A sensorless speed positioning method and system for linear motor of a suspended electromagnetic propulsion system

Abstract

A sensorless velocity measurement and positioning method and system for a linear motor in a suspended electromagnetic propulsion system is disclosed. The positioning method includes: observing unmodeled disturbances in a coordinate system using a designed disturbance observer to obtain the observed disturbance values ​​in the coordinate system; converting the observed disturbance values ​​in the coordinate system into a coordinate system and inputting them into an improved adaptive superspiral sliding mode back EMF observer to obtain the back EMF signal in the coordinate system, which is then input into a third-order orthogonal normalized phase-locked loop to obtain the position and velocity of the superconducting permanent magnet synchronous linear motor; and designing an extended state observer to input the position and velocity of the superconducting permanent magnet synchronous linear motor obtained from the third-order orthogonal normalized phase-locked loop into the extended state observer to obtain the optimized position of the superconducting permanent magnet synchronous linear motor. This invention can operate effectively in a linear motor of a suspended electromagnetic propulsion system and has good sensorless control performance.

Description

Technical Field

[0001] This invention relates to the field of levitation positioning technology, and in particular to a sensorless speed measurement and positioning method and system for a linear motor in a levitation electromagnetic propulsion system. Background Technology

[0002] Suspended electromagnetic linear propulsion technology, with its advantages of high efficiency, strong controllability, and trackless operation in maglev mode, has broad prospects and value in cutting-edge fields such as aircraft ground testing, electromagnetic railguns, electromagnetic catapults, maglev rail transportation, aerospace assisted launch, and space applications. The superconducting permanent magnet synchronous linear motor is the core actuator of the electromagnetic propulsion system. The mover relies on the superconducting permanent magnet synchronous linear motor for precise start-stop and speed-changing motion control. The motor control performance is closely related to the real-time and accurate acquisition of the mover's position and velocity signals. Only by achieving precise velocity measurement and positioning can precise position and velocity control be achieved.

[0003] Speed ​​measurement and positioning of superconducting permanent magnet synchronous linear motors rely heavily on various sensors, such as photoelectric encoders and magnetic scales. In high-speed electromagnetic linear propulsion systems, the stator length of superconducting permanent magnet synchronous linear motors ranges from tens of meters to several kilometers. Deploying sensors along the entire line would drastically increase system complexity and cost. Furthermore, when the system operates at Mach-level ultra-high speeds, extremely high demands are placed on the response speed and accuracy of the sensors. The strong vibrations at ultra-high speeds and the large-scale, open engineering environment also impose stringent requirements on the installation reliability and construction accuracy of the sensor-based speed measurement and positioning system. Therefore, the use of such sensor solutions has significant limitations, restricting their widespread application in large-scale, high-dynamic environments. Summary of the Invention

[0004] This invention provides a sensorless speed measurement and positioning method and system for linear motors in a suspended electromagnetic propulsion system, in order to solve the technical problems mentioned in the background art.

[0005] To achieve the above objectives, the technical solution of the present invention is implemented as follows: This invention provides a sensorless speed measurement and positioning method for a linear motor in a suspended electromagnetic propulsion system, comprising the following steps: S1, based on Design a disturbance observer based on the current-voltage equations in the coordinate system, and use the disturbance observer to observe... Unmodeled perturbations in the coordinate system yield Perturbation observations in the coordinate system; S2, will Perturbation observations in coordinate system transformed into The coordinate system was then input into the improved adaptive superspiral sliding mode back EMF observer, and the observations were obtained. Back electromotive force signal in coordinate system; S3. Design a third-order orthogonal normalized phase-locked loop, with The back EMF signal in the coordinate system is used as input to obtain the position and velocity of the superconducting permanent magnet synchronous linear motor. S4. Design an extended state observer. Input the position and velocity of the superconducting permanent magnet synchronous linear motor obtained by the third-order orthogonal normalized phase-locked loop into the extended state observer to obtain the optimized position of the superconducting permanent magnet synchronous linear motor.

[0006] Furthermore, step S1 specifically includes the following steps: S11, Select Current and voltage equations in a coordinate system; S12, according to A disturbance observer is constructed using the current-voltage equations in a coordinate system. An incremental bilinear discretization design is then applied to the disturbance observer, resulting in the incremental bilinear discretized disturbance observer, including... q shaft down and d An incremental bilinear discretized perturbation observer under the axis; S13. Observe using the disturbance observer after incremental bilinear discretization. Unmodeled perturbations in the coordinate system yield Perturbation observations in the coordinate system.

[0007] Furthermore, in S1 The current and voltage equations in the coordinate system are as follows: ; in, , , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system d Current, voltage, and disturbances on the shaft; , , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system q Current, voltage, and disturbances on the shaft; These represent the resistance, inductance, flux linkage, and pole pitch of a superconducting permanent magnet synchronous linear motor; the symbols for these parameters are as follows. This represents the first derivative of the parameter; The expression for the disturbance observer in S12 is as follows: ; in, , These represent the superconducting permanent magnet synchronous linear motor observed using a perturbation observer. coordinate system d Estimated current and estimated disturbance on the axis; , These represent the superconducting permanent magnet synchronous linear motor observed using a perturbation observer. coordinate system q Estimated current and estimated disturbance on the axis; This indicates the speed of the superconducting permanent magnet synchronous linear motor; For the perturbation observer gain; In S12 q The expression for the sub-axis incremental bilinear discretized perturbation observer is as follows: ; in, T Represents the base time step of discretization. n To indicate the current time, n -1 represents the previous time step. n -2 indicates the previous time step.

[0008] Furthermore, step S2 specifically includes the following steps: S21, Select Current and voltage equations in coordinate system, based on Design an improved adaptive super-helical sliding mode back EMF observer based on the current-voltage equations in the coordinate system; The improvement of the adaptive superspiral sliding mode back EMF observer lies in the built-in same-frequency filter, which is used to configure parameters according to the historical state of the superconducting permanent magnet synchronous linear motor and the changes in operating conditions to be faced. S22. Stability analysis is performed on the improved adaptive superspiral sliding mode back EMF observer to obtain the stability conditions; S23, will The disturbance in the back EMF signal in the coordinate system is input into the improved adaptive superspiral sliding mode back EMF observer. The improved adaptive superspiral sliding mode back EMF observer calculates the following based on the stability condition: The back electromotive force signal in the coordinate system.

[0009] Furthermore, in S21 The current and voltage equations in the coordinate system are as follows: ; in, , , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system Current, voltage, and disturbances on the shaft; , , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system Current, voltage, and disturbances on the shaft; , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system , Back electromotive force on the axis; The expression for the improved adaptive superspiral sliding mode back EMF observer in S2 is as follows: ; in, , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system Estimated current and estimated disturbance on the axis; , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system Estimated current and estimated disturbance on the axis; Indicates estimated current With current The difference, and = - ; Indicates estimated current With current The difference, and = - ; t Indicates time; , These represent the gains of the improved adaptive superspiral sliding mode back EMF observer; Gain , The formula for calculation is: ; ; in, Indicates the first t-nT The estimated back EMF after passing through the same frequency filter at each basic time step; Indicates the desired speed; This represents the first user-defined function. 、 、c A constant that is greater than zero; First custom variable function The formula for calculation is: ; in, Indicates the desired acceleration; d A constant that is greater than zero; In S23 The formula for calculating the back electromotive force signal in the coordinate system is as follows: ; in, , They represent coordinate system , Back potential on the coordinate axes; Indicates estimated disturbance With disturbance The difference, and = - ; Indicates estimated disturbance With disturbance The difference, and = - .

[0010] Furthermore, the stability condition in S22 is as follows: ; ; in, It is a positive number slightly greater than 1.

[0011] Furthermore, step S3 specifically includes the following steps: S31. Design a third-order orthogonal normalized phase-locked loop; S32. Analyze and provide a parameter tuning method for the third-order orthogonal normalized phase-locked loop; then determine the parameters of the third-order orthogonal normalized phase-locked loop based on the parameter tuning method, and obtain the latest third-order orthogonal normalized phase-locked loop; S33, will The back EMF signal in the coordinate system is input into the latest third-order orthogonal normalized phase-locked loop to obtain the position and velocity of the superconducting permanent magnet synchronous linear motor.

[0012] Furthermore, the closed-loop transfer function of the third-order orthogonal normalized phase-locked loop in S31 is: ; in, This represents a third-order orthogonal normalized phase-locked loop; , , This represents three undetermined parameters: the differential coefficient, the proportional coefficient, and the integral coefficient. It is a complex variable representing the frequency in the Laplace transform domain; The parameter tuning method uses a zero-pole form open-loop transfer function to determine the parameters of a third-order orthogonal normalized phase-locked loop (PLL). These parameters include the amplitude frequency, phase margin, and open-loop coefficients of the third-order orthogonal normalized PLL at the open-loop cutoff frequency. Then, the three undetermined parameters can be calculated using the amplitude frequency, phase margin, and open-loop coefficients at the open-loop cutoff frequency. , , The expression for the open-loop transfer function in pole-zero form is as follows: ; in, Represent the open-loop transfer function; , They represent two constants respectively; Indicates the open-loop coefficient; The formulas for calculating the amplitude and phase margin at the open-loop cutoff frequency are as follows: ; in, Indicates amplitude and frequency; These represent the imaginary unit and frequency, respectively. ; Indicates the open-loop cutoff frequency; Indicates phase margin; In the formula, the cutoff frequency is... The formula for calculation is: ; in, , Let represent the second user-defined variable and the third user-defined variable, respectively, and their calculation formulas are as follows: ; Based on the above formula, and by selecting the phase margin... and open-loop cutoff frequency Then, the open-loop coefficients can be calculated. and The calculation formula is: ; in, The constant represents the constant when the zeros of a third-order orthogonal normalized phase-locked loop coincide. , The actual values ​​of both, at this point, are constants. , Equal, that is ; By combining the above formulas, we can obtain the following relationship: ; Three undetermined parameters can be calculated using this relationship. , , The following are examples: .

[0013] Furthermore, step S4 specifically includes the following steps: S41. Design a simple motion model of a superconducting permanent magnet synchronous linear motor, as follows: ; in, Position of the mover of the superconducting permanent magnet synchronous linear motor; Indicates an adjustable parameter; This represents the disturbance related to the speed and position of the superconducting permanent magnet synchronous linear motor. This represents a general description of other time variables in the disturbance; the sign of the parameter. This represents the second derivative of the parameter; S42. Design an extended state observer based on a simple motion model of a superconducting permanent magnet synchronous linear motor. The expression of the extended state observer is as follows: ; in, It is an adjustable parameter. This indicates the position of the output of the third-order orthogonal normalized phase-locked loop. The position is smoothed after passing through the extended state observer; Indicates positional error; Indicates the first process variable; Indicates the second process variable; , , These are the fourth to sixth user-defined variable functions, respectively, and satisfy the following conditions: = ; and All ; , , These represent the first to the third intermediate variables, respectively. , , These represent the fourth through sixth intermediate variables, respectively; the expression for the function of the fourth user-defined variable is: ; S43. Input the position and velocity of the superconducting permanent magnet synchronous linear motor into the extended state observer, and perform noise reduction and smoothing on the position of the superconducting permanent magnet synchronous linear motor to obtain the optimized position of the superconducting permanent magnet synchronous linear motor.

[0014] A second aspect of the present invention also provides a sensorless speed measurement and positioning system, including a superconducting permanent magnet synchronous linear motor, wherein the sensorless speed measurement and positioning system is configured to perform the above-described sensorless speed measurement and positioning method.

[0015] The beneficial effects of this invention are: This invention designs a sensorless speed measurement and positioning method for a linear motor in a suspended electromagnetic propulsion system. The method internally discloses the use of a disturbance observer, an improved adaptive superspiral sliding mode back EMF observer, a third-order orthogonal normalized phase-locked loop, and an extended state observer. These observers and the third-order orthogonal normalized phase-locked loop, while considering robustness, improve the speed measurement and positioning accuracy, high-order signal tracking capability, and tracking accuracy of the superconducting permanent magnet synchronous linear motor under sensorless operation.

[0016] Furthermore, this invention uses the current and voltage signals of a superconducting permanent magnet synchronous linear motor as input to calculate the position and velocity of the motor in real time, and then uses this information for the control of the motor. This method eliminates the need for position and velocity sensors required for the superconducting permanent magnet synchronous linear motor, reducing equipment costs. Simultaneously, the elimination of the need for position and velocity sensors also lowers the required construction precision, facilitating its widespread application in large-scale, high-dynamic environments. Attached Figure Description

[0017] Figure 1 This is a control block diagram of the sensorless speed measurement and positioning method in this invention; Figure 2 This is a control block diagram of the improved adaptive superspiral sliding mode back EMF observer in this invention; Figure 3 This is a control block diagram of the third-order orthogonal normalized phase-locked loop in this invention; Figure 4 This is a control block diagram of the extended state observer in this invention; Figure 5 This is a schematic diagram of the 14m linear propulsion system in an embodiment of the present invention; Figure 6 This is a schematic diagram of the 400m linear propulsion system in an embodiment of the present invention; Figure 7 This is a schematic diagram of the speed of the superconducting permanent magnet synchronous linear motor in an embodiment of the present invention; Figure 8 This is a schematic diagram illustrating the back potential observation effect of a conventional sliding mode observer (SMO) in an embodiment of the present invention; Figure 9 This is a schematic diagram of the back potential observation effect of a conventional superspiral sliding mode observer (STSMO) in an embodiment of the present invention; Figure 10 This is a schematic diagram of the back potential observation effect of a conventional adaptive superspiral sliding mode back potential observer (ASTSMO) in an embodiment of the present invention. Figure 11 This is a schematic diagram of the back potential observation effect of the improved adaptive superspiral sliding mode back potential observer (SFF-ASTSMO) in an embodiment of the present invention; Figure 12 This is a schematic diagram of the speed of the superconducting permanent magnet synchronous linear motor under the first working condition in an embodiment of the present invention; Figure 13 This is a schematic diagram showing the position of the superconducting permanent magnet synchronous linear motor under the first working condition in an embodiment of the present invention; Figure 14 This is a schematic diagram illustrating the error between the sensorless estimated position and the sensor measured position without using a disturbance observer in an embodiment of the present invention. Figure 15 This is a schematic diagram illustrating the error between the sensorless estimated position and the sensor measured position using a disturbance observer in an embodiment of the present invention. Figure 16 This is a schematic diagram of the stator coil winding of the superconducting permanent magnet synchronous linear motor in the 14m linear propulsion system of this invention. Figure 17 This is a schematic diagram of the speed of the superconducting permanent magnet synchronous linear motor under the second operating condition in an embodiment of the present invention; Figure 18 This is a schematic diagram showing the position of the superconducting permanent magnet synchronous linear motor under the second working condition in an embodiment of the present invention; Figure 19 This is a schematic diagram illustrating the estimated position error under the condition of mutual inductance asymmetry error in an embodiment of the present invention without a disturbance observer; Figure 20 This is a schematic diagram illustrating the estimated position error under mutual inductance asymmetry error in an embodiment of the present invention with a perturbation observer; Figure 21 This is a first schematic diagram illustrating the optimization effect of the extended state observer on the estimated position information in an embodiment of the present invention; Figure 22 This is a second schematic diagram illustrating the optimization effect of the extended state observer on the estimated position information in an embodiment of the present invention; Figure 23 This is a schematic diagram of the linear propulsion system in an embodiment of the present invention. Detailed Implementation

[0018] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many other different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0019] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0020] Reference Figures 1 to 4 This application provides a sensorless speed measurement and positioning method for a linear motor in a suspended electromagnetic propulsion system, comprising the following steps: S1, based on Design a disturbance observer (DO) based on the current and voltage equations in the coordinate system, and use the disturbance observer to observe... Unmodeled perturbations in the coordinate system yield Perturbation observations in the coordinate system; S2, will Perturbation observations in coordinate system transformed into The coordinate system was then input into the improved adaptive super-twisting sliding mode observer (SFF-ASTSMO), and observations were obtained. Back electromotive force signal in coordinate system; S3. Design a third-order orthogonal normalized phase-locked loop (TO-QPLL) to... The back EMF signal in the coordinate system is used as input to obtain the position and velocity of the superconducting permanent magnet synchronous linear motor. S4. Design an extended state observer (ESO) to input the position and velocity of the superconducting permanent magnet synchronous linear motor obtained by the third-order orthogonal normalized phase-locked loop into the extended state observer to obtain the optimized position of the superconducting permanent magnet synchronous linear motor.

[0021] Figure 1The diagram shows the control block diagram of the sensorless speed measurement and positioning method. Figure 1 The one-step delay compensation method refers to the following: since the mechanical constant is much smaller than the time constant, the current speed is approximately equal to the speed at the next moment. Therefore, the value obtained by multiplying the current speed by a control cycle can be considered as the position error caused by the actual one-step delay.

[0022] This invention designs a sensorless speed measurement and positioning method for a linear motor in a suspended electromagnetic propulsion system. The method internally discloses the use of a disturbance observer, an improved adaptive superspiral sliding mode back EMF observer, a third-order orthogonal normalized phase-locked loop, and an extended state observer. These observers and the third-order orthogonal normalized phase-locked loop, while considering robustness, improve the speed measurement and positioning accuracy, high-order signal tracking capability, and tracking accuracy of the superconducting permanent magnet synchronous linear motor under sensorless operation.

[0023] Furthermore, this invention uses the current and voltage signals of a superconducting permanent magnet synchronous linear motor as input to calculate the position and velocity of the motor in real time, and then uses this information for the control of the motor. This method eliminates the need for position and velocity sensors required for the superconducting permanent magnet synchronous linear motor, reducing equipment costs. Simultaneously, the elimination of the need for position and velocity sensors also lowers the required construction precision, facilitating its widespread application in large-scale, high-dynamic environments.

[0024] In some embodiments, S1 specifically includes the following steps: S11, Select Current and voltage equations in a coordinate system; S12, according to A disturbance observer is constructed using the current-voltage equations in a coordinate system. An incremental bilinear discretization design is then applied to the disturbance observer, resulting in the incremental bilinear discretized disturbance observer, including... q shaft down and d An incremental bilinear discretized perturbation observer under the axis; S13. Observe using the disturbance observer after incremental bilinear discretization. Unmodeled perturbations in the coordinate system yield Perturbation observations in the coordinate system.

[0025] In some embodiments, in S1 The current and voltage equations in the coordinate system are as follows: ; in, , , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system dCurrent, voltage, and disturbances on the shaft; , , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system q Current, voltage, and disturbances on the shaft; These represent the resistance, inductance, flux linkage, and pole pitch of a superconducting permanent magnet synchronous linear motor; the symbols for these parameters are as follows. This represents the first derivative of the parameter; The expression for the disturbance observer in S12 is as follows: ; in, , These represent the superconducting permanent magnet synchronous linear motor observed using a perturbation observer. coordinate system d Estimated current and estimated disturbance on the axis; , These represent the superconducting permanent magnet synchronous linear motor observed using a perturbation observer. coordinate system q Estimated current and estimated disturbance on the axis; This indicates the speed of the superconducting permanent magnet synchronous linear motor; This represents the gain of the perturbation observer.

[0026] The disturbance observer established in S12 is a continuous system, currently... dq The disturbance observer in the coordinate system includes flux linkage parameters. Inaccurate measurements of these parameters, or fluctuations in the flux linkage parameters caused by the distance between the mover and stator during the operation of the superconducting permanent magnet synchronous linear motor, will lead to inaccurate observation of the disturbance signal by the observer. Furthermore... dq Coordinate system observation perturbation transformation to The most crucial aspect of coordinate systems is maintaining consistency between the motor model in both coordinate systems. Since there is no flux linkage parameter in the motor model under the coordinate system, it is necessary to eliminate the influence of the flux linkage parameter. This invention adopts the method of incremental bilinear discretization design of the disturbance observer to eliminate the flux linkage.

[0027] Because bilinear discretization performs better at high frequencies, and more importantly, under bilinear discretization, this observer can target the current difference term. Adjust the parameters to reduce the current differential term. Regarding the impact on calculations, practice shows that if the current difference term... Without being weakened, the perturbation observer after incremental bilinear discretization is prone to divergence.

[0028] by q Taking the shaft as an example, the given q The incremental bilinear discretized perturbation observer under the axis is as follows. d The design methods for the shafts are consistent.

[0029] ; in, T Represents the base time step of discretization. n To indicate the current time, n -1 represents the previous time step. n -2 indicates the previous time step.

[0030] In some embodiments, S2 specifically includes the following steps: S21, Select Current and voltage equations in coordinate system, based on Design an improved adaptive super-helical sliding mode back EMF observer based on the current-voltage equations in the coordinate system; The improvement of the adaptive superspiral sliding mode back EMF observer lies in the built-in same-frequency filter (SFF), which is used to configure parameters based on the historical state of the superconducting permanent magnet synchronous linear motor and the changes in operating conditions to be faced. S22. Stability analysis is performed on the improved adaptive superspiral sliding mode back EMF observer to obtain the stability conditions; The specific process of stability analysis is as follows: a1. First, the expression for a common adaptive superspiral sliding mode back EMF observer is constructed, as follows: ; in, , This refers to the seventh and eighth user-defined variables; Represents the seventh user-defined variable The given quantity; , These represent the algorithm gains; Indicates time-varying perturbation; This represents the seventh user-defined variable and the given quantity. The difference, i.e. ; Represents the eighth user-defined variable and the given quantity The difference, i.e. ; a2. Take a positive definite function, as follows: ; in, Represents a positive definite function; x For the seventh user-defined variable Eighth custom variable A general term; a3. Design the first custom matrix And the first custom matrix The expression is as follows: ; in, , These represent the first custom matrix. The first and second row elements; a4. The first custom matrix Substituting the expression into the positive definite function, we obtain the rewritten positive definite function, as follows: ; By rewriting the modified positive definite function as a quadratic form, we obtain the positive definite function based on the quadratic form expression, as follows: ; a5. By observing the positive definite functions expressed in quadratic form, we can see that they are radially unbounded continuous positive definite functions, except... The external system is infinitesimal, but it will not remain at a certain point when the system fails to converge. At that point, according to the chain rule, using Differentiating the positive definite function based on the quadratic form along the trajectory of the expression of the ordinary adaptive superspiral sliding mode back EMF observer, we can obtain the expression for the derivative of the first custom matrix, as follows: ; a6. If time-varying disturbance satisfy: At the same time, constant ,satisfy Then the expression for the derivative of a positive definite function is: ; in, , , These represent the second, third, and fourth custom matrices, respectively; and their expressions are as follows: ; ; ; a7. When the second custom matrix When the function is positive definite, the derivative of the positive definite function is negative definite; based on this, the second custom matrix can be deduced. The positive definite condition is: ; exist Under the condition of the second custom matrix Positive definite conditions only apply when There is a solution, which is: ; This is the stability condition for a typical adaptive superspiral sliding mode back EMF observer; a8. By combining the stability conditions of the ordinary adaptive superspiral sliding mode back EMF observer with the motor model, the stability conditions of the improved adaptive superspiral sliding mode back EMF observer can be derived.

[0031] S23, will The disturbance in the back EMF signal in the coordinate system is input into the improved adaptive superspiral sliding mode back EMF observer. The improved adaptive superspiral sliding mode back EMF observer calculates the following based on the stability condition: The back electromotive force signal in the coordinate system.

[0032] In some embodiments, in S21 The current and voltage equations in the coordinate system are as follows: ; in, , , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system Current, voltage, and disturbances on the shaft; , , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system Current, voltage, and disturbances on the shaft; , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system , Back electromotive force on the axis; The expression for the improved adaptive superspiral sliding mode back EMF observer in S2 is as follows: ; in, , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system Estimated current and estimated disturbance on the axis; , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system Estimated current and estimated disturbance on the axis; Indicates estimated current With current The difference, and = - ; Indicates estimated current With current The difference, and = - ; t Indicates time; , These represent the gains of the improved adaptive superspiral sliding mode back EMF observer; Gain , The formula for calculation is: ; ; in, Indicates the first t-nT The estimated back EMF after passing through the same frequency filter at each basic time step; Indicates the desired speed; This represents the first user-defined function. 、 、c A constant that is greater than zero; , The value of is selected according to the stability condition derived below. c Used to correct for parameter-combined operating conditions, take the smaller value; The calculation formula is as follows: ; in, This is the resonant frequency of the single-frequency filter (SFF). The gain of the same-frequency filter (SFF); through the gain It can not only filter out the small amount of high-frequency signals and low-frequency harmonics that still exist in the ordinary super-helical sliding mode observer (STSMO), but also help to eliminate outliers in the adaptive parameters. The proposed parameter adaptive method can effectively avoid the introduction of noise and delay of the observation velocity itself in the traditional adaptive method. First custom variable function The formula for calculation is: ; in, Indicates the desired acceleration; d A constant that is greater than zero;d Used to correct for parameter-combined operating conditions, take the smaller value; In S23 The formula for calculating the back electromotive force signal in the coordinate system is as follows: ; in, , They represent coordinate system , Back potential on the coordinate axes; Indicates estimated disturbance With disturbance The difference, and = - ; Indicates estimated disturbance With disturbance The difference, and = - .

[0033] In some embodiments, the stability condition in S22 is specifically as follows: ; ; in, It is a positive number slightly greater than 1.

[0034] In some embodiments, S3 specifically includes the following steps: S31. Design a third-order orthogonal normalized phase-locked loop and its closed-loop transfer function. It can be observed from the closed-loop transfer function that the third-order orthogonal normalized phase-locked loop is of the third order. S32. Analyze and provide a parameter tuning method for the third-order orthogonal normalized phase-locked loop; then determine the parameters of the third-order orthogonal normalized phase-locked loop based on the parameter tuning method, and obtain the latest third-order orthogonal normalized phase-locked loop; S33, will The back EMF signal in the coordinate system is input into the latest third-order orthogonal normalized phase-locked loop to obtain the position and velocity of the superconducting permanent magnet synchronous linear motor.

[0035] In some embodiments, the closed-loop transfer function of the third-order orthogonal normalized phase-locked loop in S31 is: ; in, The closed-loop transfer function represents the third-order orthogonal normalized phase-locked loop; , , These represent three undetermined parameters, namely the differential coefficient, proportional coefficient, and integral coefficient; It is a complex variable representing the frequency in the Laplace transform domain; The parameter tuning method uses a zero-pole form open-loop transfer function to determine the parameters of a third-order orthogonal normalized phase-locked loop (PLL). These parameters include the amplitude frequency, phase margin, and open-loop coefficients of the third-order orthogonal normalized PLL at the open-loop cutoff frequency. Then, the three undetermined parameters can be calculated using the amplitude frequency, phase margin, and open-loop coefficients at the open-loop cutoff frequency. , , The expression for the open-loop transfer function in pole-zero form is as follows: ; in, Represent the open-loop transfer function; , They represent two constants respectively; Indicates the open-loop coefficient; The formulas for calculating the amplitude and phase margin at the open-loop cutoff frequency are as follows: ; in, Indicates amplitude and frequency; These represent the imaginary unit and frequency, respectively. ; Indicates the open-loop cutoff frequency; Indicates phase margin; In the formula, the cutoff frequency is... The formula for calculation is: ; in, , Let represent the second user-defined variable and the third user-defined variable, respectively, and their calculation formulas are as follows: ; Based on the above formula, and by selecting the phase margin... and open-loop cutoff frequency Then, the open-loop coefficients can be calculated. and The calculation formula is: ; in, The constant represents the constant when the zeros of a third-order orthogonal normalized phase-locked loop coincide. , The actual values ​​of both, at this point, are constants. , Equal, that is .

[0036] By combining the above formulas, we can obtain the following relationship: ; Three undetermined parameters can be calculated using this relationship. , , The following are examples: .

[0037] In some embodiments, S4 specifically includes the following steps: S41. Design a simple motion model of a superconducting permanent magnet synchronous linear motor, as follows: ; in, Position of the mover of the superconducting permanent magnet synchronous linear motor; Indicates an adjustable parameter; This refers to a superconducting permanent magnet synchronous linear motor. q Current on the shaft; This represents the disturbance related to the speed and position of the superconducting permanent magnet synchronous linear motor. This represents a general description of other time variables in the disturbance; the sign of the parameter. This represents the second derivative of the parameter; S42. Design an extended state observer based on a simple motion model of a superconducting permanent magnet synchronous linear motor. The expression of the extended state observer is as follows: ; in, It is an adjustable parameter. This indicates the position of the output of the third-order orthogonal normalized phase-locked loop. The position is smoothed after passing through the extended state observer; Indicates positional error; Indicates the first process variable; Indicates the second process variable; , , These are the fourth to sixth user-defined variable functions, respectively, and satisfy the following conditions: = ; and All ; , , These represent the first to the third intermediate variables, respectively. , , These represent the fourth through sixth intermediate variables, respectively; the expression for the function of the fourth user-defined variable is: ; S43. Input the position and velocity of the superconducting permanent magnet synchronous linear motor into the extended state observer, and perform noise reduction and smoothing on the position of the superconducting permanent magnet synchronous linear motor to obtain the optimized position of the superconducting permanent magnet synchronous linear motor.

[0038] This invention is applied to a 14m linear propulsion system (see...) Figure 5 and Figure 23 (as shown) and the 400m superconducting linear propulsion system (see...) Figure 6 Simulation and experimental verification were performed as shown in the figure; among them, Figure 23 This is a detailed structural diagram of the 14m linear propulsion system.

[0039] A1. Accurate observation of back EMF throughout the entire process of speed change and acceleration under heavy load: Figures 8 to 11 The paper demonstrates the simulation observation effect of the adaptive superspiral sliding mode back EMF observer on the back EMF of a superconducting permanent magnet synchronous linear motor operating under the variable speed condition including the variable acceleration stage shown in Figure 7. The improved adaptive superspiral sliding mode back EMF observer (SFF-ASTSMO) has the best observation effect on the back EMF compared with the ordinary sliding mode observer (SMO), the ordinary superspiral sliding mode observer (STSMO), and the ordinary adaptive superspiral sliding mode back EMF observer (ASTSMO).

[0040] Figures 12-15 The observation position error curve of a 400m linear propulsion system operating under variable speed planning with a maximum speed of 60m / s is shown. The curve shows that the present invention can effectively correct the position observation error under large loads during variable acceleration. The designed disturbance observer improves the dynamic performance of the present invention in this part.

[0041] A2. Accurate observation of mover position when parameter mismatch exists; Due to the modular installation of the coils in the 14m linear propulsion system, the stator of the superconducting permanent magnet synchronous linear motor exhibits asymmetric mutual inductance parameters, such as... Figure 16 ,from Figure 16 As can be seen from this, under this winding method, the overlapping areas of phases AC and BC are equal and greater than the overlapping area of ​​phase AB, which results in the mutual inductance amplitude between phases AC and BC being greater than the mutual inductance amplitude between phase AB.

[0042] However, the improved adaptive super-helical sliding mode back EMF observer (SFF-ASTSMO) is based on a mutual inductance symmetric model. Related studies have shown that this degree of parameter mismatch in current motors leads to an increase in the observation position error as the current increases. Figures 17 to 20The observation position error curves of the 14m linear propulsion system under uniform acceleration planning with a maximum speed of 5.6m / s are shown. The curves show that the designed sensorless algorithm can effectively correct the position observation error when there is mutual inductance parameter mismatch, and the designed disturbance observer can effectively compensate for the error caused by mutual inductance mismatch.

[0043] Figure 21 and Figure 22 The paper presents the optimization effect of the extended state observer on the position signal output by the PLL in this invention, with and without an increasing error relative to the sensor measurement position of the motor output from the third-order orthogonal normalized phase-locked loop. As clearly shown in the figure, in both cases, the extended state observer significantly reduces the oscillation amplitude of harmonic signals in the position signal obtained from the third-order orthogonal normalized phase-locked loop, decreasing it from approximately 5 cm to around 2 cm. The designed extended state observer can effectively suppress high-frequency noise over a wide frequency range, while simultaneously reducing the amplitude of low-frequency harmonic signals present in the original position signal, thus improving position accuracy.

[0044] A second aspect of the present invention also provides a sensorless speed measurement and positioning system, including a superconducting permanent magnet synchronous linear motor, wherein the sensorless speed measurement and positioning system is configured to perform the above-described sensorless speed measurement and positioning method.

[0045] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A sensorless speed measurement and positioning method for a linear motor in a suspended electromagnetic propulsion system, characterized in that, Includes the following steps: S1, based on Design a disturbance observer based on the current-voltage equations in the coordinate system, and use the disturbance observer to observe... Unmodeled perturbations in the coordinate system yield Perturbation observations in the coordinate system; S2, will Perturbation observations in coordinate system transformed into The coordinate system was then input into the improved adaptive superspiral sliding mode back EMF observer, and the observations were obtained. Back electromotive force signal in coordinate system; S3. Design a third-order orthogonal normalized phase-locked loop, with The back EMF signal in the coordinate system is used as input to obtain the position and velocity of the superconducting permanent magnet synchronous linear motor. S4. Design an extended state observer. Input the position and velocity of the superconducting permanent magnet synchronous linear motor obtained by the third-order orthogonal normalized phase-locked loop into the extended state observer to obtain the optimized position of the superconducting permanent magnet synchronous linear motor.

2. The sensorless speed measurement and positioning method for a linear motor in a suspended electromagnetic propulsion system according to claim 1, characterized in that, S1 specifically includes the following steps: S11, Select Current and voltage equations in a coordinate system; S12, according to A disturbance observer is constructed using the current-voltage equations in a coordinate system. An incremental bilinear discretization design is then applied to the disturbance observer, resulting in the incremental bilinear discretized disturbance observer, including... q shaft down and d An incremental bilinear discretized perturbation observer under the axis; S13. Observe using the disturbance observer after incremental bilinear discretization. Unmodeled perturbations in the coordinate system yield Perturbation observations in the coordinate system.

3. The sensorless speed measurement and positioning method for a linear motor in a suspended electromagnetic propulsion system according to claim 2, characterized in that, In S1 The current and voltage equations in the coordinate system are as follows: ； in, , , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system d Current, voltage, and disturbances on the shaft; , , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system q Current, voltage, and disturbances on the shaft; These represent the resistance, inductance, flux linkage, and pole pitch of a superconducting permanent magnet synchronous linear motor; the symbols for these parameters are as follows. This represents the first derivative of the parameter; The expression for the disturbance observer in S12 is as follows: ； in, , These represent the superconducting permanent magnet synchronous linear motor observed using a perturbation observer. coordinate system d Estimated current and estimated disturbance on the axis; , These represent the superconducting permanent magnet synchronous linear motor observed using a perturbation observer. coordinate system q Estimated current and estimated disturbance on the axis; This indicates the speed of the superconducting permanent magnet synchronous linear motor; For the perturbation observer gain; In S12 q The expression for the sub-axis incremental bilinear discretized perturbation observer is as follows: ； in, T Represents the base time step of discretization. n To indicate the current time, n -1 represents the previous time step. n -2 indicates the previous time step.

4. The sensorless speed measurement and positioning method for a linear motor in a suspended electromagnetic propulsion system according to claim 3, characterized in that, S2 specifically includes the following steps: S21, Select Current and voltage equations in coordinate system, based on Design an improved adaptive super-helical sliding mode back EMF observer based on the current-voltage equations in the coordinate system; The improvement of the adaptive superspiral sliding mode back EMF observer lies in the built-in same-frequency filter, which is used to configure parameters according to the historical state of the superconducting permanent magnet synchronous linear motor and the changes in operating conditions to be faced. S22. Stability analysis is performed on the improved adaptive superspiral sliding mode back EMF observer to obtain the stability conditions; S23, will The disturbance in the back EMF signal in the coordinate system is input into the improved adaptive superspiral sliding mode back EMF observer. The improved adaptive superspiral sliding mode back EMF observer calculates the following based on the stability condition: The back electromotive force signal in the coordinate system.

5. The sensorless speed measurement and positioning method for a linear motor in a suspended electromagnetic propulsion system according to claim 4, characterized in that, In S21 The current and voltage equations in the coordinate system are as follows: ； in, , , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system Current, voltage, and disturbances on the shaft; , , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system Current, voltage, and disturbances on the shaft; , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system , Back electromotive force on the axis; The expression for the improved adaptive superspiral sliding mode back EMF observer in S2 is as follows: ； in, , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system Estimated current and estimated disturbance on the axis; , These represent the superconducting permanent magnet synchronous linear motor in... coordinate system Estimated current and estimated disturbance on the axis; Indicates estimated current With current The difference, and = - ; Indicates estimated current With current The difference, and = - ; t Indicates time; , These represent the gains of the improved adaptive superspiral sliding mode back EMF observer; Gain , The formula for calculation is: ； ； in, Indicates the first t-nT The estimated back EMF after passing through the same frequency filter at each basic time step; Indicates the desired speed; This represents the first user-defined function. 、 、c A constant that is greater than zero; First custom variable function The formula for calculation is: ； in, Indicates the desired acceleration; d A constant that is greater than zero; In S23 The formula for calculating the back electromotive force signal in the coordinate system is as follows: ； in, , They represent coordinate system , Back potential on the coordinate axes; Indicates estimated disturbance With disturbance The difference, and = - ; Indicates estimated disturbance With disturbance The difference, and = - .

6. The sensorless speed measurement and positioning method for a linear motor in a suspended electromagnetic propulsion system according to claim 5, characterized in that, The stability conditions in S22 are as follows: ； ； in, It is a positive number slightly greater than 1.

7. A sensorless speed measurement and positioning method for a linear motor in a suspended electromagnetic propulsion system according to claim 6, characterized in that, S3 specifically includes the following steps: S31. Design a third-order orthogonal normalized phase-locked loop; S32. Analyze and provide a parameter tuning method for the third-order orthogonal normalized phase-locked loop; then determine the parameters of the third-order orthogonal normalized phase-locked loop based on the parameter tuning method, and obtain the latest third-order orthogonal normalized phase-locked loop; S33, will The back EMF signal in the coordinate system is input into the latest third-order orthogonal normalized phase-locked loop to obtain the position and velocity of the superconducting permanent magnet synchronous linear motor.

8. A sensorless speed measurement and positioning method for a linear motor in a suspended electromagnetic propulsion system according to claim 7, characterized in that, The closed-loop transfer function of the third-order orthogonal normalized phase-locked loop in S31 is: ； in, This represents a third-order orthogonal normalized phase-locked loop; , , This represents three undetermined parameters: the differential coefficient, the proportional coefficient, and the integral coefficient. It is a complex variable representing the frequency in the Laplace transform domain; The parameter tuning method uses a zero-pole form open-loop transfer function to determine the parameters of a third-order orthogonal normalized phase-locked loop (PLL). These parameters include the amplitude frequency, phase margin, and open-loop coefficients of the third-order orthogonal normalized PLL at the open-loop cutoff frequency. Then, the three undetermined parameters can be calculated using the amplitude frequency, phase margin, and open-loop coefficients at the open-loop cutoff frequency. , , The expression for the open-loop transfer function in pole-zero form is as follows: ； in, Represent the open-loop transfer function; , They represent two constants respectively; Indicates the open-loop coefficient; The formulas for calculating the amplitude and phase margin at the open-loop cutoff frequency are as follows: ； in, Indicates amplitude and frequency; These represent the imaginary unit and frequency, respectively. ; Indicates the open-loop cutoff frequency; Indicates phase margin; In the formula, the cutoff frequency is... The formula for calculation is: ； in, , Let represent the second user-defined variable and the third user-defined variable, respectively, and their calculation formulas are as follows: ； Based on the above formula, and by selecting the phase margin... and open-loop cutoff frequency Then, the open-loop coefficients can be calculated. and The calculation formula is: ； in, The constant represents the constant when the zeros of a third-order orthogonal normalized phase-locked loop coincide. , The actual values ​​of both, at this point, are constants. , Equal, that is ; By combining the above formulas, we can obtain the following relationship: ； Three undetermined parameters can be calculated using this relationship. , , The following are examples: 。 9. A sensorless speed measurement and positioning method for a linear motor in a suspended electromagnetic propulsion system according to claim 8, characterized in that, S4 specifically includes the following steps: S41. Design a simple motion model of a superconducting permanent magnet synchronous linear motor, as follows: ； in, Position of the mover of the superconducting permanent magnet synchronous linear motor; Indicates an adjustable parameter; This represents the disturbance related to the speed and position of the superconducting permanent magnet synchronous linear motor. This represents a general description of other time variables in the disturbance; the sign of the parameter. This represents the second derivative of the parameter; S42. Design an extended state observer based on a simple motion model of a superconducting permanent magnet synchronous linear motor. The expression of the extended state observer is as follows: ； in, It is an adjustable parameter. This indicates the position of the output of the third-order orthogonal normalized phase-locked loop. The position is smoothed after passing through the extended state observer; Indicates positional error; Indicates the first process variable; Indicates the second process variable; , , These are the fourth to sixth user-defined variable functions, respectively, and satisfy the following conditions: = ; and All ; , , These represent the first to the third intermediate variables, respectively. , , These represent the fourth through sixth intermediate variables, respectively; the expression for the function of the fourth user-defined variable is: ； S43. Input the position and velocity of the superconducting permanent magnet synchronous linear motor into the extended state observer, and perform noise reduction and smoothing on the position of the superconducting permanent magnet synchronous linear motor to obtain the optimized position of the superconducting permanent magnet synchronous linear motor.

10. A sensorless speed measurement and positioning system, characterized in that, The system includes a superconducting permanent magnet synchronous linear motor, and a sensorless speed measurement and positioning system is configured to perform the sensorless speed measurement and positioning method according to any one of claims 1 to 9.

Images