CN110572091A - optimized sensorless control method for permanent magnet synchronous motor - Google Patents

optimized sensorless control method for permanent magnet synchronous motor Download PDF

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Publication number
CN110572091A
CN110572091A CN201910870999.8A CN201910870999A CN110572091A CN 110572091 A CN110572091 A CN 110572091A CN 201910870999 A CN201910870999 A CN 201910870999A CN 110572091 A CN110572091 A CN 110572091A
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value
current
fuzzy
coordinate system
electromotive force
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CN110572091B (en
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陈李济
马强
应保胜
李华鑫
伍娇
高维士
韩海风
王硕
张强
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Hubei University of Arts and Science
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Hubei University of Arts and Science
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/001—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using fuzzy control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/13—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
    • H02P21/24—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
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/14—Electronic commutators
    • H02P6/16—Circuit arrangements for detecting position
    • H02P6/18—Circuit arrangements for detecting position without separate position detecting elements
    • H02P6/182—Circuit arrangements for detecting position without separate position detecting elements using back-emf in windings
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/34—Modelling or simulation for control purposes

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Automation & Control Theory (AREA)
  • Fuzzy Systems (AREA)
  • Control Of Ac Motors In General (AREA)

Abstract

the invention discloses a method for optimizing sensorless control of a permanent magnet synchronous motor. The method comprises the steps of performing Clark coordinate transformation on three-phase current and three-phase voltage acquired by a sensor to obtain voltage and current under a two-phase static coordinate system, and inputting the voltage under the two-phase static coordinate system to a sliding mode current observer to obtain observed current; inputting the difference value of the observed current and the actual current into a back electromotive force observer based on a saturation function to obtain a back electromotive force estimation initial value, and adopting variable theory domain fuzzy controlAlgorithm adjustment sliding mode gain k in back electromotive force observer based on saturation functionsmo(ii) a Then, filtering the estimated initial value of the back electromotive force through a variable cutoff frequency filter to obtain a smoother back electromotive force estimated value; and then carrying out variable lag compensation design on the positions of the reversed rotors after filtering, and calculating the speed and position values of the rotor of the motor. The method can effectively weaken the shaking phenomenon, improve the speed of the rotor, has high estimation precision of the position information, and has good dynamic characteristics.

Description

Optimized sensorless control method for permanent magnet synchronous motor
Technical Field
the invention relates to the field of permanent magnet synchronous motor control, in particular to a sensorless control method for optimizing a permanent magnet synchronous motor.
Background
In the current social production, the permanent magnet synchronous motor has the characteristics of high torque ratio, convenient use, high power factor and the like, is used as a main power source output device, and the research on the control performance of the permanent magnet synchronous motor is increasingly emphasized. In a traditional permanent magnet synchronous motor control system, speed and position information of a motor rotor is generally obtained by installing a sensor, but the installation of the sensor can reduce the space of the motor system and increase the production cost, so that the system has more strict requirements on the use environment. To eliminate the adverse effects of using sensors, control algorithms in position sensorless control techniques are widely used to estimate motor rotor position and speed information. According to the algorithm applicable speed range, the sensorless control technology of the permanent magnet synchronous motor can be divided into two types: the method is suitable for low-speed operation of the motor, such as inductance measurement, high-frequency signal injection method and the like; the other method is suitable for high-speed operation in the motor, such as a method based on a motor basic model, a model reference self-adaption method, an artificial intelligence algorithm and an observer method.
the sliding mode observer has the advantages of simple algorithm, good anti-interference capability and high response speed, and has the defects that jitter can be generated due to inertia and measurement error interference, and the problem of phase delay can be generated due to the application of a low-pass filter. The current observation error in the observer is dynamically changed, so that the given fixed value of the sliding mode gain value can increase the jitter.
Disclosure of Invention
aiming at the problems, the invention discloses an optimized sensorless control method of a permanent magnet synchronous motor, which is characterized in that the position and the rotating speed information of a motor rotor are estimated by collecting the current and voltage signal values of the permanent magnet synchronous motor and then by a variable domain fuzzy sliding mode observer algorithm system module. The method disclosed by the invention not only weakens the shake of the traditional sliding-mode observer system, filters out higher harmonics in the sliding-mode observer, obtains a continuous and smooth equivalent signal, but also enhances the adaptability and robustness of the system when the load is suddenly applied to the rotating speed change and the parameter change.
The technical scheme adopted by the invention is a sensorless control method for optimizing a permanent magnet synchronous motor, which comprises the following steps:
step 1, Clark coordinate transformation is carried out on three-phase current and three-phase voltage collected by a sensor to obtain voltage and current under a two-phase static coordinate system, the voltage under the two-phase static coordinate system is input to a sliding mode current observer to obtain observed current, and then the difference value between the observed current and actual current in the sliding mode current observer is input to a back electromotive force observer based on a saturation function to obtain a back electromotive force estimated initial value;
Step 2: adjusting sliding mode gain in the back electromotive force observer based on the saturation function through a variable universe fuzzy control algorithm;
step 3, constructing a Lyapunov model by utilizing the actual value of the stator current and the observed value of the stator current, and performing stability analysis on the counter electromotive force observer model based on the saturation function;
step 4, filtering the counter electromotive force observation initial value through a variable cutoff frequency filter to obtain a filtered counter electromotive force estimation value;
Step 5, calculating a rotor rotating speed estimated value through the filtered back electromotive force, and performing variable hysteresis compensation design on the rotor position to further calculate a rotor position estimated final value;
And 6, calibrating a rotor rotating speed estimated value through a speed loop PI controller, calibrating a rotor position estimated value through a current loop controller, calculating to obtain a voltage component under a synchronous rotating coordinate system, obtaining a voltage component under a two-phase static coordinate system through inverse Park coordinate transformation, inputting the voltage component to an inverter after Space Vector Pulse Width Modulation (SVPWM), converting the voltage into three-phase alternating current through the inverter, and supplying the three-phase alternating current to a motor, wherein finally, a motor control system forms a closed-loop control loop.
Preferably, the voltage of the alpha axis in the two-phase stationary coordinate system in step 1 is uαthe beta axis voltage under the two-phase static coordinate system is uβthe alpha axis current under the two-phase static coordinate system is iαThe beta axis current under the two-phase static coordinate system is iβ，iαAnd iβthe actual value of the stator current is taken as the actual value;
the Clark coordinate transformation matrix is as follows:
in the step 1, a sliding mode current observer model is constructed, and the specific expression is as follows:
in the formula (I), the compound is shown in the specification,The observed value of the alpha axis current under the two-phase static coordinate system is obtained;is a beta axis current observed value under a two-phase static coordinate system; e.g. of the typeαestimating an initial value for the counter electromotive force of the alpha axis under a two-phase static coordinate system; e.g. of the typeβEstimating an initial value for the beta axis counter electromotive force under a two-phase static coordinate system; r and Lsrespectively a stator resistor and a stator inductor; psifIs a magnetic linkage; k is a radical ofsmoobtaining the sliding mode gain in the sliding mode observer; the sat saturation function is a switching function of the sliding-mode observer;
Wherein sat is a saturation function as a switching function in the sliding mode current observer model, and is specifically defined as follows:
wherein σ is a boundary layer of a saturation function;
In the step 1, the process of calculating the stator current observation value and the back electromotive force observation initial value of the motor under the two-phase static coordinate system is as follows:
Adopting a saturation function as a switching function, and enabling the difference value of the current observed value and the actual current of the permanent magnet synchronous motor on the alpha axis under the two-phase static coordinate systemAnd the difference between the observed current and the actual current on the beta axisAs the input value of the counter electromotive force observer, respectively calculating the observation initial value e of the counter electromotive force on the alpha axis under the two-phase static coordinate system by the counter electromotive force observer based on the saturation functionαAnd an initial value e for the observation of the back electromotive force on the beta axisβ。
When the control system slides on the sliding surface:
the initial value of the back emf estimate available is:
preferably, the step 2 of adjusting the sliding mode gain in the back electromotive force observer based on the saturation function through the variable universe fuzzy control algorithm specifically comprises the following steps:
step 2.1, fuzzification operation processing is carried out on the input signal;
The variable-universe fuzzy controller is structurally a two-dimensional fuzzy controller, and two variable-universe fuzzy controllers are respectively established on an alpha axis and a beta axis of stator current under a two-phase static coordinate system; taking the stator current alpha axis variable domain fuzzy controller establishing process as an example, the stator current is used for enabling the permanent magnet synchronous motor to be in a two-phase static coordinate system, and the difference value of the current observed value on the alpha axis and the actual current is obtaineddefining the difference as e, and calculating and deriving a difference value change rate ec of an observed value of current and actual current on an alpha axis under a two-phase static coordinate system in unit time difference, wherein the calculation formula is as follows:
wherein e (t) is the difference value between the current observed value and the actual current on the alpha axis under the two-phase static coordinate system at the moment t; Δ t is the time difference;
Then, taking a difference value e between an alpha-axis current observed value and an actual current under a two-phase static coordinate system and a difference value change rate ec thereof as two input variables of the fuzzy controller, defining an initial domain range of the input variables of the fuzzy controller as { -15,15}, and defining an initial domain range of the output variables as { -1,1 };
After the input and output domains are transformed by adding the scaling factors alpha (x) and beta (x), the input variable domain range is { -alpha (x)15, alpha (x)15}, the output variable initial domain range is { -beta (x), beta (x) }, and the scaling factor function model of the input variable domain is as follows:
Wherein x is input variable of the fuzzy controller, lambda is a first proportional coefficient, and k1Is the second proportionality coefficient, k2is a third proportionality coefficient;
the scale factor function model of the output variable discourse domain is as follows:
Where x is the variable of the input quantity of the fuzzy controller, tau1is a first exponential coefficient, τ2Is a second exponential coefficient; epsilon is a positive infinitesimal small compensation value;
then, the fuzzy language of the input and output variables of the fuzzy controller is defined as follows:
{NB、NM、NZ、PM、PB}
The input variable membership function adopts a triangular membership function, and the output variable membership function adopts a normal form membership function; then, carrying out scale transformation on a difference value e and a difference value change rate ec of the current observed value on the alpha axis and the actual current under the two-phase static coordinate system to ensure that the difference values are transformed to respective domain ranges;
the actual input of the fuzzy controller isthe input amount is varied within a range ofuniverse of discourse [ x ]min,xmax]Linear transformation is adopted, and the scale transformation expression is as follows:
wherein k is a scale factor, x0input quantity of the discourse domain range;
then converting the input quantity x into the discourse domain range0Fuzzy operation processing is carried out, the original input quantity is changed into fuzzy quantity and is represented by a corresponding fuzzy set, and a fuzzy operation function model is as follows:
x＝fz(x0)
wherein x is0is the input clearness value; fz represents the fuzzy operator; x is a fuzzy set;
step 2.2, fuzzification reasoning is carried out according to the set fuzzy rule to obtain a fuzzy output quantity M;
the method adopts a Mamdani fuzzy inference method, which is essentially a synthetic inference method, and the ith rule of a rule base is expressed as:
“If x is A and y is B,then Z is C.”
wherein, X, Y and Z represent the fuzzy linguistic variables of the system state and the control quantity, X and Y represent the input quantity, Z represents the control quantity, A, B and C represent the fuzzy linguistic variables X, Y and Z on the domain X, Y and Z of the fuzzy linguistic variables respectively, and all the rules are combined together to form a rule base;
wherein C is fuzzy output; the fuzzy relation of implications is as follows:
Ri＝(Ai×Bi)×Ci
the control rule bases can be regarded as yes or a union relation, and then the fuzzy relation mathematical formula implied by the whole rule base is as follows:
fuzzy reasoning is carried out on the input quantity of the fuzzy controller according to a fuzzy control rule table formulated by experimental operation and control experience, and a reasoning formula is as follows:
Step 2.3, deblurring processing is carried out on the fuzzy output quantity M by adopting a weighted average method, and finally the output quantity u, namely the sliding mode gain k is obtainedsmo；
Performing fuzzy resolving treatment on the fuzzy set M of the output quantity obtained by fuzzy reasoning, solving a weighted average value of each element in the fuzzy output quantity and the corresponding membership degree thereof by adopting a weighted average method to obtain a clear value Z, and converting the clear value Z in the domain range into an actual control quantity u, namely a sliding mode gain k through scale transformationsmoif Z varies within the range [ Z ]max，zmin]The actual controlled variable u varies within a range of [ u ]min，umax]its scale transform mathematical expression formulathe following were used:
Wherein k is a scale factor;
Finally, according to the dynamic difference value between the observed value of the stator current and the actual value of the current, obtaining the optimal sliding mode gain value k through variable universe fuzzy control adjustmentsmo。
preferably, the Lyapunov model in step 3 is as follows:
Wherein s isαThe difference value of the observed value and the actual value of the stator current on the alpha axis is obtained; sβthe difference value of the observed value and the actual value of the stator current on the beta axis is obtained;
and (3) carrying out derivation on the formula and substituting the derivation into a sliding mode current observer model based on a saturation function:
wherein R is stator resistance, Lsis the stator inductance, eαestimating an initial value, e, for the back electromotive force of the alpha axis in a two-phase stationary coordinate systemβEstimating an initial value, k, for the back electromotive force of the beta axis in a two-phase stationary coordinate systemsmoobtaining the sliding mode gain in the sliding mode observer;
when in useWhen, i.e. as long as eα-ksmosat(sα) < 0 and eβ-ksmosat(sβ) The inequality < 0 is true, so the stability condition of the variable universe fuzzy sliding-mode observer is as follows:
ksmo＞max(|eα|,|eβ|)。
preferably, the novel low-pass variable cut-off frequency filter in step 4 is designed as follows:
in the formula, kfis a positive number; k is a radical ofeis a normal number; omegaeIs a rotation speed control value;Is the cut-off frequency;
The filtered back emf estimate can be expressed as:
wherein the content of the first and second substances,For the estimation of the back emf of the alpha axis,Is an estimate of the beta-axis back-emf, zαFor containing counter-potential e on the alpha axisαSwitching signal, zβis beta axis containing counter potential eβand switching the signal.
Preferably, the initial value of the rotor position estimation in step 5 is set as:
Wherein the content of the first and second substances,Estimating an initial value for the rotor position;
the rotor speed estimated value is:
The rotor position variable lag compensation is designed as follows:
wherein the content of the first and second substances,Is an estimated value of the rotor speed;cut-off frequency of the low-pass filter;is a rotor position compensation value;
The final rotor position estimate is:
compared with the traditional sliding-mode observer, the improved effect of the invention is as follows:
the sliding mode gain in the conventional sliding mode observer is usually a given constant, and when the sliding mode observer is far away from the switching surface, the sliding mode gain needs to be a larger value in order to accelerate the speed of reaching the sliding mode surface, and when the sliding mode observer is near the switching surface, the sliding mode gain needs to be reduced in order to reduce shake. In order to reduce shake, the influence of different switching gains on a system is fully utilized, and a fuzzy control algorithm is adopted to dynamically adjust the sliding mode gain of the sliding mode observer.
In order to reduce the influence of the universe of discourse on the precision of fuzzy control, the patent adopts a variable universe of discourse fuzzy control method. And the universe of discourse of the common fuzzy controller is adjusted in real time by utilizing the expansion factor, so that the aim of eliminating the control dead zone is fulfilled. The cut-off frequency of the low-pass variable cut-off filter designed by the invention can be adaptively changed along with the rotation speed control, the filter can keep good filtering performance when the rotation speed is changed, and can better filter high-frequency components containing back electromotive force estimation information to obtain smoother back electromotive force estimation signals. In the conventional sliding mode observer, the lag compensation is a fixed value, so that the phase lag has compensation errors at different rotating speeds. The lag compensation of the filter is designed and adjusted to be a variable related to the control value of the rotating speed of the rotor, so that the sliding-mode observer can adaptively change the angle estimation error compensation when operating at different speeds, and the observation precision is improved.
Drawings
FIG. 1: is a block diagram of an optimized sensorless control system of a permanent magnet synchronous motor.
FIG. 2: is a schematic block diagram of a fuzzy sliding-mode observer based on a variable universe of discourse.
FIG. 3: is a membership function graph of input and output in a variable theory domain fuzzy system.
FIG. 4: is a fuzzy rule table diagram.
FIG. 5: the method is a comparison graph of the starting state and the rotating speed of the rotor of the sliding mode observer in the patent method and in two other methods.
FIG. 6: an error waveform is estimated for the method of this patent and for the other two methods.
FIG. 7: the method of this patent and the other two methods are highlighted with a partial enlargement of the load speed waveform.
FIG. 8: is a flow chart of the algorithm method of the patent.
Detailed Description
in order to facilitate the understanding and practice of the present invention for those of ordinary skill in the art, the present invention will be described in further detail with reference to the accompanying drawings and examples, it being understood that the examples described herein are for purposes of illustration and explanation only and are not intended to be limiting.
fig. 1 shows a schematic diagram of an optimized sensorless control system of a permanent magnet synchronous motor. The system comprises a permanent magnet synchronous motor, a three-phase inverter module, an SVPWM module, a vector control module and a variable universe fuzzy sliding-mode observer module. The control method adopts idthe three-phase current and voltage collected by the sensor are converted into a current component i on an alpha axis under a two-phase static coordinate system through Clark under 0 vector controlαbeta on-axis current component iβand a voltage component u on the alpha axisαbeta on-axis voltage component uβthen i isα、iβAnd uα、uβinput variable universe fuzzy sliding mode viewand a detector module. Calibrating the motor rotating speed and position information estimated by the variable universe fuzzy sliding-mode observer module through a speed loop PI controller and a current loop controller, and outputting the calibration as the voltage component on the d axis under a synchronous rotating coordinate systemvoltage component on q axisThen, the voltage component on the alpha axis under the two-phase static coordinate system is calculated through inverse Park coordinate transformationVoltage component on beta axisafter Space Vector Pulse Width Modulation (SVPWM), the voltage is input to an inverter, the voltage is converted into three-phase alternating current through the inverter and is supplied to a motor, and finally, a motor control system forms a closed-loop control loop.
The following describes a specific embodiment of the present invention with reference to fig. 1 to 4, which is a permanent magnet synchronous electric control method based on a variable universe fuzzy sliding mode observer, and specifically includes the following steps:
Step 1, as shown in fig. 2, three-phase current and three-phase voltage acquired by a sensor are converted through a Clark coordinate to obtain voltage and current under a two-phase static coordinate system, and the voltage under the two-phase static coordinate system is input to a sliding mode current observer to obtain observed current. Then inputting the difference value of the observed current and the actual current in the sliding mode current observer into a back electromotive force observer based on a saturation function to obtain a back electromotive force estimated initial value
In step 1, the voltage of the alpha axis under the two-phase static coordinate system is uαThe beta axis voltage under the two-phase static coordinate system is uβthe alpha axis current under the two-phase static coordinate system is iαthe beta axis current under the two-phase static coordinate system is iβ，iαAnd iβThe actual value of the stator current is taken as the actual value;
The Clark coordinate transformation matrix is as follows:
the sliding mode current observer model constructed in the step 1 has the following specific expression:
in the formula (I), the compound is shown in the specification,The observed value of the alpha axis current under the two-phase static coordinate system is obtained;Is a beta axis current observed value under a two-phase static coordinate system; e.g. of the typeαestimating an initial value for the counter electromotive force of the alpha axis under a two-phase static coordinate system; e.g. of the typeβEstimating an initial value for the beta axis counter electromotive force under a two-phase static coordinate system; r and LsRespectively a stator resistor and a stator inductor; psifis a magnetic linkage; k is a radical ofsmoobtaining the sliding mode gain in the sliding mode observer; the sat saturation function is a switching function of the sliding-mode observer;
wherein sat is a saturation function as a switching function in the sliding mode current observer model, and is specifically defined as follows:
Wherein σ is a boundary layer of a saturation function;
in the step 1, the process of calculating the stator current observation value and the back electromotive force observation initial value of the motor under the two-phase static coordinate system is as follows:
and (3) converting the three-phase voltage acquired by the sensor through Clark coordinates to obtain a voltage under a two-phase static coordinate system, and inputting the voltage to a sliding mode current observer to obtain an observed current. Adopting a saturation function as a switching function, and enabling the difference value of the current observed value and the actual current of the permanent magnet synchronous motor on the alpha axis under the two-phase static coordinate systemand the difference between the observed current and the actual current on the beta axisas the input value of the back electromotive force observer based on the saturation function, the observation initial value e of the back electromotive force on the alpha axis under the two-phase static coordinate system is respectively calculated by the back electromotive force observer based on the saturation functionαAnd an initial value e for the observation of the back electromotive force on the beta axisβ。
When the control system slides on the sliding surface:
the initial value of the back emf estimate available is:
Step 2: adjusting sliding mode gain in the back emf observer based on a saturation function through a variable universe fuzzy control algorithm;
The specific steps of adjusting the sliding mode gain in the back emf observer based on the saturation function through the variable universe fuzzy control algorithm in the step 2 are as follows:
Step 2.1, fuzzification operation processing is carried out on the input signal;
The variable-universe fuzzy controller is structurally a two-dimensional fuzzy controller, and two variable-universe fuzzy controllers are respectively established on an alpha axis and a beta axis of stator current under a two-phase static coordinate system; taking the stator current alpha axis variable domain fuzzy controller establishing process as an example, the stator current is used for enabling the permanent magnet synchronous motor to be in a two-phase static coordinate system, and the difference value of the current observed value on the alpha axis and the actual current is obtainedDefined as e, and calculating the observed value of the current on the alpha axis under the two-phase static coordinate system in the unit time difference andthe difference change rate ec of the actual current is calculated by the following formula:
wherein e (t) is the difference value between the current observed value and the actual current on the alpha axis under the two-phase static coordinate system at the moment t; Δ t is the time difference;
Then, taking a difference value e between an alpha-axis current observed value and an actual current under a two-phase static coordinate system and a difference value change rate ec thereof as two input variables of the fuzzy controller, defining an initial domain range of the input variables of the fuzzy controller as { -15,15}, and defining an initial domain range of the output variables as { -1,1 };
after the input and output domains are transformed by adding the scaling factors alpha (x) and beta (x), the input variable domain range is { -alpha (x)15, alpha (x)15}, the output variable initial domain range is { -beta (x), beta (x) }, and the scaling factor function model of the input variable domain is as follows:
Wherein x is input variable of the fuzzy controller, lambda is a first proportional coefficient, and k1is the second proportionality coefficient, k2is a third proportionality coefficient; the proportional coefficient value of the patent is lambda is 0.88, k1＝0.9，k2＝0.01；
the scale factor function model of the output variable discourse domain is as follows:
where x is the variable of the input quantity of the fuzzy controller, tau1is a first exponential coefficient, τ2is a second exponential coefficient; epsilon is a positive infinitesimal small compensation value;
Take values of τ respectively1＝0.9，τ2＝0.4，ε＝10-5；
then, the fuzzy language of the input and output variables of the fuzzy controller is defined as follows:
{NB、NM、NZ、PM、PB}
as shown in fig. 3, the input and output variable membership functions are triangular membership functions and normal-shaped membership functions; then, carrying out scale transformation on a difference value e and a difference value change rate ec of the current observed value on the alpha axis and the actual current under the two-phase static coordinate system to ensure that the difference values are transformed to respective domain ranges;
The actual input of the fuzzy controller isThe input amount is varied within a range ofUniverse of discourse [ x ]min,xmax]Linear transformation is adopted, and the scale transformation expression is as follows:
wherein k is a scale factor, x0input quantity of the discourse domain range;
Then converting the input quantity x into the discourse domain range0Fuzzy operation processing is carried out, the original input quantity is changed into fuzzy quantity and is represented by a corresponding fuzzy set, and a fuzzy operation function model is as follows:
x＝fz(x0)
Wherein x is0is the input clearness value; fz represents the fuzzy operator; x is a fuzzy set;
step 2.2, as shown in fig. 4, fuzzification reasoning is carried out according to the set fuzzy rule to obtain a fuzzy output quantity M;
The method adopts a Mamdani fuzzy inference method, which is essentially a synthetic inference method, and the ith rule of a rule base is expressed as:
“If x is A and y is B,then Z is C.”
Wherein, X, Y and Z represent the fuzzy linguistic variables of the system state and the control quantity, X and Y represent the input quantity, Z represents the control quantity, A, B and C represent the fuzzy linguistic variables X, Y and Z on the domain X, Y and Z of the fuzzy linguistic variables respectively, and all the rules are combined together to form a rule base;
wherein C is fuzzy output; the fuzzy relation of implications is as follows:
Ri＝(Ai×Bi)×Ci
the control rule bases can be regarded as yes or a union relation, and then the fuzzy relation mathematical formula implied by the whole rule base is as follows:
Fuzzy reasoning is carried out on the input quantity of the fuzzy controller according to a fuzzy control rule table formulated by experimental operation and control experience, and a reasoning formula is as follows:
Step 2.3, deblurring processing is carried out on the fuzzy output quantity M by adopting a weighted average method, and finally the output quantity u, namely the sliding mode gain k is obtainedsmo；
performing fuzzy resolving treatment on the fuzzy set M of the output quantity obtained by fuzzy reasoning, solving a weighted average value of each element in the fuzzy output quantity and the corresponding membership degree thereof by adopting a weighted average method to obtain a clear value Z, and converting the clear value Z in the domain range into an actual control quantity u, namely a sliding mode gain k through scale transformationsmoIf Z varies within the range [ Z ]max，zmin]The actual controlled variable u varies within a range of [ u ]min，umax]The scale transformation mathematical expression formula is as follows:
Wherein k is a scale factor;
Finally, according to the dynamic difference value between the observed value of the stator current and the actual value of the current, obtaining the optimal sliding mode gain value k through variable universe fuzzy control adjustmentsmo。
Step 3, constructing a Lyapunov model by utilizing the actual value of the stator current and the observed value of the stator current, and performing stability analysis on the sliding mode observer model in the step 1;
the Lyapunov model in the step 3 is as follows:
wherein s isαThe difference value of the observed value and the actual value of the stator current on the alpha axis is obtained; sβthe difference value of the observed value and the actual value of the stator current on the beta axis is obtained;
and (3) carrying out derivation on the formula and bringing the derivation into a sliding mode observer model:
wherein R is stator resistance, Lsis the stator inductance, eαEstimating an initial value, e, for the back electromotive force of the alpha axis in a two-phase stationary coordinate systemβEstimating an initial value, k, for the back electromotive force of the beta axis in a two-phase stationary coordinate systemsmoobtaining the sliding mode gain in the sliding mode observer;
When in usewhen, i.e. as long as eα-ksmosat(sα) < 0 and eβ-ksmosat(sβ) The inequality < 0 is true, so the stability condition of the variable universe fuzzy sliding-mode observer is as follows:
ksmo＞max(|eα|,|eβ|)。
And 4, filtering the observation initial value of the counter electromotive force in the step 1 through a variable cutoff frequency filter, and taking the rotating speed as input to enable the cutoff frequency of the low-pass filter to be adaptively changed along with the rotation control. Smoothing the initial value signal z on the back electromotive force alpha axisαBeta axis counter electromotive force difference signal zβobtaining smoother alpha-axis counter electromotive force estimation signaland beta axisupper back emf estimation signal
The novel low-pass variable cut-off frequency filter in the step 4 is designed as follows:
In the formula, kfis a positive number; k is a radical ofeIs a normal number; omegaeis a rotation speed control value;is cut-off frequency
The filtered back emf estimate can be expressed as:
wherein the content of the first and second substances,For the estimation of the back emf of the alpha axis,Is an estimate of the beta-axis back-emf, zαFor containing counter-potential e on the alpha axisαswitching signal, zβis beta axis containing counter potential eβAnd switching the signal.
Step 5, calculating a rotor rotating speed estimated value through the filtered back electromotive force, and performing variable hysteresis compensation design on the rotor position to further calculate a rotor position estimated final value;
The initial value of the rotor position estimation in the step 5 is set as:
wherein the content of the first and second substances,Estimating an initial value for the rotor position;
The rotor speed estimated value is:
the rotor position variable lag compensation is designed as follows:
wherein the content of the first and second substances,is an estimated value of the rotor speed;Cut-off frequency of the low-pass filter;Is a rotor position compensation value;
The final rotor position estimate is:
And 6, calibrating a rotor rotating speed estimated value through a speed loop PI controller, calibrating a rotor position estimated value through a current loop controller, calculating to obtain a voltage component under a synchronous rotating coordinate system, obtaining a voltage component under a two-phase static coordinate system through inverse Park coordinate transformation, inputting the voltage component to an inverter after Space Vector Pulse Width Modulation (SVPWM), converting the voltage into three-phase alternating current through the inverter, and supplying the three-phase alternating current to a motor, wherein finally, a motor control system forms a closed-loop control loop.
The feasibility of the invention is verified below in conjunction with the simulated waveforms of fig. 5-7
Fig. 5 shows a comparison graph of simulation waveforms of the rotor rotation speeds of the variable domain sliding mode observer, the fuzzy sliding mode observer and the conventional sliding mode observer when the given speed value of the motor is 1000rad/s and the reference rotation speed is 1000 r/min. It can be seen from fig. 5 that the stable running time of the rotating speed at the starting time of the variable universe fuzzy sliding mode observer is shorter than that of the other two control methods, the simulation waveform is more stable,
The buffeting phenomenon is weakened, and the actual speed change of the motor can be quickly and well followed. From fig. 6, it can be seen that the conventional slip form has stable rotation speed
The estimation error of the observer rotor speed is +/-10 r/min, the estimation error of the fuzzy sliding-mode observer rotor speed is 0.5r/min, and the estimation error of the variable-universe fuzzy sliding-mode observer rotor speed is +/-0.1 r/min. Therefore, the rotating speed estimation precision of the variable universe fuzzy sliding-mode observer is improved. As can be seen from fig. 7: when the load is suddenly added, the rotating speed output oscillation controlled by the traditional sliding-mode observer is large, which shows that the robustness is not strong and the control quality is not good. Compared with the traditional sliding mode observer and the fuzzy sliding mode observer, the variable universe fuzzy sliding mode observer has the advantages that the speed change range is smaller, the dynamic response is fast, and the time for recovering to the reference rotating speed is fast. From fig. 5 to fig. 7, it can be known that the present invention has the characteristics of short adjustment time, small overshoot, and high steady-state precision compared with the conventional control method, and also the system shake phenomenon is weakened. FIG. 8 is a flow chart of a method of the present invention.
it should be understood that parts of the specification not set forth in detail are well within the prior art.
It should be understood that the above-mentioned embodiments are described in some detail, and not intended to limit the scope of the invention, and those skilled in the art will be able to make alterations and modifications without departing from the scope of the invention as defined by the appended claims.

Claims (6)

1. a method for optimizing sensorless control of a permanent magnet synchronous motor is characterized by comprising the following steps:
step 1, Clark coordinate transformation is carried out on three-phase current and three-phase voltage collected by a sensor to obtain voltage and current under a two-phase static coordinate system, the voltage under the two-phase static coordinate system is input to a sliding mode current observer to obtain observed current, and then the difference value between the observed current and actual current in the sliding mode current observer is input to a back electromotive force observer based on a saturation function to obtain a back electromotive force estimated initial value;
step 2: adjusting sliding mode gain in the back electromotive force observer based on the saturation function through a variable universe fuzzy control algorithm;
Step 3, constructing a Lyapunov model by utilizing the actual value of the stator current and the observed value of the stator current, and performing stability analysis on the counter electromotive force observer model based on the saturation function;
Step 4, filtering the counter electromotive force observation initial value through a variable cutoff frequency filter to obtain a filtered counter electromotive force estimation value;
Step 5, calculating a rotor rotating speed estimated value through the filtered back electromotive force, and performing variable hysteresis compensation design on the rotor position to further calculate a rotor position estimated final value;
And 6, calibrating a rotor rotating speed estimated value through a speed loop PI controller, calibrating a rotor position estimated value through a current loop controller, calculating to obtain a voltage component under a synchronous rotating coordinate system, obtaining a voltage component under a two-phase static coordinate system through inverse Park coordinate transformation, inputting the voltage component to an inverter after Space Vector Pulse Width Modulation (SVPWM), converting the voltage into three-phase alternating current through the inverter, and supplying the three-phase alternating current to a motor, wherein finally, a motor control system forms a closed-loop control loop.
2. The optimized sensorless control method of a permanent magnet synchronous motor according to claim 1, characterized in that: in step 1, the voltage of the alpha axis under the two-phase static coordinate system is uαthe beta axis voltage under the two-phase static coordinate system is uβthe alpha axis current under the two-phase static coordinate system is iαThe beta axis current under the two-phase static coordinate system is iβ，iαAnd iβthe actual value of the stator current is taken as the actual value;
The Clark coordinate transformation matrix is as follows:
in the step 1, a sliding mode current observer model is constructed, and the specific expression is as follows:
In the formula (I), the compound is shown in the specification,the observed value of the alpha axis current under the two-phase static coordinate system is obtained;Is a beta axis current observed value under a two-phase static coordinate system; e.g. of the typeαEstimating an initial value for the counter electromotive force of the alpha axis under a two-phase static coordinate system; e.g. of the typeβEstimating an initial value for the beta axis counter electromotive force under a two-phase static coordinate system; r and LsRespectively a stator resistor and a stator inductor; psifIs a magnetic linkage; k is a radical ofsmoObtaining the sliding mode gain in the sliding mode observer; the sat saturation function is a switching function of the sliding-mode observer;
wherein sat is a saturation function as a switching function in the sliding mode current observer model, and is specifically defined as follows:
Wherein σ is a boundary layer of a saturation function;
In the step 1, the process of calculating the stator current observation value and the back electromotive force observation initial value of the motor under the two-phase static coordinate system is as follows:
adopting a saturation function as a switching function, and enabling the difference value of the current observed value and the actual current of the permanent magnet synchronous motor on the alpha axis under the two-phase static coordinate systemAnd the difference between the observed current and the actual current on the beta axisas the input value of the counter electromotive force observer, respectively calculating the observation initial value e of the counter electromotive force on the alpha axis under the two-phase static coordinate system by the counter electromotive force observer based on the saturation functionαAnd an initial value e for the observation of the back electromotive force on the beta axisβ；
When the control system slides on the sliding surface:
The initial value of the back emf estimate available is:
3. the optimized sensorless control method of a permanent magnet synchronous motor according to claim 1, characterized in that: the step 2 of adjusting the sliding mode gain in the back electromotive force observer based on the saturation function through the variable universe fuzzy control algorithm comprises the following specific steps:
Step 2.1, fuzzification operation processing is carried out on the input signal;
The variable-universe fuzzy controller is structurally a two-dimensional fuzzy controller, and two variable-universe fuzzy controllers are respectively established on an alpha axis and a beta axis of stator current under a two-phase static coordinate system; taking the stator current alpha axis variable domain fuzzy controller establishing process as an example, the stator current is used for enabling the permanent magnet synchronous motor to be in a two-phase static coordinate system, and the difference value of the current observed value on the alpha axis and the actual current is obtainedDefining the difference as e, and calculating and deriving a difference value change rate ec of an observed value of current and actual current on an alpha axis under a two-phase static coordinate system in unit time difference, wherein the calculation formula is as follows:
wherein e (t) is the difference value between the current observed value and the actual current on the alpha axis under the two-phase static coordinate system at the moment t; Δ t is the time difference;
Then, taking a difference value e between an alpha-axis current observed value and an actual current under a two-phase static coordinate system and a difference value change rate ec thereof as two input variables of the fuzzy controller, defining an initial domain range of the input variables of the fuzzy controller as { -15,15}, and defining an initial domain range of the output variables as { -1,1 };
After the input and output domains are transformed by adding the scaling factors alpha (x) and beta (x), the input variable domain range is { -alpha (x)15, alpha (x)15}, the output variable initial domain range is { -beta (x), beta (x) }, and the scaling factor function model of the input variable domain is as follows:
Wherein x is input variable of the fuzzy controller, lambda is a first proportional coefficient, and k1Is the second proportionality coefficient, k2is a third proportionality coefficient;
The scale factor function model of the output variable discourse domain is as follows:
Where x is the variable of the input quantity of the fuzzy controller, tau1Is a first exponential coefficient, τ2is a second exponential coefficient; epsilon is a positive infinitesimal small compensation value;
then, the fuzzy language of the input and output variables of the fuzzy controller is defined as follows:
{NB、NM、NZ、PM、PB}
the input variable membership function adopts a triangular membership function, and the output variable membership function adopts a normal form membership function; then, carrying out scale transformation on a difference value e and a difference value change rate ec of the current observed value on the alpha axis and the actual current under the two-phase static coordinate system to ensure that the difference values are transformed to respective domain ranges;
The actual input of the fuzzy controller isThe input amount is varied within a range ofUniverse of discourse [ x ]min,xmax]linear transformation is adopted, and the scale transformation expression is as follows:
wherein k is a scale factor, x0Input quantity of the discourse domain range;
Then converting the input quantity x into the discourse domain range0Fuzzy operation processing is carried out, the original input quantity is changed into fuzzy quantity and is represented by a corresponding fuzzy set, and a fuzzy operation function model is as follows:
x＝fz(x0)
Wherein x is0is the input clearness value; fz represents the fuzzy operator; x is a fuzzy set;
step 2.2, fuzzification reasoning is carried out according to the set fuzzy rule to obtain a fuzzy output quantity M;
The method adopts a Mamdani fuzzy inference method, which is essentially a synthetic inference method, and the ith rule of a rule base is expressed as:
“If x is A and y is B,then Z is C.”
wherein, X, Y and Z represent the fuzzy linguistic variables of the system state and the control quantity, X and Y represent the input quantity, Z represents the control quantity, A, B and C represent the fuzzy linguistic variables X, Y and Z on the domain X, Y and Z of the fuzzy linguistic variables respectively, and all the rules are combined together to form a rule base;
Wherein C is fuzzy output; the fuzzy relation of implications is as follows:
Ri＝(Ai×Bi)×Ci
Relationship between control rule bases can be regarded as yes or, namely, unionthen, the fuzzy relation mathematical formula implied by the whole rule base is as follows:
Fuzzy reasoning is carried out on the input quantity of the fuzzy controller according to a fuzzy control rule table formulated by experimental operation and control experience, and a reasoning formula is as follows:
Step 2.3, deblurring processing is carried out on the fuzzy output quantity M by adopting a weighted average method, and finally the output quantity u, namely the sliding mode gain k is obtainedsmo；
performing fuzzy resolving treatment on the fuzzy set M of the output quantity obtained by fuzzy reasoning, solving a weighted average value of each element in the fuzzy output quantity and the corresponding membership degree thereof by adopting a weighted average method to obtain a clear value Z, and converting the clear value Z in the domain range into an actual control quantity u, namely a sliding mode gain k through scale transformationsmoif Z varies within the range [ Z ]max，zmin]The actual controlled variable u varies within a range of [ u ]min，umax]The scale transformation mathematical expression formula is as follows:
Wherein k is a scale factor;
Finally, according to the dynamic difference value between the observed value of the stator current and the actual value of the current, obtaining the optimal sliding mode gain value k through variable universe fuzzy control adjustmentsmo。
4. The optimized sensorless control method of a permanent magnet synchronous motor according to claim 1, characterized in that: the Lyapunov model in step 3 is as follows:
wherein s isαThe difference value of the observed value and the actual value of the stator current on the alpha axis is obtained; sβThe difference value of the observed value and the actual value of the stator current on the beta axis is obtained;
And (3) carrying out derivation on the formula and substituting the derivation into a sliding mode current observer model based on a saturation function:
wherein R is stator resistance, Lsis the stator inductance, eαestimating an initial value, e, for the back electromotive force of the alpha axis in a two-phase stationary coordinate systemβestimating an initial value, k, for the back electromotive force of the beta axis in a two-phase stationary coordinate systemsmoObtaining the sliding mode gain in the sliding mode observer;
when in usewhen, i.e. as long as eα-ksmosat(sα) < 0 and eβ-ksmosat(sβ) The inequality < 0 is true, so the stability condition of the variable universe fuzzy sliding-mode observer is as follows:
ksmo＞max(|eα|,|eβ|)。
5. the optimized sensorless control method of a permanent magnet synchronous motor according to claim 1, characterized in that: the novel low-pass variable cut-off frequency filter in the step 4 is designed as follows:
In the formula, kfIs a positive number; k is a radical ofeIs a normal number; omegaeis a rotation speed control value;Is the cut-off frequency;
The filtered back emf estimate can be expressed as:
wherein the content of the first and second substances,For the estimation of the back emf of the alpha axis,Is an estimate of the beta-axis back-emf, zαFor containing counter-potential e on the alpha axisαSwitching signal, zβis beta axis containing counter potential eβand switching the signal.
6. the optimized sensorless control method of a permanent magnet synchronous motor according to claim 1, characterized in that: the initial value of the rotor position estimation in step 5 is set as:
wherein the content of the first and second substances,Estimating an initial value for the rotor position;
The rotor speed estimated value is:
The rotor position variable lag compensation is designed as follows:
wherein the content of the first and second substances,Is an estimated value of the rotor speed;cut-off frequency of the low-pass filter;Is a rotor position compensation value;
The final rotor position estimate is:
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