SRM non-inductive control method based on self-adaptive super-spiral sliding-mode observer

Abstract

The invention provides an SRM (switched reluctance motor) non-inductive control method based on a self-adaptive superspiral sliding-mode observer, and the method comprises the following steps: obtaining a phase current, a phase voltage and a rotor position estimation value of a switched reluctance motor, calculating a phase flux linkage value according to the phase current and the phase voltage, obtaining an estimated phase current value according to the phase flux linkage value and the rotor position estimation value, and calculating the phase flux linkage value according to the estimated phase current value. According to a circuit equation, a mechanical equation and an estimated phase current value of the switched reluctance motor, a sliding mode surface function of the super-spiral sliding mode observer is constructed, and according to the sliding mode surface function, the super-spiral sliding mode observer is constructed by adopting a second-order sliding mode reaching law to estimate the rotor position of the switched reluctance motor. And after the super-spiral sliding-mode observer is simplified, compensation is carried out to obtain a compensated super-spiral sliding-mode observer, the compensated super-spiral sliding-mode observer is adopted to estimate the rotating speed and the position of the switched reluctance motor, and an estimation result is further optimized in combination with adaptive control. And the robustness, the accuracy and the dynamic performance of the position estimation of the switched reluctance motor are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of motor control, and particularly relates to an SRM non-inductive control method based on an adaptive super-spiral sliding mode observer. BACKGROUND

[0002] Switched Reluctance Mechine (SRM) is increasingly applied to various occasions due to its simple structure, high fault tolerance, large power density, high efficiency and easy four-quadrant control. The torque of SRM is derived from the minimum reluctance tendency of the rotor magnetic pole and the stator winding magnetic field. The corresponding stator winding must be energized according to the real-time position of the rotor in a specific angle range. If the commutation time is inaccurate, the torque ripple will increase, the efficiency will decrease, and even the motor will lose step. Therefore, the SRM control has a high requirement for the rotor position closed loop. In actual application, a mechanical position sensor is usually selected to detect the position, which increases the complexity of the control system and makes the simple structure of SRM unattractive. At the same time, the position sensor is sensitive to changes in external environmental parameters, and the transmission accuracy is easily affected by factors such as temperature and electromagnetic interference, so the application range is greatly limited. Therefore, it is necessary to study the position sensorless control strategy.

[0003] Among the existing position sensorless control strategies, the state observer method combines the high dynamicity, full-speed adaptability and strong robustness of SRM control by fusing the model with real-time data without the need for physical sensors. It is the mainstream solution for balancing performance and cost in current position sensorless technology. Since the sliding mode observer algorithm has the advantages of adapting to dynamic load and relatively small calculation amount, it is the most commonly used among many state observer algorithms. However, the traditional sliding mode observer algorithm has the problems of large chattering and weak anti-interference ability. In view of these problems, some schemes propose a super-spiral sliding mode observer algorithm, but this method also has the problems of difficult starting, complex parameter adjustment and residual chattering.

[0004] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present application, and therefore can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0005] The embodiment of the application provides a SRM non-inductive control method based on an adaptive super-hyper-spiral sliding mode observer, which comprises the following steps: obtaining phase current, phase voltage and rotor position estimation value of a switched reluctance motor, calculating phase flux linkage value according to the phase current and the phase voltage, obtaining estimated phase current value according to the phase flux linkage value and the rotor position estimation value, constructing a sliding mode surface function of a super-hyper-spiral sliding mode observer according to a circuit equation, a mechanical equation and the estimated phase current value of the switched reluctance motor, estimating the rotor position of the switched reluctance motor by using a second-order sliding mode reaching law to construct the super-hyper-spiral sliding mode observer according to the sliding mode surface function, simplifying the super-hyper-spiral sliding mode observer to obtain a compensated super-hyper-spiral sliding mode observer, estimating the speed and position of the switched reluctance motor by using the compensated super-hyper-spiral sliding mode observer, and further optimizing the estimation result in combination with adaptive control.

[0006] Specifically, the method comprises the following steps: step 1: obtaining phase current and phase voltage of a switched reluctance motor, calculating corresponding phase flux linkage value according to a circuit equation , and inputting the calculated flux linkage value and motor rotor position estimation value (feedback position observed by the adaptive super-hyper-spiral sliding mode observer at a previous moment, that is, the feedback value is the position observed by the proposed observer at a previous moment, and the finally observed result is taken as input to complete a closed loop) of an observer into a two-dimensional interpolation data table constructed in advance, to obtain estimated phase current value under corresponding data of the motor; wherein is the resistance value of a phase winding; step 2: constructing a sliding mode surface function of a super-hyper-spiral sliding mode observer according to a circuit equation and a mechanical equation of the switched reluctance motor (wherein, is moment of inertia, is rotor mechanical angular velocity, is electromagnetic torque, is load torque, is damping coefficient, and t is time); wherein , , and are actual phase current value, estimated phase current value, estimated rotor position and phase inductance value of the switched reluctance motor; step 3: considering that the value of s is only used to determine positive and negative, and the signs of and are consistent, replacing with (The two functions are consistent in sign from the waveform), get the simplified sliding mode surface function Step 4: In order to solve the problem of limited convergence speed and severe chattering of traditional sliding mode observer, second-order sliding mode control is adopted, integral operation is introduced and nonlinear convergence law is used The super-spiral sliding mode observer is constructed to estimate the rotor position of switched reluctance motor, and the formula is ;

[0007] In the formula and are the gain values of the super-spiral sliding mode observer to be set, is the estimated rotor position of the motor (electrical angle position) by the observer is the sign function with s as the independent variable

[0008] Step 5: Let be the maximum absolute value of the disturbance of the observer, according to the convergence analysis of the super-spiral sliding mode observer, when and satisfy conditions, and can converge to zero in finite time, in order to simplify the parameter adjustment process, let , thus obtaining the simplified observer (combining the two undetermined parameters into one, simplifying the parameter adjustment difficulty), the formula is ;

[0009] In the formula is the gain value of the super-spiral sliding mode observer to be set

[0010] Step 6: In order to improve the robustness of speed estimation, make the observer still be able to observe the speed quickly with small error when there is deviation in the initial position, add a first-order term compensate the formula in step 5, the compensated formula is ,

[0011] that is θ ^ e = ∫ [ K 1 ( | s | sgn( s ) + ∫ sgn( s ) ) + K 2 sgn( s ) ] .

[0012] In the formula is the gain value of the super-spiral sliding mode observer to be set

[0013] Step 7: Estimate the speed of the switched reluctance motor, the formula is ; (the time derivative of the position is the speed)

[0014] In the formula is the estimated speed of the motor by the observer, at this time, although the rapidity and followability of speed estimation are improved due to the introduction of a first-order term, chattering is intensified, which needs to be further optimized

[0015] Step 8: On the basis of step 6 and step 7, adaptive control is introduced to dynamically adjust the observer output to cope with unknown or time-varying system uncertainties. By taking the real-time residual error of position and speed as a compensation value, the optimal value can be approximated online without upper bound information in the presence of unknown disturbances, thereby improving the accuracy and robustness of state estimation and optimizing the results of speed estimation. The adaptive calculation formula of the estimated rotor position and speed is ; that is, θ ˜ = ∫ [ ω ^ − ( θ ˜ e − θ ^ e ) l 1 ] ω ˜ = ∫ [ B J ω ^ − ( ω ˜ − ω ^ ) l 2 ]

[0016] Mechanism of action:

[0017] Let , When increases, the term increases, automatically enhancing the correction ability of the estimated position; when decreases, the term decreases, automatically weakening the correction ability of the estimated position. Similarly, when increases, the term automatically enhances the correction ability of the estimated position; when decreases, the term automatically weakens the correction ability of the estimated position. This adaptive law adjusts the error-driven correction term to dynamically match the uncertainty strength, enabling the observer to converge in position error and speed error without the upper bound of unknown disturbances, thereby improving the anti-disturbance ability.

[0018] In the formula, and are adaptive gain coefficients that need to be set, and are the motor rotor position and motor speed calculated adaptively, is the friction coefficient, is the moment of inertia.

[0019] Another embodiment provided by the application is that the two-dimensional interpolation data table is established by obtaining corresponding steady-state phase current data on discrete grid points covering a complete electrical period and an expected flux range, arranging the phase current data points into a two-dimensional regular grid, the row index of the grid corresponding to the rotor position, the column index of the grid corresponding to the flux, and the grid nodes storing corresponding current values. The grid is stored in the controller, and an interpolation algorithm is implemented, that is, for any given target flux and rotor position at runtime, the corresponding current value is obtained by automatically searching for the grid unit where it is located and using the current values of the surrounding four nodes for interpolation calculation.

[0020] Specifically, a two-dimensional interpolation data table is established The steps are as follows: ①obtaining basic data: through experimental measurement, corresponding steady-state phase current data is collected on discrete grid points covering a complete electrical cycle and a range of expected flux , that is, reaching a target flux at a specific rotor position , the required injected current;

[0021] ②constructing a regular grid: the collected data points are arranged into a two-dimensional regular grid, wherein the row index corresponds to the rotor position , the column index corresponds to the flux , and the grid node stores the corresponding current value ;

[0022] ③implementing an interpolation algorithm: the data table is stored in the controller, and an interpolation algorithm (bilinear interpolation) is implemented. For any given target flux and rotor position at runtime, the algorithm automatically finds the grid cell where it is located, and uses the current values of the surrounding four nodes to perform interpolation calculation to obtain the required current command .

[0023] Another embodiment provided by the application is that the super-spiral sliding mode observer is:

[0024]

[0025] wherein when , is bounded, and , so that the dominant term of the fast compensation current error , and the term outputs a smooth quantity through integration, so that the system can quickly converge to the sliding mode surface in a limited time , and the convergence process is basically free of chattering.

[0026] Another embodiment provided by the application is that the compensated super-spiral sliding mode observer is:

[0027]

[0028] wherein is a gain value of the super-spiral sliding mode observer to be set, is the rotor position estimated by the observer, t is time, is a compensation coefficient.

[0029] The application provides an SRM non-inductive control method based on an adaptive super-spiral sliding mode observer, which has at least the following beneficial effects:

[0030] (1) The application provides a polarization-related SRM non-inductive control method based on an adaptive super-spiral sliding mode observer, which can quickly converge from zero speed and accurately estimate the rotor position, simplify the parameter adjustment process, further reduce chattering, thereby improving the robustness, accuracy and dynamic performance of the switched reluctance motor position estimation.

[0031] (2) The polarization-related SRM non-inductive control method based on an adaptive super-spiral sliding mode observer of the application can quickly estimate the rotor position and speed from zero speed through adaptive super-spiral sliding mode control, reduce chattering, solve the problems of poor starting performance, complex parameter adjustment and residual chattering of traditional super-spiral sliding mode control, and still work normally when there is an initial position deviation, thereby improving the noise resistance and dynamic performance of the control system. Simulation verifies the effectiveness of the method, which has fast convergence speed and high robustness, greatly reduces noise while ensuring the excellent dynamic characteristics of the control system, and enhances the anti-interference ability of the control system.

[0032] (3) The application adds a fast compensation term to the observer and shifts the discontinuity to the high-order derivative of the control quantity through adaptive super-spiral sliding mode control, generates a continuous control signal under the premise of maintaining the robustness of the sliding mode, improves the convergence speed of the observer, makes the observer can quickly estimate the rotor position and speed from zero speed, reduces chattering, solves the problems of poor starting performance, complex parameter adjustment and residual chattering of traditional super-spiral sliding mode control, and still works normally when there is an initial position deviation (i.e. the convergence speed is fast enough to reach steady state within a few sampling periods), thereby improving the noise resistance and dynamic performance of the control system. Simulation verifies the effectiveness of the method, which has fast convergence speed and high robustness, greatly reduces noise while ensuring the excellent dynamic characteristics of the control system, and enhances the anti-interference ability of the control system. BRIEF DESCRIPTION OF DRAWINGS

[0033] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the application and, together with the description, serve to explain the principles of the application. It is apparent that the accompanying drawings in the following description are only some embodiments of the application, and other drawings can be obtained from these drawings without creative labor for those skilled in the art.

[0034] Fig. 1 The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the application and, together with the description, serve to explain the principles of the application. It is apparent that the accompanying drawings in the following description are only some embodiments of the application, and other drawings can be obtained from these drawings without creative labor for those skilled in the art.

[0035] Fig. 2 The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the application and, together with the description, serve to explain the principles of the application. It is apparent that the accompanying drawings in the following description are only some embodiments of the application, and other drawings can be obtained from these drawings without creative labor for those skilled in the art.

[0036] Fig. 3is a plot of the estimated speed of the motor of the present application versus the given speed at 500 rpm.

[0037] Fig. 4 is a plot of the error between the actual position and the estimated position of the motor rotor at zero initial speed for the conventional super-twisting sliding mode observer and the improved super-twisting sliding mode observer.

[0038] Fig. 5 is a plot of the estimated position of the motor rotor versus the actual position of the motor rotor at the initial position of the present application.

[0039] Fig. 6 is a plot of the estimated position of the motor rotor versus the actual position of the motor rotor at 500 rpm of the motor speed.

[0040] Fig. 7 is a plot of the actual speed versus the estimated speed of the motor of the present application when the speed of the motor is adjusted from 500 rpm to 1000 rpm. DETAILED DESCRIPTION

[0041] Example implementations will now be described more fully with reference to the accompanying drawings. Example implementations may, however, be implemented in many different forms and should not be construed as limited to the examples set forth herein; rather, these examples are provided so that this disclosure will be thorough and complete, and will fully convey the scope of example implementations to those skilled in the art. Features described in the description, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0042] In addition, the drawings are to be considered in all respects as illustrative and not restrictive; identical reference numerals have been used, where possible, to denote identical or similar features, and thus repetition of the description thereof will be omitted. Some of the blocks in the drawings are functional blocks that represent functions implemented by a piece of software or hardware rather than hardware as such. Various software elements can be stored in any type of computer-readable medium or media, which be read by a computer. One such computer-readable medium is a compact disc read-only memory (CD-ROM), a floppy disk, a RAM, and an ROM. The brain model program can be downloaded to the computer from an external data source via a computer network or a modem.

[0043] In the following, a SRM sensorless control method based on an adaptive super-twisting sliding mode observer proposed in the present example embodiment will be described in more detail.

[0044] The application provides a SRM non-inductive control method based on an adaptive hyper-spiral sliding mode observer, which comprises the following steps: obtaining phase current, phase voltage and rotor position estimation value of a switched reluctance motor, calculating phase flux linkage value according to the phase current and the phase voltage, obtaining estimated phase current value according to the phase flux linkage value and the rotor position estimation value, constructing a sliding mode surface function of a hyper-spiral sliding mode observer according to a circuit equation, a mechanical equation of the switched reluctance motor and the estimated phase current value, constructing a hyper-spiral sliding mode observer for estimating the rotor position of the switched reluctance motor according to the sliding mode surface function by using a second-order sliding mode reaching law, simplifying the hyper-spiral sliding mode observer and then performing compensation to obtain a compensated hyper-spiral sliding mode observer, estimating the speed and position of the switched reluctance motor by using the compensated hyper-spiral sliding mode observer, and further optimizing the estimation result in combination with adaptive control.

[0045] The technical scheme of the application is described in detail below with reference to the accompanying drawings and specific examples. Figs. 1 to 7 The motor used in the examples is a 1kW three-phase 12 / 8-pole switched reluctance motor.

[0046] Step one: obtaining phase current of the motor and phase voltage and calculating corresponding phase flux linkage value according to formula (1);

[0047] (1)

[0048] inputting the same to the motor rotor position estimation value fed back by the observer into a two-dimensional interpolation data table constructed in advance to obtain estimated phase current value under corresponding data of the motor .

[0049] wherein is the resistance value of a phase winding;

[0050] Step two: constructing a sliding mode surface function of a hyper-spiral sliding mode observer according to a circuit equation and a mechanical equation of the switched reluctance motor, as shown in formula (2):

[0051] (2)

[0052] wherein , , and are actual phase current value, estimated phase current value, estimated rotor position and phase inductance value of the switched reluctance motor;

[0053] Step three: considering that the value of the sliding mode surface s is only used to determine positive and negative, replacing with , the simplified sliding surface function is shown in equation (3):

[0054] (3)

[0055] Step four: using second-order sliding mode control, introducing integral operation and using nonlinear convergence law The super-spiral sliding mode observer is constructed to estimate the rotor position of the switched reluctance motor, and the formula is shown in equation (4):

[0056] (4)

[0057] In the formula, and are the gain values of the super-spiral sliding mode observer to be set, and are the estimated motor rotor position (electrical angle position) of the observer;

[0058] Step five: let be the maximum disturbance absolute value of the observer, and according to the convergence analysis of the super-spiral sliding mode observer, and satisfy , the simplified observer is shown in equation (5):

[0059] (5)

[0060] In the formula, is the gain value of the super-spiral sliding mode observer to be set;

[0061] Step six: adding a first-order term The formula in step five is compensated, and the compensated formula is shown in equation (6):

[0062] (6)

[0063] Step seven: estimating the speed of the switched reluctance motor, the formula is shown in equation (7):

[0064] (7)

[0065] In the super-spiral sliding mode control system shown in equation (8), the estimated rotor position Fig. 1 and the estimated motor speed are obtained by inputting the voltage value and the current value of the phase winding.

[0066] Step eight: constructing an adaptive control module according to equation (6) and equation (7), and the adaptive control module is shown in equation (9): Fig. 2 ​The rotor position estimated by inputting steps 6 and 7 in the adaptive control part shown and the estimated motor speed The corrected rotor position and motor speed are obtained through adaptive calculation

[0067] (8)

[0068] wherein and are adaptive gain coefficients to be set, and are the motor rotor position and motor speed obtained through adaptive calculation, is the friction coefficient, is the moment of inertia.

[0069] The range of values of each gain that stabilizes the super-hyperbolic sliding mode observer system is obtained through Lyapunov stability analysis, combined with online real-time tuning, and a set of super-hyperbolic sliding mode gains with stability and rapid convergence is ultimately obtained =243000, =4000 and adaptive gain =60000, =10000.

[0070] Fig. 3 The simulation results of the rotor estimated speed and the actual speed at 500 rpm are shown. It can be seen that the error of the rotor speed estimation after using the super-hyperbolic sliding mode optimization is about 1%, the system has high stability and accuracy, and can realize accurate estimation of the motor rotor speed. Fig. 4 The simulation results of the improved super-hyperbolic sliding mode and the traditional super-hyperbolic sliding mode in estimating the rotor position when the initial sliding mode speed is zero are shown. It can be seen that the traditional super-hyperbolic sliding mode has large chattering in the position estimation from zero speed, and the stability is poor, while the improved super-hyperbolic sliding mode can quickly close the loop from zero speed, significantly reduce the chattering, and has good steady-state performance. Fig. 5 The comparison chart of the estimated position and the actual position of the motor rotor when there is an initial position deviation is shown. It can be seen that the estimated position of the observer quickly converges to a state consistent with the actual position after a short disturbance, and has high robustness. Fig. 6 The simulation results of the estimated rotor position and the actual rotor position are shown. It can be seen that the accuracy of the rotor position estimation is very high, and the delay of the observer is within 0.0001s. Fig. 7 The simulation results of the rotor estimated speed and the actual speed when the motor speed changes are shown. When the motor speed increases from 500 rpm to 1000 rpm, the rotor speed estimated by the super-hyperbolic sliding mode observer can well follow the actual speed, and has excellent dynamic performance.

[0071] In addition, the terms "first", "second", etc. are used herein only to describe different instances, and do not imply or suggest relative importance or a number of the technical features indicated. Thus, the features defined with "first", "second" can explicitly or implicitly include one or more of the features. In the description of the embodiments of the present application, the meaning of "a plurality of" is two or more, unless otherwise explicitly and specifically limited.

[0072] In the description of the present application, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example" or "some examples" etc. means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present application, the illustrative description of the above terms is not necessarily directed to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in the present application.

[0073] The above is merely a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any skilled person in the art can easily think of various equivalent modifications or replacements within the technical scope disclosed in the present application, and these modifications or replacements should be included in the protection scope of the present application.

[0074] Other embodiments of the present application will be readily apparent to those skilled in the art upon considering the specification and practice of the application disclosed herein. The present application is intended to cover any variations, uses, or adaptations of the application following the general principles thereof and including such departures from the present disclosure as come within known use or custom in the art to which the application pertains.

Claims

1. A SRM sensorless control method based on adaptive super-twisting sliding mode observer, characterized in that, The method comprises the following steps: acquiring phase current, phase voltage and rotor position estimation value of the switched reluctance motor, calculating phase flux linkage value according to the phase current and the phase voltage, acquiring estimated phase current value according to the phase flux linkage value and the rotor position estimation value, constructing a sliding mode surface function of a super-helix sliding mode observer according to a circuit equation, a mechanical equation and the estimated phase current value of the switched reluctance motor, estimating the rotor position of the switched reluctance motor by the super-helix sliding mode observer constructed according to the sliding mode surface function and a second-order sliding mode reaching law, simplifying the super-helix sliding mode observer to obtain a compensated super-helix sliding mode observer, estimating the speed and position of the switched reluctance motor by the compensated super-helix sliding mode observer, and further optimizing the estimation result in combination with adaptive control.

2. The SRM sensorless control method based on adaptive super-twisting observer according to claim 1, wherein, The phase current, the phase current and the phase flux linkage value are related as follows: wherein, is the phase current, is the phase voltage, is the resistance value of the phase winding, is the phase flux linkage value.

3. The SRM sensorless control method based on adaptive super-twisting observer according to claim 2, wherein, The phase flux linkage value and the rotor position estimation value are used to acquire the estimated phase current value through a two-dimensional interpolation data table.

4. The SRM sensorless control method based on adaptive super-twisting observer according to claim 3, wherein, The two-dimensional interpolation data table is established by acquiring corresponding steady-state phase current data on discrete grid points covering a complete electrical period and an expected flux linkage range, arranging the phase current data points into a two-dimensional regular grid, wherein the row index of the grid corresponds to the rotor position, the column index of the grid corresponds to the flux linkage, and the grid nodes store corresponding current values, storing the grid in the controller, and implementing an interpolation algorithm, that is, for any given target flux linkage and rotor position at runtime, automatically finding the grid unit where it is located, and using the current values of the surrounding four nodes to perform interpolation calculation to obtain the corresponding current value.

5. The SRM sensorless control method based on adaptive super-twisting observer according to claim 4, wherein, The mechanical equation is: wherein is the moment of inertia, is the rotor mechanical angular velocity, is the electromagnetic torque, is the load torque, is the damping coefficient, t is time.

6. The SRM sensorless control method based on adaptive super-twisting observer according to claim 5, wherein, The sliding mode surface function s is: wherein , , and are actual phase current values, estimated phase current values, estimated rotor position and phase inductance values of the switched reluctance motor.

7. The SRM sensorless control method based on adaptive super-twisting observer according to claim 6, wherein, For the sliding mode surface function s, the following is used instead of the .

8. The SRM sensorless control method based on adaptive super-twisting observer according to claim 7, wherein, The super-helix sliding mode observer is: wherein and is a gain value of the super-twisting sliding mode observer to be set, is a rotor position of the motor estimated by the observer, is a sign function with s as an argument; wherein when is bounded, while is unbounded, the dominant term of the current error is quickly compensated , while the output of the integral term is a smooth quantity, so the system can quickly converge to the sliding surface in a finite time , and the convergence process is essentially chattering-free.

9. The SRM sensorless control method based on adaptive super-twisting observer of claim 8, wherein, The compensated super-helix sliding mode observer is: In the formula is the gain value of the super-spiral sliding mode observer to be set, is the motor rotor position estimated by the observer, t is time, is a compensation coefficient.

10. The SRM sensorless control method based on adaptive super-twisting observer according to any one of claims 1-9, characterized in that, The optimization comprises introducing adaptive control to the compensated super-helix sliding mode observer to dynamically adjust the observer output to cope with unknown or time-varying system uncertainties, and by taking the real-time residual error of the position and speed as a compensation value, the optimal value can be approached online without upper bound information in the case of unknown disturbance, thereby improving the accuracy and robustness of state estimation and optimizing the results of position and speed estimation.

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