleration and the like due to a unique zero transmission mode, is widely applied to the fields of precision numerical control machines, servo systems and the like, and also puts higher requirements on system control capacity. In recent years, with the development of control theory, a sliding mode control theory having strong robustness and nonlinear characteristics has been successfully applied to an ac servo system, but the existence of switching characteristics tends to cause a chattering phenomenon in the system and to degrade the system control accuracy, and therefore, it is necessary to suppress the chattering of the sliding mode.
Buffeting methods that attenuate sliding mode control can be broadly divided into two categories. One is to combine with a self-adaptive control machine on the basis of constructing a novel SMC of an approach law to form a self-adaptive SMC control strategy. The control strategy can effectively weaken buffeting, inhibit partial disturbance and improve dynamic response speed, but when the method inhibits the disturbance, the upper and lower boundaries of the disturbance are always assumed to be known, and the method is often difficult to realize in actual engineering. And the other type is an SMC control strategy which is organically combined with a disturbance observer on the basis of constructing a novel approximation law to form disturbance feedforward compensation. The control strategy estimates uncertain disturbances such as load disturbance and the like by using a disturbance observer, and feed-forward compensates the estimated value of the uncertain disturbances to the SMC, so that buffeting can be effectively weakened, and the response speed and robustness of a system are improved. The method has the defect of low estimation precision of generalized disturbance.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a control method, a control device and a storage medium of a permanent magnet synchronous linear motor, which can improve the dynamic and static quality, the anti-interference capability and the robustness of a system and weaken the buffeting phenomenon of sliding mode control.
In order to achieve the purpose, the invention adopts the following technical scheme:
in a first aspect, the present invention provides a method for controlling a permanent magnet synchronous linear motor, including:
obtaining an actual three-phase current value of the PMSLM, and sequentially carrying out Clark conversion and Park conversion to obtain d-axis and q-axis actual current values under a dq coordinate system;
acquiring an actual linear speed value of the PMSLM, and inputting the actual linear speed value and a q-axis actual current value into a pre-constructed state observer LESO to obtain an estimated value of generalized disturbance;
acquiring a reference linear velocity value of the PMSLM, calculating a difference value with an actual linear velocity value to acquire a velocity difference value, and inputting the velocity difference value and the estimated value into a pre-constructed sliding mode control SMC to acquire a q-axis expected current value;
obtaining a d-axis given current value, calculating a difference value with a d-axis actual current value to obtain a d-axis current difference value, and calculating a difference value according to a q-axis expected current value and a q-axis actual current value to obtain a q-axis current difference value;
respectively regulating the d-axis current difference value and the q-axis current difference value through a PI regulator to obtain d-axis expected voltage and q-axis expected voltage; obtaining expected voltages of an alpha axis and a beta axis under an alpha beta coordinate system by performing inverse Park transformation on the expected voltages of the d axis and the q axis;
and the expected alpha-axis and beta-axis voltages are modulated by SVPWM and then input to an inverter for driving a PMSLM to act to realize control.
Optionally, obtaining the actual rotor flux linkage angle θ e Said actual rotor flux linkage angle θ e For Park transformation and inverse Park transformation.
Optionally, the process of constructing the state observer LESO includes:
constructing a PMSLM electromagnetic thrust equation:
in the formula, F e As electromagnetic thrust, p n Is the number of pole pairs, tau is the pole pitch, psi f Is a secondary permanent magnet flux linkage; i.e. i q Is q-axis armature current under dq coordinate system;
constructing a PMSLM motion balance equation based on a PMSLM electromagnetic thrust equation:
wherein M is the mover mass, F e As electromagnetic thrust, F L For load thrust, B m V is the linear velocity of the air-gap magnetic field;
and (3) re-modeling the PMSLM motion balance equation by considering parameter perturbation and sudden change of load disturbance, and acquiring a PMSLM speed mathematical model considering generalized disturbance:
in the formula, # f ＝ψ f0 +Δψ f ，B m ＝B m0 +ΔB m ，B m0 、ψ f0 Respectively, the viscous friction coefficient and the nominal value, delta psi, of the secondary permanent magnet flux linkage f And Δ B m Respectively the viscous friction coefficient and the pickup amount of the secondary permanent magnet flux linkage;
based on a PMSLM speed mathematical model considering generalized disturbances, it can be known that:
f＝-a 0 v + f' is a generalized perturbation;
expanding the generalized disturbance f into a state variable, and selecting the state variable:
converting a PMSLM speed mathematical model considering generalized disturbance into a continuous expansion state space equation:
in the formula (I), the compound is shown in the specification,
c＝[1 0]，x＝[x 1 x 2 ] T u, y are input variables and output variables respectively,
derivatives of x and f';
the state equation of the state observer LESO is built on the basis of a continuous extended state-space equation:
wherein z is [ z ] 1 z 2 ] T Is the state vector of the state observer LESO, z 1 →x 1 ,z 2 →x 2 Representing the tracking signal for x and,
is the derivative of z; u. u c ＝[u y] T For combining input variables, y c For the output variable, L is the gain moment of the state observer LESOAnd (5) arraying.
Optionally, the solving of the gain matrix L of the state observer LESO includes:
parameterizing a state equation of a state observer LESO by adopting Laplace transformation to generate a characteristic equation, and placing poles of the characteristic equation at the same position (-omega) 0 )：
λ(w)＝|wI-(A-LC)|＝(w+ω 0 ) 2
Where w is the complex frequency, I is the identity matrix, ω 0 Bandwidth of the state observer LESO;
obtaining a gain matrix L according to a characteristic equation:
L＝[l 1 l 2 ] T
optionally, the obtaining the estimated value of the generalized disturbance includes:
discretizing the state equation of the state observer LESO by adopting a forward difference method to generate a discrete estimator:
in the formula, e 1 (t) is the error signal at time t, y (t) is the output variable at time t, z 1 (t)、z 2 (t) tracking signals at time t, respectively, z 1 (t+1)、z 2 (T +1) are the tracking signals at time T +1, respectively, T s For a sampling period,/ c1 、l c2 An error feedback gain matrix for the discrete estimator;
obtaining estimated value of generalized disturbance based on discrete estimator, namely tracking signal z at t +1 moment 2 ：
z 2 (t+1)＝(1-a 0 T s )z 2 (t)-a 0 b 0 T s u-l c2 T s e 1 (t)。
Optionally, the solving of the error feedback gain matrix of the discrete estimator includes:
parameterizing the discrete estimator by adopting z transformation to generate a characteristic equation:
λ(z)＝|zI-Φ E |＝(z-β) 2
where z is the complex frequency, I is the identity matrix, β is the pole of the discrete estimator,
ω 0 bandwidth of the state observer LESO;
obtaining an error feedback gain matrix of the discrete estimator according to a characteristic equation:
L c ＝[l c1 l c2 ] T
optionally, the constructing of the sliding mode control SMC includes:
establishing a PMSLM voltage equation:
in the formula u d 、u q Are the voltages of the dq axes of the primary winding, R s Is armature resistance, i d 、i q Are dq-axis armature currents, L, respectively d 、L q Dq-axis inductance, τ pole pitch, ν linear velocity of the air-gap magnetic field, ψ f Is a secondary permanent magnet flux linkage;
by using i d The rotor magnetic field orientation control of 0, and the simplified processing is carried out according to a PMSLM voltage equation and a PMSLM speed mathematical model considering generalized disturbance, so that the following can be obtained:
introducing the speed tracking signal error as a system state variable into a traditional exponential approximation law, and constructing a piecewise function exponential approximation law based on the system state variable:
in the formula, f (x) 3 ) Is a function of the segment to be used,
and f (x) 3 )>0; q is an exponential approximation term coefficient and q>0，x 3 Is a system state variable, p is more than or equal to 0 and delta>0，0<ε<1；
Taking the velocity tracking error signal and the integral signal of the velocity tracking error as input signals, and defining the state variables of the system:
in the formula, v ref Is the reference linear velocity of the air gap magnetic field;
the state variable of the system is derived and is brought into a piecewise function index approximation law to obtain a transformed function:
introducing an integral quantity of a state variable to obtain an integral sliding mode surface function:
s＝x 3 +c∫x 3 dt
in the formula, s is an integral sliding mode surface, and c is a parameter;
and (3) carrying out derivation on the integral sliding mode surface function and substituting the derivative into the transformed function to obtain a derivation function of the sliding mode surface function:
the derivation function of the sliding mode surface function is obtained by substituting the piecewise function index approximation law and the transformed function into the derivation function of the sliding mode surface function:
-f(x 3 )sgn(s)-q|x 3 | p s＝-f-b 0 i q +cx 3
the output signal of the sliding mode control SMC is:
introducing generalized disturbance estimated value z 2 Feedforward compensation is given to the sliding mode control SMC, and the final output signal of the sliding mode control SMC is obtained:
in a second aspect, the present invention provides a control apparatus for a permanent magnet synchronous linear motor, the apparatus comprising:
the current acquisition module is used for acquiring the actual three-phase current value of the PMSLM and sequentially carrying out Clark conversion and Park conversion to obtain the actual current values of the d axis and the q axis under the dq coordinate system;
the disturbance estimation module is used for acquiring an actual linear speed value of the PMSLM and inputting the actual linear speed value and a q-axis actual current value into a pre-constructed state observer LESO to obtain an estimated value of generalized disturbance;
the expected current module is used for obtaining a reference linear speed value of the PMSLM, calculating a difference value with an actual linear speed value to obtain a speed difference value, and inputting the speed difference value and the estimated value into a pre-constructed sliding mode control SMC to obtain a q-axis expected current value;
the current difference value module is used for obtaining a d-axis given current value, calculating a difference value with a d-axis actual current value to obtain a d-axis current difference value, and calculating a difference value according to a q-axis expected current value and a q-axis actual current value to obtain a q-axis current difference value;
the voltage acquisition module is used for adjusting the d-axis current difference value and the q-axis current difference value through a PI (proportional-integral) regulator respectively to acquire d-axis expected voltage and q-axis expected voltage; obtaining expected voltages of an alpha axis and a beta axis under an alpha beta coordinate system by performing inverse Park transformation on the expected voltages of the d axis and the q axis;
and the modulation control module is used for inputting the expected alpha-axis and beta-axis voltages into an inverter for driving the PMSLM to act after SVPWM modulation so as to realize control.
In a third aspect, the present invention provides a control apparatus for a permanent magnet synchronous linear motor, including a processor and a storage medium;
the storage medium is used for storing instructions;
the processor is configured to operate in accordance with the instructions to perform the steps according to the above-described method.
In a fourth aspect, the invention provides a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of the above-described method.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a control method, a device and a storage medium of a permanent magnet synchronous linear motor, 1) known part of motor information is added into a traditional LESO for improvement, so that the estimation precision of generalized disturbance can be improved under the condition of not reducing the LESO bandwidth, and the effect is particularly obvious when the motor parameters are perturbed; 2) the improved index approach law is designed by introducing a speed tracking error signal serving as a state variable into the traditional index approach law, so that the dynamic quality of sliding mode motion is effectively improved, the buffeting phenomenon of sliding mode control is weakened, and the control precision of a system is improved; the invention performs feedforward compensation on the SMC through a generalized disturbance estimated value z2 obtained by LESO observation, thereby forming an improved disturbance-resistant sliding mode speed controller, further improving the rapidity, stability, anti-jamming capability and robustness of the system, and simultaneously effectively inhibiting the buffeting phenomenon of sliding mode control.
Drawings
Fig. 1 is a flowchart of a control method for a permanent magnet synchronous linear motor according to an embodiment of the present invention;
fig. 2 is a structural diagram of a control method of a permanent magnet synchronous linear motor according to an embodiment of the present invention;
fig. 3 is a structural diagram of a state observer LESO according to an embodiment of the present invention;
FIG. 4 is a plot of delta B without considering the perturbation of the parameters, according to an embodiment of the present invention m ＝B m0 、Δψ f ＝ψ 0 Comparing the observed value of the generalized disturbance with the actual disturbance by a curve graph;
FIG. 5 is a diagram of a method for accounting for perturbation of a parameter Δ B according to an embodiment of the present invention m ＝B m0 、Δψ f ＝ψ f0 Comparing the observed value of the generalized disturbance with the actual disturbance by a curve graph;
FIG. 6 is a delta B without considering the perturbation of the parameters according to an embodiment of the present invention m ＝B m0 、Δψ f ＝ψ f0 Comparing the linear speed response curves of the 3 control strategies;
FIG. 7 is a diagram of a method for accounting for perturbation of a parameter Δ B according to an embodiment of the present invention m ＝B m0 、Δψ f ＝ψ f0 Comparing the linear speed response curves of the 3 control strategies;
FIG. 8 is a plot of delta B without considering the perturbation of the parameters, according to an embodiment of the present invention m ＝B m0 、Δψ f ＝ψ f0 Then, comparing the electromagnetic thrust response curve of the 3 control strategies;
FIG. 9 is a diagram of a method for accounting for perturbation of a parameter Δ B according to an embodiment of the present invention m ＝B m0 、Δψ f ＝ψ f0 Then, comparing the electromagnetic thrust response curve of the 3 control strategies;
FIG. 10 is a plot of Δ B without consideration of the perturbation of the parameters, according to an embodiment of the present invention m ＝B m0 、Δψ f ＝ψ f0 A plot of the dq-axis current response of the LESO-based SMC;
FIG. 11 is a diagram of a method for accounting for perturbation of a parameter Δ B according to an embodiment of the present invention m ＝B m0 、Δψ f ＝ψ f0 A plot of the dq-axis current response of the LESO-based SMC;
FIG. 12 is a delta B without considering the perturbation of the parameters according to an embodiment of the present invention m ＝B m0 、Δψ f ＝ψ f0 The dq-axis current response curve of the invention;
FIG. 13 is a graph illustrating the perturbation of the parameters Δ B according to an embodiment of the present invention m ＝B m0 、Δψ f ＝ψ f0 The dq-axis current response graph of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
The first embodiment is as follows:
as shown in fig. 1-2, an embodiment of the present invention provides a method for controlling a permanent magnet synchronous linear motor, including the following steps:
1. obtaining an actual three-phase current value (i) of the PMSLM a 、i b 、i c ) And sequentially carrying out Clark conversion and Park conversion to obtain d-axis and q-axis actual current values (i) under a dq coordinate system d 、i q )。
2. Acquiring an actual linear velocity value v of the PMSLM and an actual current value i of the q axis q Inputting a pre-constructed state observer LESO to obtain an estimated value z of generalized disturbance 2 。
3. Obtaining reference linear velocity value V of PMSLM ref And calculating the difference value with the actual linear velocity value v to obtain a velocity difference value, and comparing the velocity difference value with an estimated value z 2 Inputting a pre-constructed sliding mode control SMC to obtain a q-axis expected current value
4. Obtaining d-axis given current value (0 in the embodiment) and d-axis actual current value i d Calculating difference to obtain d-axis current difference, and obtaining the expected current value according to q-axis
And q-axis actual current value i q Make a differenceAnd calculating the value to obtain a q-axis current difference value.
5. Adjusting the d-axis current difference value and the q-axis current difference value through a PI (proportional integral) regulator to obtain d-axis expected voltage and q-axis expected voltage respectively
Obtaining the expected voltages of the alpha axis and the beta axis under an alpha beta coordinate system by carrying out inverse Park transformation on the expected voltages of the d axis and the q axis
6. Desired voltages of alpha and beta axes
And the control is realized by an inverter which is input to drive the PMSLM to act after SVPWM.
The actual linear velocity value can be obtained from the PMSLM through the grating ruler, and meanwhile, the actual rotor flux linkage angle theta is obtained e Actual rotor flux linkage angle θ e For Park transformation and inverse Park transformation.
Specifically, the method comprises the following steps: as shown in fig. 3, the construction process of the state observer LESO includes:
s1, constructing a PMSLM electromagnetic thrust equation:
in the formula, F e As electromagnetic thrust, p n Is the number of pole pairs, tau is the pole pitch, psi f Is a secondary permanent magnet flux linkage; i.e. i q Is q-axis armature current under dq coordinate system;
s2, constructing a PMSLM motion balance equation based on the PMSLM electromagnetic thrust equation:
wherein M is the mover mass, F e As electromagnetic thrust, F L For load thrust, B m Is a viscous coefficient of friction, v isLinear velocity of the air gap magnetic field;
s3, the PMSLM motion balance equation is modeled again in consideration of parameter perturbation and sudden change of load disturbance, and a PMSLM speed mathematical model considering generalized disturbance is obtained:
in the formula, # f ＝ψ f0 +Δψ f ，B m ＝B m0 +ΔB m ，B m0 、ψ f0 Respectively, the viscous friction coefficient and the nominal value, delta psi, of the secondary permanent magnet flux linkage f And Δ B m Respectively the viscous friction coefficient and the amount of pickup of the secondary permanent magnet flux linkage;
s4, based on the PMSLM speed mathematical model considering the generalized disturbance, the following can be obtained:
f＝-a 0 v + f' is a generalized perturbation;
s5, expanding the generalized disturbance f into a state variable, and selecting the state variable:
s6, converting the PMSLM speed mathematical model considering the generalized disturbance into a continuous expansion state space equation:
in the formula (I), the compound is shown in the specification,
C＝[1 0]，x＝[x 1 x 2 ] T u and y are input variables and output variables respectively,
derivatives of x and f';
s7, establishing a state equation of a state observer LESO on the basis of the continuous expansion state space equation:
wherein z is [ z ] 1 z 2 ] T Is the state vector of the state observer LESO, z 1 →x 1 ,z 2 →x 2 Representing the tracking signal for x and is,
is the derivative of z; u. of c ＝[u y] T For combining input variables, y c L is the gain matrix of the state observer LESO for the output variable. The solving of the gain matrix L of the state observer LESO comprises:
parameterizing a state equation of a state observer LESO by adopting Laplace transformation to generate a characteristic equation, and placing poles of the characteristic equation at the same position (-omega) 0 )：
λ(w)＝|wI-(A-IC)|＝(w+ω 0 ) 2
Where w is the complex frequency, I is the identity matrix, ω 0 Bandwidth of the state observer LESO;
obtaining a gain matrix L according to a characteristic equation:
L＝[l 1 l 2 ] T
s8, obtaining the estimated value of the generalized disturbance includes:
discretizing the state equation of the state observer LESO by adopting a forward difference method to generate a discrete estimator:
in the formula, e 1 (t) is the error signal at time t, y (t) is the output variable at time t, z 1 (t)、z 2 (t) tracking signals at time t, respectively, z 1 (t+1)、z 2 (T +1) are the tracking signals at time T + 1, respectively, T s For a sampling period,/ c1 、l c2 An error feedback gain matrix for the discrete estimator;
obtaining estimated value of generalized disturbance based on discrete estimator, namely tracking signal z at t +1 moment 2 ：
z 2 (t+1)＝(1-a 0 T s )z 2 (t)-a 0 b 0 T s u-l c2 T s e 1 (t)
The solving of the error feedback gain matrix of the discrete estimator comprises:
parameterizing the discrete estimator by adopting z transformation to generate a characteristic equation:
λ(z)＝|zI-Φ E |＝(z-β) 2
where z is the complex frequency, I is the identity matrix, β is the pole of the discrete estimator,
ω 0 bandwidth of the state observer LESO;
obtaining an error feedback gain matrix of the discrete estimator according to a characteristic equation:
L c ＝[l c1 l c2 ] T
specifically, the method comprises the following steps: the construction of the sliding mode control SMC comprises the following steps:
(1) establishing a PMSLM voltage equation:
in the formula u d 、u q Are the voltages of the dq axes of the primary winding, R s Is armature resistance, i d 、i q Respectively dq-axis armature current, L d 、L q Respectively dq-axis inductance,. tau.polar distance,. v linear velocity of air-gap magnetic field,. psi f Is a secondary permanent magnet flux linkage;
(2) by using i d The rotor magnetic field orientation control of 0, and the simplified processing is carried out according to a PMSLM voltage equation and a PMSLM speed mathematical model considering generalized disturbance, so that the following can be obtained:
(3) introducing the speed tracking signal error into a traditional exponential approximation law as a system state variable, and constructing a piecewise function exponential approximation law based on the system state variable:
in the formula, f (x) 3 ) In the form of a piecewise function of a linear function,
and f (x) 3 )>0; q is an exponential approximation term coefficient and q>0，x 3 Is a system state variable, p is more than or equal to 0 and delta>0，0<ε<1；
(4) Taking the velocity tracking error signal and the integral signal of the velocity tracking error as input signals, and defining the state variables of the system:
in the formula, v ref Is the reference linear velocity of the air gap magnetic field;
(5) the state variable of the system is derived and is brought into a piecewise function index approximation law to obtain a transformed function:
(6) introducing an integral quantity of a state variable to obtain an integral sliding mode surface function:
s＝x 3 +c∫x 1 dt
in the formula, s is an integral sliding mode surface, and c is a parameter;
(7) and (3) carrying out derivation on the integral sliding mode surface function and substituting the derivative into the transformed function to obtain a derivation function of the sliding mode surface function:
(8) the derivation function of the sliding mode surface function is obtained by substituting the piecewise function index approximation law and the transformed function into the derivation function of the sliding mode surface function:
-f(x 3 )sgn(s)-q|x 3 | p s＝-f-b 0 i q +cx 3
(9) the output signal of the sliding mode control SMC is:
(10) introducing generalized disturbance estimated value z 2 Feedforward compensation is carried out on the sliding mode control SMC, and the final output signal of the sliding mode control SMC is obtained as follows:
to verify the validity of the proposed control strategy, simulation verification was performed in MATLAB/Simulink. By using i d A vector control scheme of 0. The traditional SMC, the LESO-based SMC and the scheme provided by the method, namely the sliding mode control SMC based on the state observer LESO, are subjected to simulation comparison, and the parameters of the permanent magnet synchronous linear motor are shown in the table 1.
TABLE 1 permanent magnet synchronous Linear Motor parameters
In order to verify the starting performance and the disturbance compensation performance of the control strategy, the motor adopts an idle-load starting mode, and the linear speed of a rotor is given to be 2 m/s; adding 100N load disturbance at 0.15 s; the load disturbance was abruptly reduced to 50N at 0.25 s.
As can be seen from fig. 4-5, when the load disturbance changes suddenly and the parameter perturbs, the state observer LESO can estimate the generalized disturbance amount (except for the motor start-up phase) more quickly and accurately, so as to compensate the generalized disturbance amount to the improved sliding mode speed controller in time and effectively.
As can be seen from fig. 6-7, the control strategy proposed herein enables a fast tracking of a given speed at startup with no significant overshoot, compared to conventional SMCs and LESO-based SMCs.
When load disturbance mutation and parameter perturbation occur, the control performance of the SMC based on the LESO and the SMC based on the state observer LESO is superior to that of the traditional SMC, and a local enlarged image shows that the state observer LESO can quickly and accurately estimate the generalized disturbance quantity and can timely and effectively compensate the generalized disturbance quantity for the sliding mode control SMC, so that the linear speed response can quickly recover the steady state and effectively reduce linear speed fluctuation and overshoot when the load disturbance mutation and the parameter perturbation occur.
From fig. 8-9, it can be seen that, during sudden load disturbance and parameter perturbation, both the LESO-based SMC and the control strategy proposed herein are superior to the conventional SMC, and from the partially enlarged views, the electromagnetic thrust response of the control strategy proposed herein is faster in response speed, smaller in overshoot, and stronger in disturbance rejection and robustness.
As can be seen from fig. 10-11 and 12-13, compared to the LESO-based SMC, the dq-axis current response of the control strategy proposed herein is significantly shortened in overshoot time at start-up, and the dq-axis current response is substantially unaffected by load disturbances and parameter perturbations, enabling fast tracking of changes in load torque.
Example two:
the invention provides a control device of a permanent magnet synchronous linear motor, which comprises:
the current acquisition module is used for acquiring the actual three-phase current value of the PMSLM and sequentially carrying out Clark conversion and Park conversion to obtain the actual current values of the d axis and the q axis under the dq coordinate system;
the disturbance estimation module is used for acquiring an actual linear speed value of the PMSLM and inputting the actual linear speed value and a q-axis actual current value into a pre-constructed state observer LESO to obtain an estimated value of generalized disturbance;
the expected current module is used for acquiring a reference linear velocity value of the PMSLM, calculating a difference value with an actual linear velocity value to acquire a velocity difference value, and inputting the velocity difference value and an estimation value into a pre-constructed sliding mode control SMC to acquire a q-axis expected current value;
the current difference value module is used for obtaining a d-axis given current value, calculating a difference value with a d-axis actual current value to obtain a d-axis current difference value, and calculating a difference value according to a q-axis expected current value and a q-axis actual current value to obtain a q-axis current difference value;
the voltage acquisition module is used for adjusting the d-axis current difference value and the q-axis current difference value through a PI (proportional-integral) regulator respectively to acquire d-axis expected voltage and q-axis expected voltage; obtaining expected voltages of an alpha axis and a beta axis under an alpha beta coordinate system by performing inverse Park transformation on the expected voltages of the d axis and the q axis;
and the modulation control module is used for inputting the alpha-axis and beta-axis expected voltages after SVPWM modulation into an inverter for driving the PMSLM to act so as to realize control.
Example three:
based on the first embodiment, the invention provides a control device of a permanent magnet synchronous linear motor, which comprises a processor and a storage medium, wherein the processor is used for processing a control signal;
a storage medium to store instructions;
the processor is configured to operate in accordance with instructions to perform steps in accordance with the above-described method.
Example four:
based on the first embodiment, the present invention provides a computer-readable storage medium, on which a computer program is stored, which when executed by a processor implements the steps of the above method.
The invention provides a PMSLM improved SMC method based on model-assisted LESO (LeSO). As shown in figure 1, firstly, a PMSLM speed mathematical model considering generalized disturbance is established, a speed tracking error signal is taken as a system state variable and is introduced into a traditional index approximation law, the improved index approximation law based on the system state variable is designed, and the improved index approximation law is applied to an integral sliding mode surface to obtain a control quantity containing the generalized disturbance; secondly, the generalized disturbance is estimated by designing a model to assist the LESO, and the estimated value is feedforward compensated to the improved SMC, so that the speed control of the PMSLM under the generalized disturbance is finally realized. The control method provided by the invention improves the dynamic and static quality, the anti-interference capability and the robustness of the system, and simultaneously effectively weakens the buffeting phenomenon of sliding mode control.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (10)
1. A control method of a permanent magnet synchronous linear motor is characterized by comprising the following steps:
obtaining an actual three-phase current value of the PMSLM, and sequentially carrying out Clark conversion and Park conversion to obtain d-axis and q-axis actual current values under a dq coordinate system;
acquiring an actual linear speed value of the PMSLM, and inputting the actual linear speed value and a q-axis actual current value into a pre-constructed state observer LESO to obtain an estimated value of generalized disturbance;
acquiring a reference linear velocity value of the PMSLM, calculating a difference value with an actual linear velocity value to acquire a velocity difference value, and inputting the velocity difference value and the estimated value into a pre-constructed sliding mode control SMC to acquire a q-axis expected current value;
obtaining a d-axis given current value, calculating a difference value with a d-axis actual current value to obtain a d-axis current difference value, and calculating a difference value according to a q-axis expected current value and a q-axis actual current value to obtain a q-axis current difference value;
adjusting the d-axis current difference value and the q-axis current difference value through a PI (proportional integral) regulator respectively to obtain d-axis expected voltage and q-axis expected voltage; obtaining expected voltages of an alpha axis and a beta axis under an alpha beta coordinate system by performing inverse Park transformation on the expected voltages of the d axis and the q axis;
and the expected alpha-axis and beta-axis voltages are modulated by SVPWM and then input to an inverter for driving a PMSLM to act to realize control.
2. The method of claim 1, further comprising obtaining an actual rotor flux linkage angle θ e Said actual rotor flux linkage angle θ e For Park transformation and inverse Park transformation.
3. The control method of a permanent magnet synchronous linear motor according to claim 1, wherein the construction process of the state observer LESO includes:
constructing a PMSLM electromagnetic thrust equation:
in the formula, F e As electromagnetic thrust, p n Is the number of pole pairs, tau is the pole pitch, psi f Is a secondary permanent magnet flux linkage; i.e. i q Is q-axis armature current under dq coordinate system;
constructing a PMSLM motion balance equation based on a PMSLM electromagnetic thrust equation:
wherein M is the mover mass, F e As electromagnetic thrust, F L For load thrust, B m The coefficient of viscous friction is adopted, and v is the linear velocity of an air gap magnetic field;
and (3) re-modeling the PMSLM motion balance equation by considering parameter perturbation and sudden change of load disturbance, and acquiring a PMSLM speed mathematical model considering generalized disturbance:
in the formula, # f ＝ψ f0 +Δψ f ，B m ＝B m0 +ΔB m ，B m0 、ψ f0 Respectively, the viscous friction coefficient and the nominal value, delta psi, of the secondary permanent magnet flux linkage f And Δ B m Respectively the viscous friction coefficient and the pickup amount of the secondary permanent magnet flux linkage;
based on the PMSLM speed mathematical model considering the generalized disturbance, it can be known that:
f＝-a 0 v + f' is a generalized perturbation;
expanding the generalized disturbance f into a state variable, and selecting the state variable:
converting a PMSLM speed mathematical model considering generalized disturbance into a continuous expansion state space equation:
in the formula (I), the compound is shown in the specification,
C＝[1 0]，x＝[x 1 x 2 ] T u and y are input variables and output variables respectively,
derivatives of x and f';
the state equation of the state observer LESO is established on the basis of a continuous extended state-space equation:
wherein z is [ z ] 1 z 2 ] T Is the state vector of the state observer LESO, z 1 →x 1 ,z 2 →x 2 Representing the tracking signal for x and is,
is the derivative of z; u. u c ＝[u y] T For combining input variables, y c L is the gain matrix of the state observer LESO for the output variable.
4. A method of controlling a permanent magnet synchronous linear motor according to claim 3, wherein the solving of the gain matrix L of the state observer LESO comprises:
parameterizing a state equation of a state observer LESO by adopting Laplace transformation to generate a characteristic equation, and placing poles of the characteristic equation at the same position (-omega) 0 )：
λ(w)＝|wI-(A-LC)|＝(w+ω 0 ) 2
Where w is the complex frequency, I is the identity matrix, ω 0 Is observation of stateBandwidth of the LESO;
obtaining a gain matrix L according to a characteristic equation:
L＝[l 1 l 2 ] T
5. the method of claim 3, wherein obtaining the estimate of the generalized disturbance comprises:
discretizing the state equation of the state observer LESO by adopting a forward difference method to generate a discrete estimator:
in the formula, e 1 (t) is the error signal at time t, y (t) is the output variable at time t, z 1 (t)、z 2 (t) tracking signals at time t, respectively, z 1 (t+1)、z 2 (T +1) are the tracking signals at time T +1, respectively, T s For a sampling period,/ c1 、l c2 An error feedback gain matrix for the discrete estimator;
obtaining estimated value of generalized disturbance, namely tracking signal z at t +1 moment based on discrete estimator 2 ：
z 2 (t+1)＝(1-a 0 T s )z 2 (t)-a 0 b 0 T s u-l c2 T s e 1 (t)。
6. The method of claim 5, wherein the solving of the error feedback gain matrix of the discrete estimator comprises:
parameterizing the discrete estimator by adopting z transformation to generate a characteristic equation:
λ(z)＝|zI-Φ E |＝(z-β) 2
where z is the complex frequency, I is the identity matrix, β is the pole of the discrete estimator,
ω 0 bandwidth of the state observer LESO;
obtaining an error feedback gain matrix of the discrete estimator according to a characteristic equation:
L c ＝[l c1 l c2 ] T
7. the control method of a permanent magnet synchronous linear motor according to claim 5, wherein the constructing of the sliding mode control SMC comprises:
establishing a PMSLM voltage equation:
in the formula u d 、u q Are the primary winding dq-axis voltages, R, respectively s Is armature resistance, i d 、i q Respectively dq-axis armature current, L d 、L q Respectively dq-axis inductance,. tau.polar distance,. v linear velocity of air-gap magnetic field,. psi f Is a secondary permanent magnet flux linkage;
by using i d The method comprises the following steps of (1) carrying out directional control on a rotor magnetic field of 0, and carrying out simplified processing according to a PMSLM voltage equation and a PMSLM speed mathematical model considering generalized disturbance to obtain:
introducing the speed tracking signal error into a traditional exponential approximation law as a system state variable, and constructing a piecewise function exponential approximation law based on the system state variable:
in the formula, f (x) 3 ) In the form of a piecewise function of a linear function,
and f (x) 3 )>0; q is an exponential approximation term coefficient and q>0，x 3 Is a system state variable, p is more than or equal to 0 and delta>0，0<ε<1；
Taking the velocity tracking error signal and the integral signal of the velocity tracking error as input signals, and defining the state variables of the system:
in the formula, v ref Is the reference linear velocity of the air gap magnetic field;
the state variable of the system is derived and is brought into a piecewise function index approximation law to obtain a transformed function:
introducing an integral quantity of a state variable to obtain an integral sliding mode surface function:
s＝x 3 +c∫x 3 dt
in the formula, s is an integral sliding mode surface, and c is a parameter;
and (3) carrying out derivation on the integral sliding mode surface function and substituting the derivative into the transformed function to obtain a derivation function of the sliding mode surface function:
the derivation function of the sliding mode surface function is obtained by substituting the piecewise function index approximation law and the transformed function into the derivation function of the sliding mode surface function:
-f(x 3 )sgn(s)-q|x 3 | p s＝-f-b 0 i q +cx 3
the output signal of the sliding mode control SMC is:
introducing generalized disturbance estimated value z 2 Feedforward compensation is carried out on the sliding mode control SMC, and the final output signal of the sliding mode control SMC is obtained as follows:
8. a control apparatus of a permanent magnet synchronous linear motor, the apparatus comprising:
the current acquisition module is used for acquiring the actual three-phase current value of the PMSLM and sequentially carrying out Clark conversion and Park conversion to obtain the actual current values of the d axis and the q axis under the dq coordinate system;
the disturbance estimation module is used for acquiring an actual linear speed value of the PMSLM and inputting the actual linear speed value and a q-axis actual current value into a pre-constructed state observer LESO to obtain an estimated value of generalized disturbance;
the expected current module is used for obtaining a reference linear speed value of the PMSLM, calculating a difference value with an actual linear speed value to obtain a speed difference value, and inputting the speed difference value and the estimated value into a pre-constructed sliding mode control SMC to obtain a q-axis expected current value;
the current difference value module is used for obtaining a d-axis given current value, calculating a difference value with a d-axis actual current value to obtain a d-axis current difference value, and calculating a difference value according to a q-axis expected current value and a q-axis actual current value to obtain a q-axis current difference value;
the voltage acquisition module is used for adjusting the d-axis current difference value and the q-axis current difference value through a PI (proportional integral) regulator respectively to acquire d-axis expected voltage and q-axis expected voltage; obtaining expected voltages of an alpha axis and a beta axis under an alpha beta coordinate system by performing inverse Park transformation on the expected voltages of the d axis and the q axis;
and the modulation control module is used for inputting the alpha-axis and beta-axis expected voltages after SVPWM modulation into an inverter for driving the PMSLM to act so as to realize control.
9. A control device of a permanent magnet synchronous linear motor is characterized by comprising a processor and a storage medium;
the storage medium is used for storing instructions;
the processor is configured to operate in accordance with the instructions to perform the steps of the method according to any one of claims 1 to 7.
10. Computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 7.
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