Space repetitive disturbance learning based linear active disturbance rejection control method for suspension system

Abstract

The application provides a linear active disturbance rejection control method for a levitation system based on spatial repeated disturbance learning, which is used for a normal-conductance electromagnetic levitation system, and the method first decomposes a generalized total disturbance during operation of an electromagnetic levitation vehicle into spatial repeated disturbance and non-repeated residual disturbance; then aligns the residual disturbance estimated by LESO (Linear Extended State Observer) output after SRDL (Spatial Repeated Disturbance Learning) compensation to a unified line coordinate; constructs a spatial learning gain according to a local spatial correlation coefficient and an energy threshold of residual disturbance of adjacent operation batches, updates a spatial repeated disturbance atlas, and then introduces the atlas as a feedforward compensation into a control law of an observer, so that the observer estimates the residual disturbance after compensation; and the bandwidth of the observer is reduced after the atlas tends to be stable; the application can reduce the real-time observation burden of LESO on repeated disturbance by learning the repeated disturbance related to the spatial position under the conditions of a definite fixed load, a fixed experimental track and repeated operation, and introducing the repeated disturbance as a feedforward compensation into LADRC (Linear Active Disturbance Rejection Control).

Description

Technical Field

[0001] This invention relates to the field of control of conventional electromagnetic levitation experimental vehicles, and in particular to a linear active disturbance rejection control method for levitation systems based on spatial repetitive disturbance learning. Specifically, it relates to a single-point levitation linear active disturbance rejection control method that utilizes spatial repetitive information from a fixed experimental track. Background Technology

[0002] The conventional electromagnetic levitation vehicle achieves non-contact levitation through the attraction between the electromagnet and the ferromagnetic track, serving as a typical experimental platform for studying open-loop instability, model uncertainty, measurement noise, and external disturbance suppression in electromagnetic levitation systems. Single-levitation-point systems exhibit rapid gap dynamics and limited stability margins. Local geometric errors, installation errors, joint characteristics, and sensor reference variations in the track can cause fluctuations in the levitation gap and control current. When the experimental vehicle repeatedly runs along the same fixed track section, the aforementioned disturbances related to the track's spatial position may recur across different batches, while transient external disturbances, noise, and differences in operating conditions are non-repetitive components.

[0003] Currently, to address the issues of maglev suspension stability, load variation adaptability, and model parameter uncertainty, various technical solutions exist, including PID parameter adjustment, electromagnetic force feedback, sliding mode control, and neural network approximation. Chinese invention patent CN102303544B adjusts PID suspension parameters using load pressure signals; Chinese invention patent CN112297864B observes suspension force based on actual gap and current and generates control current; and Chinese invention patent application CN111806246A utilizes a second-order sliding mode surface and an online RBF neural network to improve adaptability to model uncertainties and external disturbances.

[0004] The above scheme mainly utilizes real-time measurements during the current operation for closed-loop adjustment. It fails to address the characteristic of the experimental vehicle repeatedly operating within the same fixed track section by establishing a disturbance map mechanism that aligns with uniform mileage coordinates, manages separately according to the operating direction, and selects learning intensity based on local spatial similarity and noise energy thresholds. To prevent non-repetitive noise from historical data from being incorporated into the feedforward compensation, it is also necessary to clarify the map initialization, effective operating range, stability criteria, bandwidth switching conditions, and map failure handling when the track, coordinates, and load change. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a linear active disturbance rejection control (ALDRC) method for levitation systems based on spatial repetitive disturbance learning. Under defined fixed loads, fixed experimental tracks, and repetitive operation conditions, the method learns repetitive disturbances related to spatial location and introduces them as feedforward compensation into LADRC to reduce the real-time observation burden of repetitive disturbances on LESO.

[0006] This invention proposes a linear active disturbance rejection control method for levitation systems based on spatial repetitive disturbance learning. By learning repetitive disturbances related to spatial position under specific fixed loads, fixed experimental tracks, and repetitive operation conditions, and introducing them as feedforward compensation into LADRC, the real-time observation burden of repetitive disturbances on LESO can be reduced.

[0007] The present invention adopts the following technical solution.

[0008] A linear active disturbance rejection control (ADR) method for levitation systems based on spatially repetitive disturbance learning (SRDL) is proposed for conventional electromagnetic levitation (EMS) systems. The method first decomposes the generalized total disturbance during the operation of the electromagnetic levitation vehicle into spatially repetitive disturbances and non-repetitive residual disturbances. Then, the residual disturbance estimate output by the observer (LESO) after SRDL compensation is aligned to a unified track coordinate system. A spatial learning gain is constructed based on the local spatial correlation coefficient and energy threshold of residual disturbances from adjacent operating batches to update the spatially repetitive disturbance map. This map is then used as feedforward compensation in the observer's control law, enabling the observer to primarily estimate the compensated residual disturbance. Finally, the observer bandwidth is reduced after the map stabilizes. This method is applicable to the field of maglev train control, effectively utilizing spatial prior information on fixed tracks, reducing the observation burden on LESO, and improving the stability and reliability of the levitation control system.

[0009] The control method learns repetitive disturbances related to the spatial position of the electromagnetic levitation vehicle under defined fixed load, fixed experimental track, and repetitive operation conditions, and introduces them as feedforward compensation into LADRC to reduce the real-time observation burden of LESO on repetitive disturbances. It is applied to a single-point levitation system of a conventional electromagnetic levitation vehicle using a fast current inner loop. In the levitation system, the electromagnetic levitation vehicle used to simulate a maglev train repeatedly runs on the same fixed experimental track section with unchanged track structure and line coordinate reference, and the spatial position along the track is provided by the positioning and mileage system. Preferably, an electromagnetic levitation vehicle with a fast current inner loop, a nominal single-point equivalent levitation mass of 13.5 kg, a rated levitation gap of 4 mm, and the ability to repeatedly run along the same fixed experimental track section and obtain position or mileage information is used.

[0010] The electromagnetic levitation system is a single-point levitation system for a conventional electromagnetic levitation vehicle, and the control method includes the following steps;

[0011] Step S1: Taking the single electromagnet-track suspension point of the normally conducting electromagnetic levitation vehicle as the control object, construct a nonlinear electromechanical coupling model, perform incremental linearization near the rated suspension operating point, and rewrite it into the LADRC second-order standard form under the condition of fast current inner loop.

[0012] Step S2: Decompose the generalized total disturbance of the outer ring of the suspension gap into repeating disturbances related to the spatial position of the fixed experimental track and non-repeating residual disturbances related to the running batch;

[0013] Step S3: Establish a spatial domain repetitive perturbation iterative learning mechanism: For the maglev train simulated by a conventional electromagnetic levitation vehicle in the first step... Disturbance observation data of LESO during the second run After forward-reverse low-pass filtering, it is mapped to the line spatial domain, at the position Select a local window, calculate the local spatial correlation coefficient and learning gain, and update the [number]th [window]. Spatial repetitive perturbation pattern of each run;

[0014] Step S4: Place the first The spatial repetitive disturbance map corresponding to each run is used as prior information of the fixed track and introduced into the LADRC observer prediction model and control law based on linear active disturbance rejection control to perform feedforward compensation for the repetitive disturbance, and the non-repetitive residual disturbance after compensation is estimated by LESO.

[0015] Step S1 specifically includes the following steps:

[0016] Step S11: Under ideal conditions, taking vertically downward as the positive direction, the vertical dynamic equation of the single-point suspension system is established as follows:

[0017] ,

[0018] ;

[0019] Among them, in the single-point suspension system of the conventional electromagnetic levitation vehicle, The mass of the electromagnet; For suspension gap; It is the acceleration due to gravity; It is electromagnetic attraction; The permeability of vacuum; The effective magnetic pole area of ​​the electromagnet; This represents the number of turns in the electromagnet coil. The coil current; The comprehensive electromagnetic force coefficient;

[0020] Step S12: Based on the characteristics of the electromagnet's winding circuit, establish the voltage and current equations as follows:

[0021] ,

[0022] ;

[0023] in, The voltage of the electromagnet; This is the equivalent resistance of the coil; This is the equivalent inductance of the coil;

[0024] Step S13: Based on steps S11-S12, establish a state-space model of the single-point suspension system, and at the equilibrium point... Linearization of the surrounding area yields:

[0025] ,

[0026] ;

[0027] in, The velocity is in the vertical direction; This is the gap value at the equilibrium point; This is the equilibrium point current value;

[0028] Step S14: The linearized dynamic equation of the outer ring of the suspension gap is obtained from step S13, and is expressed as follows:

[0029]

[0030] in, This represents the equivalent term calculated from linearization error, parameter perturbation, external line disturbance, non-ideal dynamics of the current loop, and unmodeled factors into the gap acceleration channel;

[0031] Let the equivalent control input of the outer loop of the gap be the current, and take the nominal input gain as... ,

[0032] The linearized dynamic equations can be rewritten in the second-order canonical form commonly used in LADRC as follows:

[0033]

[0034] in, To control the input quantity, i.e., the current quantity; This refers to the generalized total disturbance.

[0035] Step S2 specifically includes the following steps:

[0036] Step S21: Let the maglev train's first... The spatial position along the line during the second run is The line section is , Provided by the positioning and odometer system of the maglev train; the generalized total disturbance is decomposed into:

[0037]

[0038] in, For the first The equivalent disturbance components that repeatedly appear depending on the spatial location of the line during each operation; For the first Non-repetitive disturbances during the next run;

[0039] Step S22: The spatial repetition perturbation estimation map obtained before the next run is as follows: After introducing spatial repetition perturbation compensation, the residual perturbation that LESO needs to estimate can be expressed as:

[0040]

[0041] in, Repeatedly perturb the residuals of the unlearned space.

[0042] Step S3 specifically includes the following steps:

[0043] Step S31: The spatial repeating perturbation map is updated after each run. By performing forward-reverse low-pass filtering and spatial mapping using the positioning and mileage information provided by the maglev train's positioning and mileage system, the following results are obtained:

[0044]

[0045] in, For position The residual perturbation estimate at the corresponding location; It is a forward-reverse low-pass filter; These are repetitive items that should be learned; Non-repeating items that should not be learned;

[0046] Step S32: At position Select nearby local window Within that window, the first The estimated value of the spatial residual perturbation of the next run is , No. The estimated value of the spatial residual perturbation of the next run is , These are the spatial coordinates inside the window; both are essentially defined within... The continuous curve on the curve, since the actual residual estimated signal is bounded within a finite line interval after filtering and spatial interpolation, can be regarded as Hilbert space. The elements in the function space are used to measure the similarity between two curve segments using the inner product and norm in the function space.

[0047] for Two functions in and The local inner product and norm are as follows:

[0048] ,

[0049] ;

[0050] Let the normalized inner product of two local spatial signals be... This quantity has the same form as the cosine similarity in a finite-dimensional vector space, and is used to describe the directional consistency of two function curves within a local window; the larger its value, the more obvious the trend of the two curves changing in the same direction within the window; the smaller its value, the more likely the two curves lack a stable and consistent shape.

[0051] make , The local spatial correlation coefficient is defined as:

[0052]

[0053] Step S33: If the local spatial correlation coefficient is not directly used as a compensation quantity, but is used to generate a learning gain for spatial variation, and the correlation judgment is easily affected by noise when the local residual energy is too low, define the learning gain. exist or When it is 0, , Conversely, the learning gain is defined as:

[0054]

[0055] in, To achieve maximum learning gain; The threshold for repeatability determination; Let be a saturation function, defined as:

[0056]

[0057] but Its function is to determine whether the residual disturbance at a certain spatial location is learnable. The learning intensity at this location is further determined by the learning correction amount written into the spatial repeating perturbation map, which is then weighted by correlation. In summary, the update formula for the spatial repeating perturbation map is:

[0058]

[0059] Step S34: After the perturbation map has been fully learned, reduce the observer bandwidth to balance the contradiction between perturbation estimation and noise amplification.

[0060] The specific steps of step S4 are as follows:

[0061] Step S41: From the second-order model of the outer ring of the suspension gap established in step S1, it can be seen that the first... The system meets the requirements during the next runtime.

[0062]

[0063] As the number of batches increases Approaching step by step , The spatial repetition component in the model will be reduced, and the disturbance burden that LESO needs to estimate in real time will be reduced accordingly.

[0064] Step S42: Select observer state variables , , ,have to Then the continuously expanding state space of step S41 is described by the formula:

[0065]

[0066] in, , , , , , The nominal value used to control the input gain;

[0067] because The data still includes non-repetitive disturbances, learning residuals, parameter perturbations, non-ideal dynamics of the current loop, and unmodeled factors, making it difficult to obtain accurate analytical expressions. Therefore, the state variables of the observer are typically used. State variables of the controller Make an estimate;

[0068] The design of a linear extended state observer based on SRDL is as follows:

[0069]

[0070] in, , This is the estimated gap value; This is an estimated value for the gap speed; This is an estimate of the residual disturbance; , , , For observer gain, The observer bandwidth is used to adjust the state and residual perturbation estimation rate of LESO; LESO still corrects the state estimate by outputting observation errors, but its prediction model incorporates a spatially repeating perturbation estimation term, making... The estimated object is transformed into the compensated residual disturbance. ;

[0071] Set the desired gap as For setpoint control near the rated clearance, there are , ;

[0072] Intermediate control quantity Generated via proportional-derivative feedback:

[0073]

[0074] in, For proportional feedback gain; For differential feedback gain;

[0075] Considering the general form of trajectory tracking, we can extend it as follows:

[0076]

[0077] To make the gap acceleration approximately satisfy It is necessary to compensate for the spatial repetitive disturbances given by the SRDL map and the residual disturbance estimates given by LESO. The LADRC control law based on SRDL is designed as follows:

[0078] .

[0079] In the single-point levitation system of a conventional electromagnetic levitation vehicle, when track maintenance or structural adjustment, changes in the origin or mileage calibration of the line coordinates, changes in the correspondence of the running direction, abnormalities in the positioning system, or changes in the nominal single-point equivalent levitation mass, the control method freezes and clears the spatial repetitive disturbance spectrum in the affected direction, restores the high observer bandwidth, and re-completes the spectrum learning.

[0080] The control method is used for a fixed load condition where the nominal single-point equivalent suspended mass is fixed at 13.5 kg; in the fixed load condition, the trolley's running track is the same fixed experimental track section where the structural state and spatial coordinate reference remain unchanged between adjacent running batches; the control method's first... The trajectory used in this run for learning Within the corresponding learning interval, the data is continuous and monotonous. When the control method is used, the parking, reversing, positioning anomalies, and mileage jump intervals of the car do not participate in the map update. Spatial repetitive disturbance maps are established for the car's forward and reverse movement respectively.

[0081] When the normally conducting electromagnetic levitation vehicle is an experimental vehicle, the nominal single-point equivalent levitation mass of the experimental vehicle is... It weighs 13.5 kg and has a rated suspension gap. The equivalent resistance of the coil is 0.004 m. The equivalent inductance near the equilibrium point is 0.59 Ω. The overall electromagnetic force coefficient is 0.028 H. It is 5.5992 × 10⁻ 5 N·m² / A², gravitational acceleration g is taken as 9.8 m / s²; corresponding theoretical equilibrium current Approximately 6.15 A, nominal current input gain It is approximately -3.1877 m·s⁻²·A⁻¹.

[0082] This invention discloses a linear active disturbance rejection control (LADRC) method for a normally conducting (EMS) electromagnetic levitation system based on spatial repetitive disturbance learning (SRDL), relating to the field of maglev train levitation control. It is applicable to electromagnetic levitation vehicles that use a fast current inner loop, have a nominal single-point equivalent levitation mass of 13.5 kg, a rated levitation gap of 4 mm, and repeatedly run along the same fixed experimental track section, and can obtain position or mileage information. The method of this invention provides a solution to the problem that the levitation control system under the condition of repeated operation on a fixed line has a high dependence on LESO, and that LESO has an inherent contradiction between disturbance estimation lag and measurement noise amplification.

[0083] Compared with the prior art, the present invention has the following advantages and technical effects:

[0084] This invention addresses the repetitive spatial perturbation map of a normally conducting electromagnetic levitation vehicle operating under a fixed nominal single-point load of 13.5 kg, a rated gap of 4 mm, a fast current inner loop, and the same fixed experimental track section. It establishes a map managed according to the direction of operation. By employing zero-phase filtering, a unified spatial grid, local spatial similarity, an energy threshold based on a noise reference, and a clear map stability criterion, the risk of non-repetitive noise being learned is reduced. Furthermore, by dividing the work between map feedforward compensation and LESO residual perturbation estimation, the observer burden is reduced within the applicable boundaries. The map is reset when the track, coordinates, or load conditions change, preventing the continued use of failed priors for control. This method is clearly structured, highly adaptable, and helps reduce tracking errors in levitation control systems and improve the smoothness of control inputs, demonstrating significant engineering application value. Attached Figure Description

[0085] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0086] Appendix Figure 1 This is a schematic diagram of the single-point suspension system structure provided in an embodiment of the present invention;

[0087] Appendix Figure 2 This is a schematic diagram of the method flow provided in an embodiment of the present invention;

[0088] Appendix Figure 3This is a schematic diagram of the algorithm block provided in an embodiment of the present invention. Detailed Implementation

[0089] To make the objectives, technical solutions, scope of application, and parameter definitions of this invention clearer, the following description is based on the single-point levitation parameters of the laboratory conventional electromagnetic levitation vehicle and the accompanying drawings.

[0090] This embodiment uses a normally conducting electromagnetic levitation experimental trolley employing a fast current inner loop as an example. The trolley repeatedly runs along the same fixed experimental track section, and the positioning and odometer system can provide position data corresponding to the unified track coordinates. The single-point levitation outer loop adopts SRDL-LADRC: the spatial perturbation map only learns the residual perturbation components that stably repeat at the same track position in adjacent running batches, while non-repeating components are estimated in real time by LESO; maps are established for forward and reverse runs respectively.

[0091] As shown in Table 1, Figure 1 , Figure 2 and Figure 3 As shown, a linear active disturbance rejection control method for a suspension system based on spatial repetitive disturbance learning is presented. The specific implementation conditions and steps of this embodiment are as follows:

[0092] like Figure 1 As shown, a linear active disturbance rejection control (ADR) method for levitation systems based on spatially repetitive disturbance learning (SRDL) is proposed for conventional electromagnetic levitation (EMS) systems. The method first decomposes the generalized total disturbance during the operation of the electromagnetic levitation vehicle into spatially repetitive disturbances and non-repetitive residual disturbances. Then, the residual disturbance estimate output by the observer (LESO) after SRDL compensation is aligned to a unified line coordinate system. A spatial learning gain is constructed based on the local spatial correlation coefficient and energy threshold of residual disturbances from adjacent operating batches to update the spatially repetitive disturbance map. This map is then used as feedforward compensation in the observer's control law, enabling the observer to primarily estimate the compensated residual disturbance. Finally, the observer bandwidth is reduced after the map stabilizes. This method is applicable to the field of maglev train control, effectively utilizing spatial prior information on fixed lines, reducing the observation burden on LESO, and simultaneously improving the stability and reliability of the levitation control system.

[0093] The control method learns repetitive disturbances related to the spatial position of the electromagnetic levitation vehicle under defined fixed load, fixed experimental track, and repetitive operation conditions, and introduces them as feedforward compensation into LADRC to reduce the real-time observation burden of LESO on repetitive disturbances. It is applied to a single-point levitation system of a conventional electromagnetic levitation vehicle using a fast current inner loop. In the levitation system, the electromagnetic levitation vehicle used to simulate a maglev train repeatedly runs on the same fixed experimental track section with unchanged track structure and line coordinate reference, and the spatial position along the track is provided by the positioning and mileage system. Preferably, an electromagnetic levitation vehicle with a fast current inner loop, a nominal single-point equivalent levitation mass of 13.5 kg, a rated levitation gap of 4 mm, and the ability to repeatedly run along the same fixed experimental track section and obtain position or mileage information is used.

[0094] The electromagnetic levitation system is a single-point levitation system for a conventional electromagnetic levitation vehicle, and the control method includes the following steps;

[0095] Step S1: Taking the single electromagnet-track suspension point of the normally conducting electromagnetic levitation vehicle as the control object, construct a nonlinear electromechanical coupling model, perform incremental linearization near the rated suspension operating point, and rewrite it into the LADRC second-order standard form under the condition of fast current inner loop.

[0096] Step S2: Decompose the generalized total disturbance of the outer ring of the suspension gap into repeating disturbances related to the spatial position of the fixed experimental track and non-repeating residual disturbances related to the running batch;

[0097] Step S3: Establish a spatial domain repetitive perturbation iterative learning mechanism: For the maglev train simulated by a conventional electromagnetic levitation vehicle in the first step... Disturbance observation data of LESO during the second run After forward-reverse low-pass filtering, it is mapped to the line spatial domain, at the position Select a local window, calculate the local spatial correlation coefficient and learning gain, and update the [number]th [window]. Spatial repetitive perturbation pattern of each run;

[0098] Step S4: Place the first The spatial repetitive disturbance map corresponding to each run is used as prior information of the fixed track and introduced into the LADRC observer prediction model and control law based on linear active disturbance rejection control to perform feedforward compensation for the repetitive disturbance, and the non-repetitive residual disturbance after compensation is estimated by LESO.

[0099] Step S1 specifically includes the following steps:

[0100] Step S11: Under ideal conditions, taking vertically downward as the positive direction, the vertical dynamic equation of the single-point suspension system is established as follows:

[0101] ,

[0102] ;

[0103] Among them, in the single-point suspension system of the conventional electromagnetic levitation vehicle, The mass of the electromagnet; For suspension gap; It is the acceleration due to gravity; It is electromagnetic attraction; The permeability of vacuum; The effective magnetic pole area of ​​the electromagnet; This represents the number of turns in the electromagnet coil. The coil current; The overall electromagnetic force coefficient;

[0104] Step S12: Based on the characteristics of the electromagnet's winding circuit, establish the voltage and current equations as follows:

[0105] ,

[0106] ;

[0107] in, The voltage of the electromagnet; This is the equivalent resistance of the coil; This is the equivalent inductance of the coil;

[0108] Step S13: Based on steps S11-S12, establish a state-space model of the single-point suspension system, and at the equilibrium point... Linearization of the surrounding area yields:

[0109] ,

[0110] ;

[0111] in, The velocity is in the vertical direction; This is the gap value at the equilibrium point; This is the equilibrium point current value;

[0112] Step S14: The linearized dynamic equation of the outer ring of the suspension gap is obtained from step S13, and is expressed as follows:

[0113]

[0114] in, This represents the equivalent term calculated from linearization error, parameter perturbation, external line disturbance, non-ideal dynamics of the current loop, and unmodeled factors into the gap acceleration channel;

[0115] Let the equivalent control input of the outer loop of the gap be the current, and take the nominal input gain as... ,

[0116] The linearized dynamic equations can be rewritten in the second-order canonical form commonly used in LADRC as follows:

[0117]

[0118] in, To control the input quantity, i.e., the current quantity; This refers to the generalized total disturbance.

[0119] Step S2 specifically includes the following steps:

[0120] Step S21: Let the maglev train's first... The spatial position along the line during the second run is The line section is , Provided by the positioning and odometer system of the maglev train; the generalized total disturbance is decomposed into:

[0121]

[0122] in, For the first The equivalent disturbance components that repeatedly appear depending on the spatial location of the line during each operation; For the first Non-repetitive disturbances during the next run;

[0123] Step S22: The spatial repetition perturbation estimation map obtained before the next run is as follows: After introducing spatial repetition perturbation compensation, the residual perturbation that LESO needs to estimate can be expressed as:

[0124]

[0125] in, Repeatedly perturb the residuals of the unlearned space.

[0126] Step S3 specifically includes the following steps:

[0127] Step S31: The spatial repeating perturbation map is updated after each run. By performing forward-reverse low-pass filtering and spatial mapping using the positioning and mileage information provided by the maglev train's positioning and mileage system, the following results are obtained:

[0128]

[0129] in, For position The residual perturbation estimate at the corresponding location; It is a forward-reverse low-pass filter; These are repetitive items that should be learned; Non-repeating items that should not be learned;

[0130] Step S32: At position Select nearby local window Within that window, the first The estimated value of the spatial residual perturbation of the next run is , No. The estimated value of the spatial residual perturbation of the next run is , These are the spatial coordinates inside the window; both are essentially defined within... The continuous curve on the curve, since the actual residual estimated signal is bounded within a finite line interval after filtering and spatial interpolation, can be regarded as Hilbert space. The elements in the function space are used to measure the similarity between two curve segments using the inner product and norm in the function space.

[0131] for Two functions in and The local inner product and norm are as follows:

[0132] ,

[0133] ;

[0134] Let the normalized inner product of two local spatial signals be... This quantity has the same form as the cosine similarity in a finite-dimensional vector space, and is used to describe the directional consistency of two function curves within a local window; the larger its value, the more obvious the trend of the two curves changing in the same direction within the window; the smaller its value, the more likely the two curves lack a stable and consistent shape.

[0135] make , The local spatial correlation coefficient is defined as:

[0136]

[0137] Step S33: If the local spatial correlation coefficient is not directly used as a compensation quantity, but is used to generate a learning gain for spatial variation, and the correlation judgment is easily affected by noise when the local residual energy is too low, define the learning gain. exist or When it is 0, , Conversely, the learning gain is defined as:

[0138]

[0139] in, To achieve maximum learning gain; The threshold for repeatability determination; Let be a saturation function, defined as:

[0140]

[0141] but Its function is to determine whether the residual disturbance at a certain spatial location is learnable. The learning intensity at this location is further determined by the learning correction amount written into the spatial repeating perturbation map, which is then weighted by correlation. In summary, the update formula for the spatial repeating perturbation map is:

[0142]

[0143] Step S34: After the perturbation map has been fully learned, reduce the observer bandwidth to balance the contradiction between perturbation estimation and noise amplification.

[0144] The specific steps of step S4 are as follows:

[0145] Step S41: From the second-order model of the outer ring of the suspension gap established in step S1, it can be seen that the first... The system meets the requirements during the next runtime.

[0146]

[0147] As the number of batches increases Approaching step by step , The spatial repetition component in the model will be reduced, and the disturbance burden that LESO needs to estimate in real time will be reduced accordingly.

[0148] Step S42: Select observer state variables , , ,have to Then the continuously expanding state space of step S41 is described by the formula:

[0149]

[0150] in, , , , , , The nominal value used to control the input gain;

[0151] because The data still includes non-repetitive disturbances, learning residuals, parameter perturbations, non-ideal dynamics of the current loop, and unmodeled factors, making it difficult to obtain accurate analytical expressions. Therefore, the state variables of the observer are typically used. State variables of the controller Make an estimate;

[0152] The design of a linear extended state observer based on SRDL is as follows:

[0153]

[0154] in, , This is the estimated gap value; This is an estimated value for the gap speed; This is an estimate of the residual disturbance; , , , For observer gain, The observer bandwidth is used to adjust the state and residual perturbation estimation rate of LESO; LESO still corrects the state estimate by outputting observation errors, but its prediction model incorporates a spatially repeating perturbation estimation term, making... The estimated object is transformed into the compensated residual disturbance. ;

[0155] Set the desired gap as For setpoint control near the rated clearance, there are , ;

[0156] Intermediate control quantity Generated via proportional-derivative feedback:

[0157]

[0158] in, For proportional feedback gain; For differential feedback gain;

[0159] Considering the general form of trajectory tracking, we can extend it as follows:

[0160]

[0161] To make the gap acceleration approximately satisfy It is necessary to compensate for the spatial repetitive disturbances given by the SRDL map and the residual disturbance estimates given by LESO. The LADRC control law based on SRDL is designed as follows:

[0162] .

[0163] In the single-point levitation system of a conventional electromagnetic levitation vehicle, when track maintenance or structural adjustment, changes in the origin or mileage calibration of the line coordinates, changes in the correspondence of the running direction, abnormalities in the positioning system, or changes in the nominal single-point equivalent levitation mass, the control method freezes and clears the spatial repetitive disturbance spectrum in the affected direction, restores the high observer bandwidth, and re-completes the spectrum learning.

[0164] The control method is used for a fixed load condition where the nominal single-point equivalent suspended mass is fixed at 13.5 kg; in the fixed load condition, the trolley's running track is the same fixed experimental track section where the structural state and spatial coordinate reference remain unchanged between adjacent running batches; the control method's first... The trajectory used in this run for learning Within the corresponding learning interval, the data is continuous and monotonous. When the control method is used, the parking, reversing, positioning anomalies, and mileage jump intervals of the car do not participate in the map update. Spatial repetitive disturbance maps are established for the car's forward and reverse movement respectively.

[0165] When the normally conducting electromagnetic levitation vehicle is an experimental vehicle, the nominal single-point equivalent levitation mass of the experimental vehicle is... It weighs 13.5 kg and has a rated suspension gap. The equivalent resistance of the coil is 0.004 m. The equivalent inductance near the equilibrium point is 0.59 Ω. The overall electromagnetic force coefficient is 0.028 H. It is 5.5992 × 10⁻ 5 N·m² / A², gravitational acceleration g is taken as 9.8 m / s²; corresponding theoretical equilibrium current Approximately 6.15 A, nominal current input gain It is approximately -3.1877 m·s⁻²·A⁻¹.

[0166] The specific implementation object, load, and operational boundaries in this example are as follows:

[0167] This embodiment applies to a fixed nominal load condition with a single-point equivalent suspended mass of 13.5 kg. Large-scale load variations without rebalancing and control parameter tuning are not considered as directly applicable conditions. The track is the same fixed experimental track section, maintaining the track structure, coordinate origin, and mileage calibration unchanged between adjacent running batches; track deformation is ignored during modeling. The trolley should be able to obtain continuous position or mileage signals, and the data segments used for learning require continuous and monotonic position over time.

[0168] Table 1

[0169]

[0170] In this example, the bottom of the maglev vehicle is connected to the top surface of the upper arm of the box girder by an air spring. The bottom surface of the upper arm is equipped with a linear motor stator parallel to the top surface of the track. The bottom arm of the box girder is equipped with an electromagnet and a sensor group parallel to the bottom surface of the track. When the vehicle is in a suspended state, the linear motor stator floats above the top surface of the track, and the electromagnet and sensor group are adjacent to the bottom surface of the track.

[0171] The above description is merely a preferred embodiment of the present invention, used to illustrate the technical solution of the present invention, and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, or improvements made by those skilled in the art based on the above disclosure without departing from the technical essence of the present invention, and applied to other fields, should be covered within the scope of protection of the present invention.

Claims

1. A linear active disturbance rejection control method for levitation systems based on spatial repetitive disturbance learning, applicable to conventional electromagnetic levitation systems, characterized by: The method first decomposes the generalized total disturbance of the electromagnetic levitation vehicle into spatially repetitive disturbances and non-repetitive residual disturbances during operation; then aligns the residual disturbance estimate of the LESO output after SRDL compensation to a unified line coordinate; constructs a spatial learning gain based on the local spatial correlation coefficient and energy threshold of the residual disturbances of adjacent operating batches, updates the spatially repetitive disturbance map, and then introduces the map as a feedforward compensation into the control law of the observer so that the observer can estimate the compensated residual disturbance. And reduce the observer bandwidth after the spectrum stabilizes.

2. The linear active disturbance rejection control method for a suspension system based on spatial repetitive disturbance learning according to claim 1, characterized in that: The control method learns repetitive disturbances related to the spatial position of the electromagnetic levitation vehicle under defined fixed load, fixed experimental track, and repetitive operation conditions, and introduces them as feedforward compensation into LADRC to reduce the real-time observation burden of LESO on repetitive disturbances. It is applied to a normal-conducting electromagnetic levitation system with a fast current inner loop. In the levitation system, the electromagnetic levitation vehicle used to simulate a maglev train runs on an experimental track section with fixed track structure and line coordinate reference, and the spatial position along the track is provided by the positioning and odometer system.

3. The linear active disturbance rejection control method for a suspension system based on spatial repetitive disturbance learning according to claim 2, characterized in that: The electromagnetic levitation system is a single-point levitation system for a conventional electromagnetic levitation vehicle, and the control method includes the following steps; Step S1: Taking the single electromagnet-track suspension point of the normally conducting electromagnetic levitation vehicle as the control object, construct a nonlinear electromechanical coupling model, perform incremental linearization near the rated suspension operating point, and rewrite it into the LADRC second-order standard form under the condition of fast current inner loop. Step S2: Decompose the generalized total disturbance of the outer ring of the suspension gap into repeating disturbances related to the spatial position of the fixed experimental track and non-repeating residual disturbances related to the running batch; Step S3: Establish a spatial domain repetitive perturbation iterative learning mechanism: For the maglev train simulated by a conventional electromagnetic levitation vehicle in the first step... Disturbance observation data of LESO during the second run After forward-reverse low-pass filtering, it is mapped to the line spatial domain, at the position Select a local window, calculate the local spatial correlation coefficient and learning gain, and update the [number]th [window]. Spatial repetitive perturbation pattern of each run; Step S4: Place the first The spatial repeating disturbance map corresponding to each run is used as prior information of the fixed orbit and introduced into the LADRC observer prediction model and control law to perform feedforward compensation for the repeating disturbance, and the non-repeating residual disturbance after compensation is estimated by LESO.

4. The linear active disturbance rejection control method for a suspension system based on spatial repetitive disturbance learning according to claim 3, characterized in that: Step S1 specifically includes the following steps: Step S11: Under ideal conditions, taking vertically downward as the positive direction, the vertical dynamic equation of the single-point suspension system is established as follows: ， ； Among them, in the single-point suspension system of the conventional electromagnetic levitation vehicle, The mass of the electromagnet; For suspension gap; It is the acceleration due to gravity; It is electromagnetic attraction; The permeability of vacuum; The effective magnetic pole area of ​​the electromagnet; This represents the number of turns in the electromagnet coil. The coil current; The comprehensive electromagnetic force coefficient; Step S12: Based on the characteristics of the electromagnet's winding circuit, establish the voltage and current equations as follows: ， ； in, The voltage of the electromagnet; This is the equivalent resistance of the coil; This is the equivalent inductance of the coil; Step S13: Based on steps S11-S12, establish a state-space model of the single-point suspension system, and at the equilibrium point... Linearization of the surrounding area yields: ， ； in, The velocity is in the vertical direction; This is the gap value at the equilibrium point; This is the equilibrium point current value; Step S14: The linearized dynamic equation of the outer ring of the suspension gap is obtained from step S13, and is expressed as follows: in, This represents the equivalent term calculated from linearization error, parameter perturbation, external line disturbance, non-ideal dynamics of the current loop, and unmodeled factors into the gap acceleration channel; Let the equivalent control input of the outer loop of the gap be the current, and take the nominal input gain as... , The linearized dynamic equations can be rewritten in LADRC second-order canonical form as follows: in, To control the input quantity, i.e., the current quantity; This refers to the generalized total disturbance.

5. The linear active disturbance rejection control method for a suspension system based on spatial repetitive disturbance learning according to claim 4, characterized in that: Step S2 specifically includes the following steps: Step S21: Let the maglev train's first... The spatial position along the line during the second run is The line section is , Provided by the positioning and odometer system of the maglev train; the generalized total disturbance is decomposed into: in, For the first The equivalent disturbance components that repeatedly appear depending on the spatial location of the line during each operation; For the first Non-repetitive disturbances during the next run; Step S22: The spatial repetition perturbation estimation map obtained before the next run is as follows: After introducing spatial repetition perturbation compensation, the residual perturbation that LESO needs to estimate is expressed as: in, Repeatedly perturb the residuals of the unlearned space.

6. The linear active disturbance rejection control method for a suspension system based on spatial repetitive disturbance learning according to claim 5, characterized in that: Step S3 specifically includes the following steps: Step S31: The spatial repeating perturbation map is updated after each run. By performing forward-reverse low-pass filtering and spatial mapping using the positioning and mileage information provided by the maglev train's positioning and mileage system, the following results are obtained: in, For position The residual perturbation estimate at the corresponding location; It is a forward-reverse low-pass filter; These are repetitive items that should be learned; Non-repeating items that should not be learned; Step S32: At position Select nearby local window Within that window, the first The estimated value of the spatial residual perturbation of the next run is , No. The estimated value of the spatial residual perturbation of the next run is , Spatial coordinates inside the window; defined in A continuous curve on the Hilbert space, after filtering and spatial interpolation, is bounded within a finite line interval; this curve is thus considered as Hilbert space. The elements in the function space are used to measure the similarity between two curve segments using the inner product and norm in the function space; for functions in and The local inner product and norm are as follows: ， ； Let the normalized inner product of two local spatial signals be... This quantity has the same form as the cosine similarity in a finite-dimensional vector space and is used to describe the directional consistency of two function curves within a local window. make , The local spatial correlation coefficient is defined as: Step S33: If the local spatial correlation coefficient is used to generate the spatially varying learning gain, define the learning gain. exist or When it is 0, , Conversely, the learning gain is defined as: in, To achieve maximum learning gain; The threshold for repeatability determination; Let be a saturation function, defined as: but Its function is to determine whether the residual disturbance at a certain spatial location is learnable. The learning intensity at this location is further determined by the learning correction amount written into the spatial repeating perturbation map, which is then weighted by correlation. The update formula for the spatial repeating perturbation map is: Step S34: After the perturbation map has been fully learned, reduce the observer bandwidth to balance the contradiction between perturbation estimation and noise amplification.

7. The linear active disturbance rejection control method for a suspension system based on spatial repetitive disturbance learning according to claim 6, characterized in that: The specific steps of step S4 are as follows: Step S41: From the second-order model of the outer ring of the suspension gap established in step S1, it can be seen that the first... The system meets the requirements during the next runtime. As the number of batches increases Approaching step by step , The spatial repetition component in the model will be reduced, and the disturbance burden that LESO needs to estimate in real time will be reduced accordingly. Step S42: Select observer state variables , , ,have to Then the continuously expanding state space of step S41 is described by the formula: in, , , , , , The nominal value used to control the input gain; like The model still includes non-repetitive perturbations, learning residuals, parameter perturbations, non-ideal dynamics of the current loop, and unmodeled factors, employing the observer's state variables. State variables of the controller Make an estimate; The design of a linear extended state observer based on SRDL is as follows: in, , This is the estimated gap value; This is an estimated value for the gap speed; This is an estimate of the residual disturbance; , , , For observer gain, The observer bandwidth is used to adjust the state and residual perturbation estimation rate of LESO; a spatially repeating perturbation estimation term is added to the LESO prediction model to make... The estimated object is transformed into the compensated residual disturbance. ; Set the desired gap as For setpoint control near the rated clearance, there are , ; Intermediate control quantity Generated via proportional-derivative feedback: in, For proportional feedback gain; For differential feedback gain; Considering the trajectory tracking form, we can extend it as follows: To make the gap acceleration approximately satisfy It is necessary to compensate for the spatial repetitive disturbances given by the SRDL map and the residual disturbance estimates given by LESO. The LADRC control law based on SRDL is designed as follows: 。 8. The linear active disturbance rejection control method for a suspension system based on spatial repetitive disturbance learning according to claim 7, characterized in that: In the single-point levitation system of a conventional electromagnetic levitation vehicle, when track maintenance or structural adjustment, changes in the origin or mileage calibration of the line coordinates, changes in the correspondence of the running direction, abnormalities in the positioning system, or changes in the nominal single-point equivalent levitation mass, the control method freezes and clears the spatial repetitive disturbance spectrum in the affected direction, restores the high observer bandwidth, and re-completes the spectrum learning.

9. The linear active disturbance rejection control method for a suspension system based on spatial repetitive disturbance learning according to claim 7, characterized in that: The control method is used for a fixed load condition where the nominal single-point equivalent suspension mass is a fixed value; in the fixed load condition, the trolley's running track is the same fixed experimental track section where the structural state and spatial coordinate reference remain unchanged between adjacent running batches; the control method's first... The trajectory used in this run for learning It is continuous and monotonic within the corresponding learning interval.

10. The linear active disturbance rejection control method for a suspension system based on spatial repetitive disturbance learning according to claim 9, characterized in that: In the control method, the parking, reversing, positioning anomalies and mileage jump intervals of the car are not included in the map update. Spatial repetitive disturbance maps are established for the car's forward and reverse movement respectively.

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