CN113659904B - SPMSM sensorless vector control method based on nonsingular rapid terminal sliding mode observer - Google Patents

SPMSM sensorless vector control method based on nonsingular rapid terminal sliding mode observer Download PDF

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CN113659904B
CN113659904B CN202110959409.6A CN202110959409A CN113659904B CN 113659904 B CN113659904 B CN 113659904B CN 202110959409 A CN202110959409 A CN 202110959409A CN 113659904 B CN113659904 B CN 113659904B
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sliding mode
function
current
equation
state
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CN113659904A (en
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郑诗程
刘志鹏
赵卫
郎佳红
方四安
徐磊
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Anhui University of Technology AHUT
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • 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
    • H02P21/18—Estimation of position or speed
    • 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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
    • 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
    • H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
    • H02P21/32—Determining the initial rotor position
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H02P25/024—Synchronous motors controlled by supply frequency
    • H02P25/026—Synchronous motors controlled by supply frequency thereby detecting the rotor position
    • 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
    • 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
    • H02P27/12—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 pulsing by guiding the flux vector, current vector or voltage vector on a circle or a closed curve, e.g. for direct torque 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
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/60—Other road transportation technologies with climate change mitigation effect
    • Y02T10/64—Electric machine technologies in electromobility

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  • Control Of Motors That Do Not Use Commutators (AREA)

Abstract

The invention discloses an SPMSM sensorless vector control method based on a nonsingular rapid terminal sliding mode observer, and belongs to the technical field of motor control. The method comprises the steps of firstly establishing a voltage mathematical model of the permanent magnet synchronous motor based on a two-phase static coordinate system, and reconstructing the voltage mathematical model into a stator current state equation; secondly, designing an integral non-singular sliding mode surface by taking a current observation error as a state variable, and deducing a composite control law to obtain an extended back electromotive force; finally, the back electromotive force is reconstructed, high-frequency filtering is realized, and the position of the motor rotor is extracted based on the principle of a software phase-locked loopSum speed ofAnd the sensorless control of the motor is realized. Compared with the traditional sliding mode observer, the invention can accurately estimate the position and the speed information of the motor rotor in the zero low-speed stage and the medium-high-speed stage, has stronger robustness, can effectively inhibit buffeting in a control system, solves the problem of phase lag, and has better steady-state precision and dynamic performance of the system.

Description

SPMSM sensorless vector control method based on nonsingular rapid terminal sliding mode observer
Technical Field
The invention relates to the technical field of motor control, in particular to an SPMSM sensorless vector control method based on a nonsingular rapid terminal sliding mode observer.
Background
The permanent magnet synchronous motor has the advantages that the energy density is high, the noise generated during operation is low, the torque fluctuation is lower than that of other motors, and the maintenance is easy, so that the permanent magnet synchronous motor is widely applied to military and commercial unmanned aerial vehicles, and electric vehicles and national defense and military which are quite hot at present, and the permanent magnet synchronous motor control speed regulation system becomes a hot spot for domestic and foreign research. In practical application of the system, a sensor is generally adopted to directly acquire rotor position and rotation speed information. However, installing such mechanical sensors increases the cost of the overall system, and has certain requirements for the surrounding working environment, which limits the scope of use of the system, and also causes some insurmountable problems for the performance of the system. The home and abroad scholars have made a great deal of researches on the position and the rotating speed of the motor rotor by replacing the traditional mechanical sensor with a sensorless control algorithm.
The sensorless technology of the permanent magnet synchronous motor is mainly divided into two main categories, namely a model observer method for medium and high speeds and a salient pole tracking method for zero and low speeds. The sensorless control method suitable for medium and high speed is to extract position and speed information by using the back electromotive force of a motor, and the main methods include a sliding mode observer method, a model self-adaption method, a disturbance observer method and the like. The sliding mode observer is designed based on the deviation between the actual value of the stator current and the observed value obtained by the mathematical model of the motor and combines the sliding mode variable structure theory. However, due to the special discontinuity of the sliding mode control, buffeting cannot be completely eliminated, and only new method inhibition can be found. The conventional sliding mode observer also has phase lag, generates high-frequency signals and noise, and can further amplify errors when estimating the rotor position based on a forward and backward tangent function. Many students have conducted intensive studies on the buffeting problem, the phase delay, the rotor position estimation and other problems of the sliding mode algorithm.
In the period 2020, pages 28-33 of journal "journal of motor and control application", a new sliding mode observer design for sensorless permanent magnet synchronous motor based on improved filter is proposed, which uses an S-type function as a switching function to reduce buffeting, and at the same time, a cascade filter formed by combining a low-pass filter and a complex filter is used when high-frequency filtering is performed on counter electromotive force, so as to reduce measurement noise and measurement error. However, the system uses a low-pass filter when filtering high-frequency buffeting and noise in back electromotive force, which causes certain phase lag, and a large error is recognized on the initial rotor position when the motor is started. In addition, the overshoot of the system is larger, the dynamic response process is poorer, and the defects existing in the dynamic response process are not further studied.
The journal "journal of the university of western traffic" at volume 50, pages 87-91,99 provides a novel nonsingular terminal sliding mode observer (NFTSMO) based on a tracking differentiator, designs an integral nonsingular rapid terminal sliding mode surface, adopts the tracking differentiator to realize the accurate tracking of counter electromotive force, realizes a filtering function, can accurately track a given value when a motor control system runs stably, and can accurately estimate the position of a rotor. However, the method has the following defects: when load torque is applied to the motor to generate a step, the system cannot well follow a given value, the disturbance resistance is poor, and meanwhile, the estimation error after disturbance is applied can be further increased. In addition, the mathematical model is complex when the tracking differentiator is designed, and the system also contains a sign function, so that the designed sliding mode control algorithm system has poor performance.
Disclosure of Invention
1. Technical problem to be solved by the invention
Aiming at the problems that a sliding mode observer is used for estimating the position and speed information of a motor rotor in a permanent magnet synchronous motor control speed regulation system, high-frequency buffeting, noise, phase delay and the like can occur, the invention provides an SPMSM sensorless vector control method based on a nonsingular rapid terminal sliding mode observer, and the sensorless vector control of a surface-mounted permanent magnet synchronous motor can be realized. In practical application, the position and the speed of the motor rotor are effectively tracked, the running cost of the motor is reduced, and the steady-state precision and the dynamic performance of the system are improved.
2. Technical proposal
In order to achieve the above purpose, the technical scheme provided by the invention is as follows:
the invention discloses an SPMSM sensorless vector control method based on a nonsingular rapid terminal sliding mode observer, which comprises the following steps:
step one, establishing a voltage state equation of the permanent magnet synchronous motor based on a two-phase static coordinate system alpha beta, reconstructing the voltage state equation into a stator current state equation, and constructing a current state observation equation;
step two, sampling three-phase current i abc And three-phase voltage u abc Calculating a current error state equation;
step three, designing a sliding mode surface function S of a novel nonsingular rapid terminal sliding mode observer by taking a current observation error as a state variable (t) And designing a sliding mode surface equivalent control function V based on the current error state equation and the sliding mode surface function eq And a switching control function V sw The stability of the composition is proved by using a Lyapunov function stability criterion;
step four, reconstructing the extended counter electromotive force by using an extended Kalman filter, and extracting a counter electromotive force estimated valueFinally, the motor rotor position is estimated based on the phase-locked loop principle>And speed->
3. Advantageous effects
Compared with the prior art, the technical scheme provided by the invention has the following remarkable effects:
the SPMSM sensorless vector control method based on the nonsingular rapid terminal sliding mode observer effectively suppresses the problems of high-frequency buffeting, large torque pulsation and the like in the traditional sliding mode observer, selects an extended Kalman filter to reconstruct counter electromotive force, smoothes the waveform of the counter electromotive force, realizes high-frequency filtering, and simultaneously solves the problem of phase lag of the traditional observer. The novel sliding mode of the system has small dependence on motor parameters and strong anti-interference capability, and the position and the speed of a motor rotor can be accurately estimated at the zero low-speed stage and the medium-high-speed stage. Compared with the traditional singular sliding mode observer, the system overcomes the problem of singularity.
Drawings
FIG. 1 is a sensorless vector control block diagram of a NFTSMO-based surface mounted permanent magnet synchronous motor (SPMSM) in the present invention;
FIG. 2 is a schematic diagram of a novel non-singular fast terminal sliding mode observer (NFTSMO) in accordance with the present invention;
FIG. 3 is a schematic diagram of a conventional Sliding Mode Observer (SMO);
FIG. 4 is a block diagram of an Extended Kalman Filter (EKF) architecture;
FIG. 5 is a schematic diagram of a PLL;
FIG. 6 (a) is a waveform diagram showing the comparison of the predicted rotational speed and the actual rotational speed by the control method of the present invention; (b) Comparing a waveform diagram with a predicted rotating speed and an actual rotating speed for a traditional Sliding Mode Observer (SMO);
FIG. 7 (a) is a waveform diagram showing the comparison of the predicted rotational speed and the actual rotational speed error by the control method of the present invention; (b) Comparing a waveform diagram with a predicted rotating speed error and an actual rotating speed error of a traditional Sliding Mode Observer (SMO);
FIG. 8 (a) is a graph showing three-phase current versus waveform for a sudden change from no load to load using the control method of the present invention; (b) A waveform diagram is compared with three-phase current when a traditional Sliding Mode Observer (SMO) suddenly changes from no load to load;
fig. 9 (a) is a waveform diagram of the back electromotive force on the α axis after one time filtering according to the present invention; (b) The alpha-axis back electromotive force waveform chart is filtered by an extended Kalman filter;
FIG. 10 (a) is a graph of predicted rotor position versus actual rotor position using the control method of the present invention; (b) The rotor position and actual rotor position are predicted for a conventional Sliding Mode Observer (SMO) versus a waveform map.
Detailed Description
For a further understanding of the present invention, the present invention will be described in detail with reference to the drawings and examples.
Example 1
Fig. 1 is a block diagram of SPMSM sensorless vector control of a surface mount permanent magnet synchronous motor (SPMSM) based on NFTSMO according to this embodiment. As shown in FIG. 1, ASR is a rotating speed regulator, ACR is a current regulator, and a PI regulator double closed-loop vector control scheme with a rotating speed outer ring and a current inner ring is adopted. After PI regulation and Park inverse transformation, the alpha beta axis given voltage u is obtained α ，u β As the input value of the SVPWM, the on-off of the thyristor of the inverter is controlled by adjusting the duty ratio of PWM waveform, thereby realizing the double closed-loop speed regulation of the permanent magnet synchronous motor.
Sampling three-phase current i abc And three-phase voltage u abc After Park coordinate transformation, the two-phase static coordinate value i is obtained αβ The deviation obtained after the difference with the observed value of the stator current is used as a state variable for designing a nonsingular rapid terminal sliding mode surface function, a sliding mode control law is designed by combining a terminal attractor function, the extended counter electromotive force is reconstructed through an extended Kalman filter and then is subjected to secondary filtering, and finally the speed of a motor is predicted through a software phase-locked loop (PLL) principleAnd rotor position->The method comprises the following specific steps:
step one, establishing a voltage state equation of a Permanent Magnet Synchronous Motor (PMSM) based on a two-phase stationary coordinate system alpha beta, reconstructing the voltage state equation into a stator current state equation, and constructing a current state observation equation:
in order to simplify the analysis, assuming that the three-phase PMSM is an ideal motor, knowing the three-phase voltage equation under the natural coordinate system ABC, the voltage state equation under the two-phase static coordinate system can be obtained through Clark coordinate transformation:
wherein ,Ld 、L q For stator inductance to be in dq axis component, R s Is stator resistance omega e In order to obtain the electric angular velocity,is a differential operator, [ u ] α u β ] T For the stator voltage to be in the alpha beta axis component, [ i ] α i β ] T For the stator current to be in the alpha beta axis component, [ E ] α E β ] T To extend the back electromotive force (EMF) in the αβ axis component, and satisfy:
in the formula,θe For the electrical angle of the rotor position,is rotor flux linkage, [ i ] d i q ] T The stator current is a component in the dq axis.
And (3) deforming the formula (1) and reconstructing the formula into a stator current state equation:
the embodiment is directed to a surface mounted three-phase permanent magnet synchronous motor (SPMSM), which comprises: l (L) d ＝L q ＝L s ，L s For stator inductance, all formulae hereafter apply L s And (3) representing.
To obtain an estimate of the extended back emf, a current state observer equation is constructed as:
in the formula,is a currentState observation value, [ u ] α u β ] T For control input of observer, [ V ] α V β ] T The law function is controlled at the alpha beta axis for the sliding mode surface.
Step two, sampling three-phase current i abc And three-phase voltage u abc The current i under the two-phase static coordinate system alpha beta is obtained through Clark coordinate transformation αβ Sum voltage u αβ Calculating a current error state equation according to the stator current state equation and the current state observation equation:
referring to fig. 2, it can be known from the design thought of the conventional sliding mode surface that the current error is used as the state variable of the sliding mode surface function, and the novel nonsingular sliding mode surface function is designed on the basis of the conventional sliding mode observer. The present embodiment adopts a given rotational speedOuter ring (S)>The deviation of a given current and a feedback current is subjected to PI regulation to obtain a direct-axis voltage +.>And quadrature axis voltage->Obtaining a voltage value u under a two-phase static coordinate system through Park inverse transformation α ，u β The voltage space vector modulation SVPWM is input, and the on-off of the thyristor of the inverter is controlled by adjusting the duty ratio of PWM waveform, so that the double closed-loop speed regulation of the permanent magnet synchronous motor is realized.
Therefore, it is necessary to obtain a current error value by sampling the three-phase current i output from the three-phase permanent magnet synchronous motor abc And three-phase voltage u abc The current i under the two-phase static coordinate system is obtained through Clark coordinate transformation αβ Sum voltage u αβ ，u αβ As input to the current state observer, the current state observer valueAnd two-phase current i αβ And the compared current observation errors are used as the input of the design of a novel nonsingular rapid terminal sliding mode surface. And (3) obtaining a stator current error state equation after the formula (2) and the formula (3) are subjected to difference:
in the formula,is the current observation error [ V ] α V β ] T The law function is controlled at the alpha beta axis for the sliding mode surface.
Step three, designing a sliding mode surface function S of a novel nonsingular rapid terminal sliding mode observer by taking a current observation error as a state variable (t) Designing a sliding mode surface equivalent control function V based on a current error state equation and a sliding mode surface function eq And a switching control function V sw And the stability is proved by Lyapunov (Lyapunov) stability criterion:
and taking the current observation error as a state variable for designing a novel nonsingular rapid terminal sliding mode surface, introducing a terminal attractor concept, and designing a novel nonsingular rapid terminal sliding mode surface function by combining the terminal attractor function.
Terminal attractor function ofAnd (3) after deforming the function, carrying out integral solution on two sides of the function to obtain the product:
wherein: p is p>q is positive odd number, x (0) Is the initial state of the system state variable x, t (r) The time required for the state variable x in the terminal attractor to reach the equilibrium point x=0 from the initial state. The terminal attractor model indicates that the system state can converge to the equilibrium point in a limited time, asThe end attractor has the characteristic of accelerating convergence near the equilibrium point. The embodiment adds an integral link when designing a novel sliding mode surface, can smooth torque pulsation, has the effect of weakening buffeting, and can not generate a second derivative of a state variable when designing a sliding mode control law.
The novel nonsingular rapid terminal sliding mode surface function is designed as follows:
wherein ,is a saturation function>Is hyperbolic tangent function, delta, gamma>0，/>And p is>q is positive odd number, delta is boundary layer thickness, < ->
When the system state enters the sliding mode, there areNamely:
the formula (8) is modified into:
as can be seen from equation (9), when the error state is far from the equilibrium point, the state convergence rate is determined by the linear termPlays a main role and adds a saturation function to make the currentThe error has saturation characteristic, and the system can quickly converge on a sliding mode surface on a preset control track; when the error state is closer to the balance point, the state convergence rate is determined by the nonlinear term +>Plays a main role. Thus, the first and second substrates are bonded together,
in the sliding stage, the nonsingular rapid terminal sliding mode surface (7) can realize global rapid convergence, andthe method does not contain the state that the index is negative, and avoids the singular phenomenon.
As can be seen from equation (2), the extended back emf is required to obtain the back emf value before extracting the motor rotor position and speed information, and therefore the sliding mode control law V of the new sliding mode observer is required. The sliding mode control law is controlled by an equivalent control function V eq And a switching control function V sw Composition is prepared. The equivalent control function is that the system is in an ideal sliding mode area under the assumption that the modeling of the system is accurate and has no influence of other factors and no external disturbanceOn the premise of solving the obtained average control quantity. From the equation (5) and the equation (7), the equivalent control function is:
wherein a, b E R + 。
Switching control function V sw The system state is forced to switch near the sliding mode surface, and robust control over uncertainty and disturbance is realized. Switching control function V sw The method is formed by compounding a fast power approach law and a terminal attractor function, namely:
V sw ＝-k|S| μ h(S)-ε|S| υ (11)
wherein k is>0，0<μ<1，0<ε<1。
The sliding mode control law function obtained from equation (10) and equation (11) is:
in analyzing the sliding mode variable structure control, it is necessary to satisfy a certain control characteristic, and it is known in the analysis that the system state variable can be converged within a certain time. In order to ensure the stability of the system, a Lyapunov (Lyapunov) function is selected to judge the stability of the system:
in V form α For example, pair V α The derivation is as follows:
in { |S α |≤(min(|E α |/k) 1/μ (|E α |/ε) 1/υ Within the number of the two-dimensional space,is negatively determined, and the same theory can prove +.>And also negative, the system can be proven to be stable.
Step four, reconstructing the extended back electromotive force (EMF) by using an Extended Kalman Filter (EKF) to extract a back electromotive force estimated valueFinally, the motor rotor position is estimated based on the phase-locked loop Principle (PLL)>And speed->
When the sliding mode control system is designed, a low-buffeting switching control function is used for replacing an absolute value function, but when the sliding mode switching motion is performed on the sliding mode surface, a plurality of high-frequency signals and higher harmonics are generated, and the estimated extended counter electromotive force is based on the fact that the estimated counter electromotive force has larger ripple waves. Therefore, an integral link is added when the nonsingular sliding mode surface is designed to carry out primary filtering on the back electromotive force waveform, and a smoother back electromotive force waveform is obtained.
However, in practical application, a large amount of system noise and measurement noise are often associated with high-frequency signals, the ripple component existing in back electromotive force is not filtered out in an integration link, and meanwhile, a low-pass filter is used in a traditional sliding mode observer to cause phase delay. Therefore, in order to suppress the interference of noise and remove the high-frequency ripple component, and to eliminate the delay phase, the accuracy of identifying the electrical angle of the rotor position is higher. Referring to fig. 4, a kalman filter is introduced to perform secondary filtering on the back electromotive force obtained after filtering by the integrator, in fact, the kalman filter is equivalent to performing primary reconstruction on the back electromotive force, and the back electromotive force after double filtering is used as an input of a sliding mode observer, so that the control system can be adaptively adjusted, buffeting can be suppressed to the greatest extent, and estimation errors can be reduced.
Deriving the formula (2):
in the formula,[Vα V β ] T The control law function is controlled by the sliding mode surface and has alpha and beta axis components and omega e Is the electric angular velocity, theta e For the electrical angle of the rotor position,for rotor flux linkage->Is the rate of change of the motor speed. The frequency of system sampling is far greater than the change rate of motor rotation speed, so that the system can be approximately zero-processed.
The formula (15) is simplified as follows:
from the formulas (15) and (16), the mathematical expression of the kalman filter can be deduced as:
in the formula,is the component, k, of the back electromotive force in alpha beta axis after being filtered by a Kalman filter k Is the filter coefficient of the Kalman filter.
The new sliding mode observer equation after reconstruction is:
where m is a real number.
Since the sliding mode control is accompanied by the generation of high-frequency signals in a sliding mode, phase delay and high-frequency noise exist in the counter electromotive force obtained in the traditional sliding mode observer, the rotor position and speed are obtained based on an arctangent function in the traditional sliding mode observer, the high-frequency signals are directly introduced into the counter electromotive force, the rotor position is estimated by taking the arctangent value after dividing the counter electromotive force, and the electric angle error is amplified in one step. To overcome this disadvantage, rotor position and speed information is modulated from the back emf based on the phase-locked loop principle, as shown in fig. 5. The back emf after double filtering is used as the input of the phase-locked loop,
when estimating rotor positionWith the actual rotor positionθ is arranged e The difference is small, namely: />At this time, it can be considered thatThe simplified formula (19) is obtained:
the parameters of the PI regulator are adjusted based on the phase-locked loop Principle (PLL) to accurately estimate the rotor position electrical angle and the electrical angular velocity.
The design process of the method of the embodiment is verified through a Matlab/Simulink simulation platform. The SPMSM sensorless vector control system based on the conventional Sliding Mode Observer (SMO) and the novel non-singular fast terminal sliding mode observer (NFTSMO) were compared by simulation. The parameters of the permanent magnet synchronous motor are as follows: given rotational speedStator resistor R s =0.258 Ω, ac-dc axis inductance L d ＝L q = 0.827mH, rotor flux linkage +.>Pole pair number p=4, damping coefficient b=0n·m·s, moment of inertia j=0.0065 kg·m 2 . No-load motor (T) m =0n·m) start, the system given rotation speed is +.>When the motor control system operates at 0.1s, the load torque changes from the idle running state to T suddenly m =10n·m, the system given rotational speed remains +.>The time for which the simulation was run was 0.2s.
As can be seen from an analysis of fig. 6, the system is started to operate at a given rotational speed in an idle stateWhen the two control algorithms reach a given value quickly, the overshoot of the novel sliding mode observer control system is smaller by about 4.8% and the overshoot of the traditional observer control system is about 5.6% as can be seen from the locally amplified waveform diagram at the initial stage of reaching the given value in the response process. Applying T to the system at 0.1s m As can be seen from fig. 6, the motor speed basically does not change when the novel sliding mode observer control system suddenly adds load disturbance, the speed amplitude jump range is stabilized near a given value quickly within + -3 rad/min, and the response process is faster; the amplitude of the step of the motor speed is larger (+/-30 rad/min) when the traditional sliding mode observer control system suddenly loads disturbance, and the speed is reduced after the load disturbance is applied.
Analyzing fig. 7 (a), the rotational speed error of the novel sliding mode control is very small during the no-load operation or the steady operation with load, the rotational speed error of the motor is almost the same as the steady operation during the sudden load disturbance, and as can be seen from fig. 7 (b), the rotational speed error of the motor has a larger range deviation in the zero low speed stage when the motor is started under the conventional sliding mode observer, and the rotational speed error is very large during the steady operation. Therefore, the novel nonsingular rapid terminal sliding mode observer-based sensorless control system can effectively inhibit buffeting of the sliding mode control system.
As can be seen from fig. 8, under the control of the low buffeting switching function, the three-phase current fluctuation under the novel sliding mode observer is small, and the three-phase stator current can reach a stable state quickly after load disturbance is applied at 0.1S; as can be seen from fig. 9, the back emf is filtered once by the integral sliding mode observer and then filtered higher-order after the back emf is reconstructed, resulting in a smoothed back emf estimate.
As can be seen from fig. 10, when estimating the rotor position based on the Nonsingular Fast Terminal Sliding Mode Observer (NFTSMO), the accuracy of identifying the initial rotor position is higher in the zero low speed stage of motor start, and the rotor position is accurately tracked in the middle and high speed steady state operation stage, and the tracking accuracy is 0.01052%; the traditional Sliding Mode Observer (SMO) has larger error in estimating the position of the motor rotor in the zero low-speed stage of motor start, and can generate phase hysteresis, and the tracking precision of the traditional Sliding Mode Observer (SMO) is 0.02514% in the middle-high-speed steady-state operation stage.
The invention and its embodiments have been described above by way of illustration and not limitation, and the invention is illustrated in the accompanying drawings and described in the drawings in which the actual structure is not limited thereto. Therefore, if one of ordinary skill in the art is informed by this disclosure, the structural mode and the embodiments similar to the technical scheme are not creatively designed without departing from the gist of the present invention.

Claims (5)

1. The SPMSM sensorless vector control method based on the nonsingular rapid terminal sliding mode observer is characterized by comprising the following steps:
step one, establishing a voltage state equation of the permanent magnet synchronous motor based on a two-phase static coordinate system alpha beta, reconstructing the voltage state equation into a stator current state equation, and constructing a current state observation equation;
step two, sampling three-phase current i abc And three-phase voltage u abc Calculating a current error state equation;
step three, designing a sliding mode surface function S of a novel nonsingular rapid terminal sliding mode observer by taking a current observation error as a state variable (t) And designing a sliding mode surface equivalent control function V based on the current error state equation and the sliding mode surface function eq And a switching control function V sw The stability of the composition is proved by using a Lyapunov function stability criterion;
step four, reconstructing the extended counter electromotive force by using an extended Kalman filter, and extracting a counter electromotive force estimated valueFinally, the motor rotor position is estimated based on the phase-locked loop principle>And speed->
In the third step, the current observation error is used as a state variable for designing a novel nonsingular rapid terminal sliding mode surface, a terminal attractor concept is introduced, and a novel nonsingular rapid terminal sliding mode surface function is designed by combining a terminal attractor function;
terminal attractor function ofAnd (3) after deforming the function, carrying out integral solution on two sides of the function to obtain the product:
wherein: p is p>q is positive odd number, x (0) Is the initial state of the system state variable x, t r The time required for the state variable x in the terminal attractor to reach the equilibrium point x=0 from the initial state;
the novel nonsingular rapid terminal sliding mode surface function is designed as follows:
wherein ,is a saturation function>Is hyperbolic tangent function, delta, gamma>0，/>And p is>q is positive odd number, delta is boundary layer thickness, < ->
In the third step, when the system state enters the sliding mode, there is
The formula (8) is modified into:
as can be seen from equation (9), when the error state is far from the equilibrium point, the state convergence rate is determined by the linear termThe system has the main function, and simultaneously, a saturation function is added to enable the current error to have saturation characteristics, so that the system can quickly converge on a sliding mode surface on a preset control track; when the error state is closer to the balance point, the state convergence rate is determined by the nonlinear term +>Plays a main role;
in the third step, the equivalent control function V eq And a switching control function V sw The sliding mode control law V is composed, and as can be seen from the formula (5) and the formula (7), the equivalent control function is:
wherein a, b E R + ；
Switching control function V sw The method is formed by compounding a fast power approach law and a terminal attractor function, namely:
V sw ＝-k|S| μ h(S)-ε|S| υ (11)
wherein k is>0，0<μ<1，0<ε<1；
The sliding mode control law function obtained from equation (10) and equation (11) is:
in the third step, a Lyapunov function is selected to judge the stability of the system:
for V α The derivation is as follows:
in { |S α |≤(min(|E α |/k) 1/μ (|E α |/ε) 1/υ Within the number of the two-dimensional space,is negatively fixed, and is in the same way as in the first aspect->And is also negative, i.e. the system is proven to be stable.
2. The SPMSM sensorless vector control method based on the nonsingular fast terminal sliding mode observer according to claim 1, wherein the SPMSM sensorless vector control method is characterized in that: in the first step, the voltage state equation of the three-phase permanent magnet synchronous motor under a two-phase static coordinate system is obtained through Clark coordinate transformation as shown in formula (1),
wherein ,Ld 、L q For stator inductance to be in dq axis component, R s Is stator resistance omega e In order to obtain the electric angular velocity,is a differential operator, [ u ] α u β ] T For the stator voltage to be in the alpha beta axis component, [ i ] α i β ] T For the stator current to be in the alpha beta axis component, [ E ] α E β ] T To extend the back electromotive force (EMF) in the αβ axis component, and satisfy:
in the formula,θe For the electrical angle of the rotor position,is rotor flux linkage, [ i ] d i q ] T For the stator current in the dq axis component;
and (3) deforming the formula (1) and reconstructing the formula into a stator current state equation:
in the surface-mounted three-phase permanent magnet synchronous motor, L d ＝L q ＝L s Is a stator inductance;
to obtain an estimate of the extended back emf, a current state observer equation is constructed as:
in the formula,is the current state observation value, [ u ] α u β ] T For control input of observer, [ V ] α V β ] T The law function is controlled at the alpha beta axis for the sliding mode surface.
3. The SPMSM sensorless vector control method based on the nonsingular fast terminal sliding mode observer according to claim 2, wherein the SPMSM sensorless vector control method is characterized in that: in the second step, three-phase current i output by the three-phase permanent magnet synchronous motor is collected abc And three-phase voltage u abc The current i under the two-phase static coordinate system is obtained through Clark coordinate transformation αβ Sum voltage u αβ The method comprises the steps of carrying out a first treatment on the surface of the Will u αβ As input to the current state observer, the current state observations are comparedAnd current i αβ Defined as the current observation error, the stator current error state equation is derived according to equation (3) and equation (4):
in the formula,is the current observation error [ V ] α V β ] T The law function is controlled at the alpha beta axis for the sliding mode surface.
4. The SPMSM sensorless vector control method based on the nonsingular fast terminal sliding mode observer according to claim 3, wherein the SPMSM sensorless vector control method is characterized in that: in the fourth step, the derivation is carried out on the formula (2):
in the formula,[Vα V β ] T The control law function is controlled by the sliding mode surface and has alpha and beta axis components and omega e Is the electric angular velocity, theta e For the electrical angle of the rotor position,for rotor flux linkage->Is the rate of change of the motor speed;
the formula (15) is simplified as follows:
from the formulas (15) and (16), the mathematical expression of the kalman filter can be deduced as:
in the formula,is the component, k, of the back electromotive force in alpha beta axis after being filtered by a Kalman filter k Is the filter coefficient of the Kalman filter;
the new sliding mode observer equation after reconstruction is:
where m is a real number.
5. The SPMSM sensorless vector control method based on the nonsingular fast terminal sliding mode observer according to claim 4, wherein the method comprises the following steps: in the fourth step, the back electromotive force after double filtering is used as the input of the phase-locked loop, and the difference equation of the back electromotive force of the motor output by the phase-locked loop is as follows:
when estimating rotor positionAnd actually measured rotor position theta e The difference is small, i.e.)>At this time, it can be considered that
Obtaining the product (19)
The rotor position electrical angle and the electrical angular velocity can be accurately estimated by adjusting the parameters of the PI regulator based on the phase-locked loop principle.
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