CN115459658B - A PMSM speed sensorless control method based on improved sliding mode observer - Google Patents
A PMSM speed sensorless control method based on improved sliding mode observer Download PDFInfo
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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
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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
- H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
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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
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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
- H02P21/18—Estimation of position or speed
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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
- H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
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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
- 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
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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
- 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
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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
- 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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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
- H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
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Abstract
本发明涉及一种基于改进滑模观测器的PMSM无速度传感器控制方法，包括如下步骤：如下步骤：步骤1：建立三相永磁同步电机的数学模型，根据所述数学模型设计传统滑模观测器，基于所述传统滑模观测器估计定子电流和反电动势；步骤2：基于饱和函数建立改进滑模观测器，对所述传统滑模观测器的趋近律进行改进；步骤3：采用低通滤波器和卡尔曼滤波器对所述改进滑模观测器观测到的结果进行二级滤波，得到转子角度信息本发明通过平滑切换的饱和函数解决传统滑模观测器的切换抖振问题；通过低通滤波器和卡尔曼滤波器组成的二级滤波解决了传统滑模观测器输出噪声的问题。采用本发明提出的控制方法得到的估算精度更高，鲁棒性更好。
The present invention relates to a PMSM speed sensorless control method based on an improved sliding mode observer, comprising the following steps: Step 1: Establishing a mathematical model of a three-phase permanent magnet synchronous motor, designing a traditional sliding mode observer according to the mathematical model, and estimating stator current and back electromotive force based on the traditional sliding mode observer; Step 2: Establishing an improved sliding mode observer based on a saturation function, calculating the reaching law of the traditional sliding mode observer Improvement; Step 3: Use a low-pass filter and a Kalman filter to perform secondary filtering on the results observed by the improved sliding mode observer to obtain rotor angle information The present invention solves the switching chattering problem of the traditional sliding mode observer through a smoothly switched saturation function; solves the output noise problem of the traditional sliding mode observer through a two-stage filter composed of a low-pass filter and a Kalman filter. The estimation accuracy obtained by the control method proposed by the present invention is higher and the robustness is better.
Description
Technical Field
The invention relates to the field of alternating current servo motor control, in particular to a PMSM (permanent magnet synchronous motor) speed-free sensor control method based on an improved sliding mode observer.
Background
The permanent magnet synchronous motor (PERMANENT MAGNET Synchronous Motor, PMSM) is widely applied in the field of alternating current servo due to the advantages of small volume, light weight, high efficiency and the like. Rotor position and speed signals are very important in PMSM systems, however, conventional mechanical sensors are susceptible to temperature, magnetic fields and other external disturbances, and are increasingly unable to meet the accuracy requirements of the system, so no speed sensor control begins to appear.
The control method of the speed-free sensor mainly comprises two types, namely a high-frequency signal injection method suitable for low speed, including a rotation high-frequency voltage signal method and a pulse high-frequency voltage signal method, and a motor fundamental frequency model-based method suitable for high speed, including a stator flux linkage estimation method, a model reference self-adaption method, a state observer estimation method, an artificial intelligence estimation method and the like. The sliding mode observer belongs to one of the state observers, and is based on the principle that back electromotive force is estimated through the input voltage and current, and then the position and the rotating speed information of the stator are calculated through the back electromotive force. The system has the advantages of simple structure, no dependence on a mathematical model of system accuracy, no influence of internal parameters and external interference, and strong robustness. The disadvantage is also the commonality of slip mode control, i.e. buffeting is difficult to eliminate. And the sliding mode observer itself cannot solve the problem of rotor position estimation at different rotational speeds.
Disclosure of Invention
The invention provides a PMSM (permanent magnet synchronous motor) speed-free sensor control method based on an improved sliding mode observer, which aims to solve the technical problems.
In order to solve the technical problems, the invention provides a PMSM speed-free sensor control method based on an improved sliding mode observer, which comprises the following steps:
Step 1, establishing a mathematical model of a three-phase permanent magnet synchronous motor, designing a traditional sliding mode observer according to the mathematical model, and estimating stator current and counter electromotive force based on the traditional sliding mode observer;
Step 2, establishing an improved sliding mode observer based on a saturation function, and approaching law of the traditional sliding mode observer Carrying out improvement;
Step 3, adopting a low-pass filter and a Kalman filter to carry out secondary filtering on the result observed by the improved sliding mode observer to obtain rotor angle information
Preferably, the approach lawThe method comprises the following steps:
ε=kωref,
where S is the slip plane, a is the boundary layer thickness, ω ref is the given rotational speed, k is the adjustable coefficient, sgn is the switching function, ε is the switching gain.
Preferably, step 2 further comprises constructing a lyapunov function, performing stability analysis on the improved sliding mode observer,
Wherein, L s is a stator inductance, R s is a stator resistance,I α、iβ is the component of the stator current alpha and beta axis under the two-phase stationary coordinate system,The estimated values of stator currents of alpha and beta axes are respectively, E α、Eβ is the electromotive force components of the alpha and beta axes respectively, epsilon is the gain,
When ε > max (E α,Eβ), the presence-reachable and stable conditions are satisfied.
Preferably, in step 3, the rotor angle information is obtained through calculation of an arctangent function after the secondary filtering
AndThe alpha and beta axis electromotive force component estimated values are respectively.
Preferably, the step 3 further comprises compensating the rotor angle information:
Wherein, Is the compensated rotor angle information and,Is an estimate of the angular velocity after the second-order filtering,Is the cut-off frequency estimate of the low pass filter.
Preferably, the angular velocity expression obtained after compensation is:
And phi f is a permanent magnet flux linkage.
Preferably, the low pass filter employs a variable cut-off frequency:
h and g are variable parameters.
Compared with the prior art, the PMSM speed-free sensor control method based on the improved sliding mode observer has the following advantages:
The method comprises the steps of designing a traditional sliding mode observer to estimate stator current and counter electromotive force according to a permanent magnet motor model, designing a new saturation function to replace a switching function, improving the control law of the sliding mode observer, and finally obtaining more accurate position information of a rotor through the secondary filtering of a low-pass filter and a Kalman filter with variable cut-off frequency. The rotating speed error of the improved sliding mode observer is smaller, and the estimation result is more accurate.
Drawings
FIG. 1 is a flow chart of a method of PMSM speedless sensor control based on an improved sliding mode observer in accordance with one embodiment of the present invention;
FIG. 2 is a schematic diagram of a conventional sliding mode observer according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a low-pass filter according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of the second order filtering according to an embodiment of the present invention;
FIG. 5 is a simulation block diagram of a permanent magnet synchronous motor according to an embodiment of the present invention;
FIG. 6 is a graph comparing back EMF of a conventional sliding mode observer with that of an embodiment of the present invention;
FIG. 7 is a graph comparing the rotational speed observation errors of a conventional sliding mode observer at a rated rotational speed according to an embodiment of the present invention;
FIG. 8 is a load torque speed diagram of an embodiment of the present invention;
fig. 9 is a torque waveform diagram of an embodiment of the present invention.
Detailed Description
In order to more fully describe the technical aspects of the invention, specific examples are set forth below to demonstrate technical effects, and it should be emphasized that these examples are intended to illustrate the invention and are not to be limiting.
The PMSM speed-free sensor control method based on the improved sliding mode observer provided by the invention, as shown in figure 1, comprises the following steps:
Step 1, establishing a mathematical model of a three-phase permanent magnet synchronous motor, designing a traditional sliding mode observer according to the mathematical model, and estimating stator current and counter electromotive force based on the traditional sliding mode observer;
Step 2, establishing an improved sliding mode observer based on a saturation function, and approaching law of the traditional sliding mode observer Carrying out improvement;
Step 3, adopting a low-pass filter and a Kalman filter to carry out secondary filtering on the result observed by the improved sliding mode observer to obtain rotor angle information
The method comprises the steps of designing a traditional sliding mode observer to estimate stator current and counter electromotive force according to a permanent magnet motor model, designing a new saturation function to replace a switching function, improving the control law of the sliding mode observer, and finally obtaining more accurate position information of a rotor through the secondary filtering of a low-pass filter and a Kalman filter with variable cut-off frequency. The rotating speed error of the improved sliding mode observer is smaller, and the estimation result is more accurate.
Specifically, it is first assumed that the permanent magnet synchronous motor is in an ideal state, and the following assumptions are made:
(1) The magnetomotive force of the permanent magnet is fixed;
(2) The back emf of the motor is sinusoidal;
(3) The motor rotor is not provided with a damping winding;
(4) The induced electromotive force and the air gap magnetic field of the motor are sinusoidal, and all harmonic waves of the magnetic field are not considered;
(5) The three-phase stator windings are symmetrically distributed in the stator space, the armature resistances in the three-phase windings are equal, and the inductances in the three-phase windings are also equal;
(6) Eddy current loss in a permanent magnet saturated motor of a motor core is not considered;
(7) The influence of the ambient temperature around the motor on the motor is not considered.
And establishing a state equation of voltage and flux linkage under a natural coordinate system under the condition that the condition is satisfied. The transformation into d-q coordinate system was studied. The model of the permanent magnet synchronous motor under the d-q coordinate system is as follows:
λq＝Lqiq (2)
λd＝Ldid+Lmdidf (3)
ωe＝npωr (4)
Wherein i d、iq is the d and q axis components of stator current, U d、Uq is the d and q axis components of stator voltage, R s is the stator resistance, L d、Lq is the d and q axis inductance of stator, omega e is the rotor electric angular velocity, omega r is the rotor mechanical angular velocity, lambda d、λq is the d and q axis stator flux linkage, L md is the d axis mutual inductance, i df is the d axis equivalent magnetizing current, and n p is the pole pair number.
The electromagnetic torque and mechanical torque equations of the permanent magnet synchronous motor are as follows:
Te＝3np[LmdIdfiq+(Ld-Lq)idiq]/2 (5)
Wherein T e is electromagnetic torque.
Because of lambda d＝λq, the electromagnetic torque equation of the motor can be simplified as:
The mathematical model of the permanent magnet synchronous motor in the alpha-beta static coordinate system is as follows:
The voltage equation is:
The flux linkage equation is:
The torque equation is:
Wherein i α and i β are stator currents of alpha and beta axes, and theta is an included angle between the N pole of the rotor and the a-phase axis; And Is the flux linkage component of the alpha and beta axes, and phi f is the permanent magnet flux linkage.
The sliding mode observer (Sliding mode observer, SMO) is developed from sliding mode control, inherits the advantages of sliding mode variable structure control, and the structure principle is shown in fig. 2.
From the formulae (7), (8) and (9):
the sliding mode observer builds a mathematical model from the errors of the reference current and the feedback current:
Wherein the method comprises the steps of The stator current estimated values of the alpha and beta axes are given, K is a constant, and sgn is a switching function.
Subtracting equations (11) and (12) from each other yields:
Wherein the method comprises the steps of
When the slip form enters the arrival phase, i.e. moves on the slip form face:
E α、Eβ is the alpha and beta axis electromotive force components, respectively.
The following problems exist from the schematic diagram of the conventional Sliding Mode Observer (SMO) and the formula of the control law:
(1) Conventional SMO uses a sign function (sign function) as a switching function, which is a discontinuous step function. When the system is switched at high frequency, serious system buffeting can occur, and the accuracy and stability of the control system are greatly reduced.
(2) In conventional SMO, a low pass filter is used to filter out high frequency harmonics in the back-emf signal. This delay is particularly pronounced in high speed motor control systems, since the use of a low pass filter can cause delay problems in the control system. In addition, the existence of the phase delay requires the control system to compensate the delay, which makes the calculation amount in the system large, increases the system load, reduces the system response speed and influences the timeliness of the control system.
(3) Conventional SMO uses an arctangent function to calculate the speed and position of the rotor, which has a large error.
Therefore, there is a need for improvements over conventional SMOs based on the foregoing.
The approach law of a sliding mode observer determines the ability of the observer to suppress buffeting. The sign function has the problem of discontinuous switching process, and is easy to cause instability of the system. The magnitude of the switching gain of the approach law determines both the approach speed and the magnitude of the buffeting after the arrival phase. The following novel approach laws are proposed for the two problems:
ε=kωref,
where S is the slip plane, a is the boundary layer thickness, ω ref is the given rotational speed, k is the adjustable coefficient, sgn is the switching function, ε is the switching gain.
The new saturation function is a continuous function and proper boundary layer thickness can reduce and improve overall buffeting, but can affect the accuracy of the system. The switching gain epsilon introduces a rotational speed and is adjusted by an adjustable coefficient k to achieve an adaptive effect.
Then constructing a Lyapunov function, performing stability analysis on the improved sliding mode observer,
Wherein, L s is a stator inductance, R s is a stator resistance,I α、iβ is the component of the stator current alpha and beta axis under the two-phase stationary coordinate system,The estimated values of stator currents of alpha and beta axes are respectively, E α、Eβ is the electromotive force components of the alpha and beta axes respectively, epsilon is the gain,
From this, it can be seen that the presence of the reachable and stable conditions can be satisfied as long as ε > max (E α,Eβ).
The results observed by the improved sliding mode observer still have a large amount of high-frequency harmonic components and noise, which affect the estimation of the rotor position, so that a filter is often adopted for processing. The input signal is directly filtered by a common filter, and then rotor position and speed information is obtained through rotor position estimation, as shown in fig. 3.
The Low pass filter (Low PASS FILTER, LPF) transfer function is:
wherein ω c is the cut-off frequency.
The expansion back electromotive force after LPF filters out the high-frequency harmonic wave is as follows:
And The alpha and beta axis electromotive force component estimated values are respectively.
The high-frequency harmonic component also changes because the rotational speed changes due to external interference during the operation of the motor. The fixed cut-off frequency does not meet the system requirements at this point, and therefore the fixed cut-off frequency low pass filter is replaced by a variable cut-off frequency.
Wherein the method comprises the steps ofIs the estimated value of the angular velocity after two-stage filtering, h and g are variable parameters, and the aim is to adjust the optimal cut-off frequency for different rotation speed occasions.
Although passing through the low pass filter, the system output still has a ripple component. The conventional back electromotive force observer still has overlarge error in estimating the rotor position by using an arctangent function, and cannot solve the problem of ripple components, so that a Kalman filter is adopted for secondary filtering, and the schematic diagram is shown in fig. 4.
The Kalman filter state equation is:
Wherein M is the gain of the Kalman filter, and the response speed and the vibration condition of the system can be influenced by the magnitude of M, so that the stability of the system can be ensured by selecting proper parameters.
In some embodiments, in step 3, the rotor angle information is obtained by calculation of an arctangent function after the second-order filtering
AndThe alpha and beta axis electromotive force component estimated values are respectively.
The rotor position must be angularly compensated because the characteristics of the secondary filtering necessarily cause a phase delay in the signal. Therefore, step 3 of the present invention further comprises compensating for the rotor angle information:
Wherein, Is the compensated rotor angle information and,Is an estimate of the angular velocity after the second-order filtering,Is an estimate of the cut-off frequency of the low pass filter.
Can be rewritten into 21
Bringing equation 23 to equation 9, the compensated angular velocity expression is:
In order to verify the correctness of the control method provided by the application, a simulation structure diagram of the permanent magnet synchronous motor is built in a simulink, as shown in fig. 5.
The specific parameters of the motor are stator resistance R=2.46 Ω, d-axis and q-axis inductances L d＝Lq =6.35 mH, and permanent magnet flux linkageMoment of inertia j=1.02 g·m 2, viscous friction coefficient b=0.0001, pole pair number p=4, rated rotational speed 3000r/min, inverter switching frequency 15kHz.
Given a motor speed of 1000r/min, a simulation waveform of the back EMF of the PMSM sliding mode observer is shown in FIG. 6. As can be seen from fig. 5, the conventional sliding mode observer is a shaded portion, and the improved sliding mode observer proposed by the present application is a solid line portion. The buffeting of the shadow part is larger, and the high-frequency components are more, so that the observation result of the improved sliding mode observer is higher in accuracy. FIG. 7 shows the rotational speed observation errors of two sliding mode observers at the rated rotational speed, and it can be seen that the rotational speed error of the conventional sliding mode observer is 20r/min, and the accuracy of the improved sliding mode observer is higher within 10 r/min. The rotation speed error and the counter electromotive force observation diagram are combined, so that the delay and the error exist in the traditional sliding mode observer because of a filter and an arctangent function, but the situation that the phase delay is improved by using the two-stage filtering in the improved sliding mode observer is improved, and the position error is also greatly improved.
To verify the anti-interference performance of the permanent magnet system, 10n·m of load torque was increased 0.5 seconds after the permanent magnet system was started in idle, resulting in fig. 8 and 9. Therefore, the invention has good anti-interference capability, the sudden change of load does not cause great influence on the system, and the system can be restored to a steady state within 0.02 s.
In summary, the PMSM (permanent magnet synchronous motor) speed-less sensor control method based on the improved sliding mode observer solves the problem of switching buffeting of the traditional sliding mode observer by smoothing a switching function and introducing self-adaptive switching gain, performs better filtering on noise output by the sliding mode observer through a low-pass filter with a variable cut-off frequency, then adds a Kalman filter to further remove ripple components, and performs angular velocity compensation to obtain more accurate observation results. Simulation results show that the control method provided by the invention has higher estimation accuracy and better robustness.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (6)
1. A PMSM speed-less sensor control method based on an improved sliding mode observer, comprising the steps of:
step 1, establishing a mathematical model of a three-phase permanent magnet synchronous motor, designing a sliding mode observer according to the mathematical model, and estimating stator current and counter electromotive force based on the sliding mode observer;
step 2, an improved sliding mode observer is established based on a saturation function, and an approach law S of the sliding mode observer is improved:
Step 3, adopting a low-pass filter and a Kalman filter to carry out secondary filtering on the result observed by the improved sliding mode observer to obtain rotor angle information
The approach lawThe method comprises the following steps:
ε=kωref,
where S is the slip plane, a is the boundary layer thickness, ω ref is the given rotational speed, k is the adjustable coefficient, sgn is the switching function, ε is the switching gain.
2. The PMSM speedless sensor control method according to claim 1, wherein step 2 further comprises constructing a lyapunov function, performing stability analysis on the improved sliding mode observer,
Wherein, L s is a stator inductance, R s is a stator resistance,I α、iβ is the component of the stator current alpha and beta axis under the two-phase stationary coordinate system,The estimated values of stator currents of alpha and beta axes are respectively, E α、Eβ is the electromotive force components of the alpha and beta axes respectively, epsilon is the gain,
When ε > max (E α,Eβ), the presence-reachable and stable conditions are satisfied.
3. The PMSM speed-free sensor control method based on the improved sliding mode observer according to claim 1, wherein in step 3, the rotor angle information is obtained through calculation of an arctangent function after the secondary filtering
AndThe alpha and beta axis electromotive force component estimated values are respectively.
4. The PMSM speed-less sensor control method based on an improved sliding mode observer according to claim 3, wherein said step 3 further comprises compensating for said rotor angle information:
Wherein, Is the compensated rotor angle information and,Is an estimate of the angular velocity after the second-order filtering,Is the cut-off frequency estimate of the low pass filter.
5. The PMSM speed-free sensor control method based on the improved sliding mode observer according to claim 4, wherein the angular velocity expression obtained after compensation is:
And phi f is a permanent magnet flux linkage.
6. The PMSM speedless sensor control method based on the improved sliding mode observer according to claim 1, wherein the low pass filter adopts a variable cut-off frequency:
h and g are variable parameters.
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