A DEA trajectory tracking control method and system

Abstract

This invention discloses a DEA trajectory tracking control method and system, belonging to the field of intelligent control technology for soft robots. The method includes: acquiring the real-time voltage of the DEA, the DEA resampling current, and the real-time ground true displacement of the DEA; acquiring the NARX displacement prediction value based on the real-time voltage, DEA resampling current, and DEA real-time ground true displacement; acquiring the real-time trajectory tracking error based on the preset DEA displacement trajectory and the NARX displacement prediction value; acquiring the feedback correction amount based on the real-time trajectory tracking error and a pre-trained MPC feedback control model, and acquiring the total DEA trajectory control amount based on the feedback correction amount and a preset ILC feedforward control amount; wherein, the construction process of the pre-trained MPC feedback control model includes: training the preset MPC feedback control initial model based on preset first excitation conditions, preset constraints, pre-calibrated DEA, and MPC predicted displacement to obtain the pre-trained MPC feedback control model. The DEA trajectory tracking control method provided by this invention can achieve high-precision trajectory tracking control of the DEA.

Description

Technical Field

[0001] This invention relates to the field of intelligent control technology for soft robots, and in particular to a DEA trajectory tracking control method and system. Background Technology

[0002] With the rapid development of soft robot technology, dielectric elastomer actuators (DEA) have become one of the core components of soft robot drive control due to their significant advantages of light weight, large deformation, high energy density, and fast response. At the same time, the electrical parameters of DEA itself will change dynamically with its own deformation. This characteristic provides a natural technical basis for realizing displacement self-sensing and getting rid of dependence on external displacement sensors.

[0003] Despite the aforementioned advantages and self-sensing potential of DEA under the current technological background, there are still many problems to be solved in practical applications: On the one hand, traditional DEA control relies on external laser displacement sensors to achieve displacement detection and closed-loop control, which not only limits the robot's mobility in narrow spaces (such as cable trenches and pipes), but also leads to a serious under-sensing dilemma when external sensors fail, significantly reducing control stability; on the other hand, existing DEA self-sensing modeling methods often simplify it to a capacitor or resistor-capacitor circuit model, ignoring the complex nonlinear characteristics of DEA itself, such as asymmetric hysteresis, creep, and rate-dependent hysteresis, resulting in low self-sensing modeling accuracy, affecting control performance, and failing to meet the high-precision control requirements of equipment such as cable inspection robot dogs in complex terrain. Summary of the Invention

[0004] The present invention aims to provide a DEA trajectory tracking control method and system to solve the above-mentioned technical problems, avoid the limitation of control scenarios caused by the DEA's reliance on external displacement sensors, and achieve high-precision trajectory tracking control of the DEA.

[0005] To address the aforementioned technical problems, this invention provides a DEA trajectory tracking control method, comprising: Based on the DEA to be controlled, obtain the real-time voltage of the DEA, the resampled current of the DEA, and the real-time ground true displacement of the DEA. NARX displacement prediction values ​​are obtained based on DEA real-time voltage, DEA resampling current, DEA real-time ground true displacement, and a preset NARX prediction model. Real-time trajectory tracking error is obtained based on preset DEA displacement trajectory and NARX displacement prediction value; The feedback correction amount is obtained based on the real-time trajectory tracking error and the pre-trained MPC feedback control model, and the total DEA trajectory control amount is obtained based on the feedback correction amount and the preset ILC feedforward control amount. The construction process of the pre-trained MPC feedback control model includes: Based on the preset first excitation conditions, preset constraints and pre-calibrated DEA, several first DEA calibration voltages and several MPC predicted displacements are obtained, and based on the several MPC predicted displacements and the preset benchmark MPC displacement trajectory, several training trajectory tracking errors are obtained. An MPC optimization objective function is constructed based on several first DEA calibration voltages and several training trajectory tracking errors. The initial model of MPC feedback control is trained with the goal of minimizing the MPC optimization objective function until the first preset convergence condition is met, thus obtaining the pre-trained MPC feedback control model.

[0006] In the above scheme, by inputting the real-time DEA voltage, DEA resampling current, and real-time ground true displacement of the DEA into a preset NARX prediction model, the DEA displacement can be sensed in real time without external displacement sensors, and the predicted NARX displacement value can be obtained, thus providing a basis for the calculation of the real-time trajectory tracking error. Next, the real-time trajectory tracking error is obtained through the preset DEA displacement trajectory and the predicted NARX displacement value, providing a reference for subsequent feedback control correction. Then, by constructing an MPC optimization objective function and training a preset MPC feedback control initial model with the goal of minimizing the MPC optimization objective function, a pre-trained MPC feedback control model can be obtained when the preset first convergence condition is met, which is used to optimize the DEA control quantity. Finally, the real-time trajectory tracking error is input into the pre-trained MPC feedback control model to obtain the feedback correction quantity, and the feedback correction quantity is fused with the preset ILC feedforward control quantity to obtain the total DEA trajectory control quantity. This allows for precise compensation of the nonlinear characteristics of the DEA through feedforward control, while effectively suppressing unknown disturbances in the DEA through feedback control, ultimately achieving high-precision trajectory tracking control of the DEA.

[0007] Furthermore, the step of acquiring the real-time voltage of the DEA, the resampling current of the DEA, and the real-time ground true displacement of the DEA based on the DEA to be controlled includes: Based on the DEA to be controlled, obtain the real-time voltage, real-time current and real-time ground true displacement of the DEA; Median filtering is applied to the real-time DEA current to obtain a smoothed DEA current; The smoothed DEA current is resampled based on a preset control period to obtain the DEA resampled current.

[0008] In the above scheme, by collecting the real-time voltage, real-time current, and real-time ground true displacement of the DEA to be controlled, raw electrical parameters and displacement reference data can be provided for subsequent current processing and displacement error calculation. Next, by performing median filtering on the real-time DEA current, spike noise and random interference during the current acquisition process can be effectively eliminated to obtain a smoothed DEA current, ensuring the accuracy and stability of the current parameters and avoiding noise affecting the accuracy of subsequent displacement prediction. Then, by resampling the smoothed DEA current through a preset control cycle, the sampling time axis of the current data can be strictly aligned with the preset control cycle to obtain the resampled DEA current, ensuring the consistency of the timing of the electrical parameters input to the NARX prediction model and improving the accuracy of displacement prediction.

[0009] Furthermore, in obtaining the predicted NARX displacement value based on DEA real-time voltage, DEA resampling current, DEA real-time ground true displacement, and a preset NARX prediction model, the construction process of the preset NARX prediction model includes: The pre-calibrated DEA is excited based on the preset second excitation condition to obtain several second DEA calibration voltages, several DEA calibration resampling currents, several DEA calibration current integrals, and several first DEA ground true displacements. A NARX training set is constructed based on several second DEA calibration voltages, several DEA calibration resampling currents, and several DEA calibration current integrals. Several NARX displacement prediction values ​​are obtained based on the NARX training set and the preset NARX initial prediction model. The NARX performance function is constructed based on several NARX displacement prediction values ​​and several first DEA ground true displacement values. The preset NARX prediction initial model is trained with the goal of minimizing the NARX performance function until the preset second convergence condition is met, and the preset NARX prediction model is obtained.

[0010] In the above scheme, by stimulating the pre-calibrated DEA with a preset second excitation condition and collecting several second DEA calibration voltages, several DEA calibration resampling currents, several DEA calibration current integrals, and several first DEA ground true displacements, a NARX training set and actual ground displacements that closely match the actual characteristics of the DEA can be provided for training the preset NARX initial prediction model. Next, by inputting the constructed NARX training set into the preset NARX initial prediction model, several NARX displacement prediction values ​​are obtained, providing a basis for subsequent model optimization. Then, a NARX performance function is constructed using the several NARX displacement prediction values ​​and several first DEA ground true displacements, and the preset NARX initial prediction model is trained with the goal of minimizing this performance function, achieving iterative optimization of the NARX model parameters until a preset second convergence condition is met, thus obtaining the preset NARX prediction model and ensuring accurate self-sensing prediction of DEA displacements.

[0011] Furthermore, in obtaining the feedback correction amount based on the real-time trajectory tracking error and the pre-trained MPC feedback control model, and obtaining the total DEA trajectory control amount based on the feedback correction amount and the preset ILC feedforward control amount, the process of obtaining the preset ILC feedforward control amount includes: Excite the pre-calibrated DEA based on the preset third excitation condition, obtain several third DEA voltages and several second DEA ground true displacements, and train the preset asymmetric hysteresis initial model and the preset creep initial model based on the several third DEA voltages and several second DEA ground true displacements respectively to obtain the asymmetric hysteresis model and the creep model, and construct a static nonlinear model based on the asymmetric hysteresis model and the creep model. Based on the preset second excitation condition and the static nonlinear model, several static DEA ground true displacements are obtained, and based on the several static DEA ground true displacements, the preset dynamic linear initial model is trained to obtain the dynamic linear model. A Hammerstein dynamic model is constructed based on static nonlinear models and dynamic linear models; Preset ILC feedforward control values ​​are obtained based on preset control parameters and the Hammerstein dynamic model.

[0012] In the above scheme, a pre-calibrated DEA is excited by a preset third excitation condition to obtain several third DEA voltages and several second DEA ground true displacements. Based on these third DEA voltages and second DEA ground true displacements, a preset asymmetric hysteresis initial model and a preset creep initial model are trained respectively, resulting in the asymmetric hysteresis model and creep model. A static nonlinear model is constructed, which can accurately fit the asymmetric hysteresis and creep characteristics in the static nonlinear characteristics of the DEA, laying the static characteristic foundation for the subsequent construction of the Hammerstein dynamic model. Next, several static DEA ground true displacements are obtained by using the preset second excitation condition and the static nonlinear model. Based on these static DEA ground true displacements, a preset dynamic linear initial model is trained, resulting in the dynamic linear model, which can fit the dynamic response characteristics of the DEA and achieve accurate characterization of the DEA's dynamic characteristics. Then, by combining the static nonlinear model and the dynamic linear model, a Hammerstein dynamic model is constructed, which can completely reproduce the static nonlinear characteristics and dynamic linear characteristics of the DEA from electrical input to mechanical output, providing an accurate model for solving the ILC feedforward control quantity. Finally, the known nonlinearity of the DEA is accurately compensated by preset control parameters and the Hammerstein dynamic model to obtain the preset ILC feedforward control quantity, which can provide a basis for the fusion of subsequent feedback correction quantity and preset ILC feedforward control quantity.

[0013] Further, the pre-calibrated DEA is excited based on a preset third excitation condition to obtain several third DEA voltages and several second DEA ground true displacements. Based on these third DEA voltages and second DEA ground true displacements, a preset asymmetric hysteresis initial model and a preset creep initial model are trained respectively to obtain an asymmetric hysteresis model and a creep model. A static nonlinear model is then constructed based on the asymmetric hysteresis model and the creep model, including: The pre-calibrated DEA is excited based on the preset third excitation condition to obtain several third DEA voltages and several second DEA ground true displacements. A nonlinear training set is constructed based on several third DEA voltages; Several asymmetric hysteresis displacement prediction values ​​were obtained based on a nonlinear training set and a pre-set asymmetric hysteresis initial model. Several predicted creep displacement values ​​were obtained based on a nonlinear training set and a preset creep initial model. An asymmetric hysteresis performance function is constructed based on several asymmetric hysteresis displacement predictions and several second DEA ground true displacements. The preset asymmetric hysteresis initial model is trained with the goal of minimizing the asymmetric hysteresis performance function until the preset third convergence condition is met, and the asymmetric hysteresis model is obtained. A creep performance function is constructed based on several predicted creep displacement values ​​and several second DEA ground true displacement values. The creep performance function is minimized to train the preset creep initial model until the preset fourth convergence condition is met, and the creep model is obtained. A static nonlinear model is constructed based on the asymmetric hysteresis model and the creep model.

[0014] In the above scheme, the pre-calibrated DEA is excited by a preset third excitation condition to obtain several third DEA voltages and several second DEA ground true displacements, which can provide calibration data that fits the actual working state for modeling the static nonlinear characteristics of the DEA. Next, by inputting the nonlinear training set into a preset asymmetric hysteresis initial model and a preset creep initial model respectively, several asymmetric hysteresis displacement prediction values ​​and several creep displacement prediction values ​​can be obtained respectively. The obtained asymmetric hysteresis displacement prediction values ​​can provide a reference for the performance optimization of the asymmetric hysteresis model, and the obtained creep displacement prediction values ​​can provide a reference for the performance optimization of the creep model. Then, an asymmetric hysteresis performance function is constructed using several asymmetric hysteresis displacement prediction values ​​and several second DEA ground true displacements. The preset asymmetric hysteresis initial model is trained with the goal of minimizing this function until the preset third convergence condition is met. This allows for iterative optimization of the model parameters, resulting in an asymmetric hysteresis model that accurately fits the asymmetric hysteresis characteristics of the DEA. Subsequently, a creep performance function is constructed using several predicted creep displacement values ​​and several true ground displacement values ​​of the second DEA. A pre-defined initial creep model is trained with the goal of minimizing this function until a pre-defined fourth convergence condition is met. This allows for iterative optimization of the model parameters, resulting in a creep model that accurately fits the creep characteristics of the DEA. Finally, a static nonlinear model is constructed using an asymmetric hysteresis model and a creep model. This integrates the static nonlinear characteristics of the DEA, forming a static nonlinear model that provides static characteristic support for the subsequent construction of the Hammerstein dynamic model.

[0015] Further, the step of obtaining several static DEA ground truth displacements based on a preset second excitation condition and a static nonlinear model, and training a preset dynamic linear initial model based on these several static DEA ground truth displacements to obtain a dynamic linear model includes: Several static DEA ground true displacements are obtained based on the preset second excitation condition and the static nonlinear model. A dynamic linear training set is constructed based on several static DEA ground truth displacements; Several predicted dynamic linear displacement values ​​are obtained based on the dynamic linear training set and the preset dynamic linear initial model; A dynamic linear performance function is constructed based on several predicted dynamic linear displacements and several static DEA ground truth displacements. The preset dynamic linear initial model is trained with the goal of minimizing the dynamic linear performance function until the preset fifth convergence condition is met, and the dynamic linear model is obtained.

[0016] In the above scheme, by pre-setting the second excitation condition and the static nonlinear model, several static DEA ground truth displacements reflecting only the dynamic response can be obtained, thus providing a foundation for the subsequent training of the pre-set dynamic linear initial model. Next, by inputting the dynamic linear training set into the pre-set dynamic linear initial model, several predicted dynamic linear displacements are obtained, providing a reference for the performance optimization of the dynamic linear model and supporting the initial fitting of the DEA dynamic characteristics. Then, a dynamic linear performance function is constructed using the predicted dynamic linear displacements and several static DEA ground truth displacements. The pre-set dynamic linear initial model is trained with the goal of minimizing this dynamic linear performance function until the pre-set fifth convergence condition is met. This allows for iterative optimization of the model parameters, resulting in a dynamic linear model that accurately characterizes the DEA dynamic response, providing dynamic characteristic support for the subsequent construction of a complete Hammerstein dynamic model.

[0017] Furthermore, the step of obtaining the preset ILC feedforward control quantity based on preset control parameters and the Hammerstein dynamic model includes: The simulated displacement sequence is obtained based on the preset control parameters and the Hammerstein dynamic model, and the initial tracking error sequence is obtained based on the simulated displacement sequence and the preset simulated DEA displacement trajectory. The preset control parameters are corrected based on the initial tracking error sequence and the preset ILC evolution model to obtain the corrected control parameters. The first tracking error sequence is obtained based on the corrected control parameters, the Hammerstein dynamic model and the preset simulated DEA displacement trajectory. If the first tracking error sequence satisfies the preset fifth convergence condition, the corrected control parameters are used as the preset ILC feedforward control quantity.

[0018] In the above scheme, a simulated displacement sequence is obtained through preset control parameters and a Hammerstein dynamic model. This simulated displacement sequence is then combined with a preset simulated DEA displacement trajectory to obtain an initial tracking error sequence. This captures the DEA trajectory deviation under the preset control parameters, providing an initial basis for the iterative correction of the ILC feedforward control parameters. Next, the preset control parameters are corrected using the initial tracking error sequence and a preset ILC evolution model to obtain corrected control parameters. Then, the first tracking error sequence is obtained by combining the corrected control parameters, the Hammerstein dynamic model, and the preset simulated DEA displacement trajectory. It is then determined whether the first tracking error sequence satisfies the preset fifth convergence condition. If it does, the corrected control parameter that meets the preset fifth convergence condition is determined as the preset ILC feedforward control quantity. This ensures that the obtained preset ILC feedforward control quantity can compensate for the nonlinear characteristics of the DEA, providing a precise and effective basic control quantity for subsequently obtaining the total control quantity of the DEA trajectory.

[0019] Further, the step of obtaining several first DEA calibration voltages and several MPC predicted displacements based on preset first excitation conditions, preset constraints, and pre-calibrated DEA, and obtaining several training trajectory tracking errors based on the several MPC predicted displacements and preset reference MPC displacement trajectories, includes: The pre-calibrated DEA is excited based on the preset first excitation conditions and preset constraints to obtain several first DEA calibration voltages; Several MPC predicted displacements are obtained based on a preset MPC feedback control initial model and several first DEA calibration voltages. Based on several MPC predicted displacements and preset benchmark MPC displacement trajectories, several training trajectory tracking errors are obtained.

[0020] In the above scheme, by stimulating the pre-calibrated DEA with preset first excitation conditions and preset constraints, several first DEA calibration voltages that conform to the hardware characteristics and actual control constraints can be provided for training the preset MPC feedback control initial model. Next, by inputting these first DEA calibration voltages into the preset MPC feedback control initial model, several MPC predicted displacements are obtained, enabling preliminary prediction of DEA displacements and providing a reference for subsequent trajectory tracking error calculation. Then, by comparing these MPC predicted displacements with the preset baseline MPC displacement trajectory, several training trajectory tracking errors are obtained, capturing the deviation between the predicted values ​​of the preset MPC feedback control initial model and the desired trajectory, providing a basis for subsequent iterative optimization of the model.

[0021] This invention provides a DEA trajectory tracking control system, comprising a data acquisition module, a NARX displacement prediction module, an error calculation module, and a control quantity generation module, specifically: The data acquisition module is used to acquire the real-time voltage of the DEA, the resampling current of the DEA, and the real-time ground true displacement of the DEA based on the DEA to be controlled. The NARX displacement prediction module is used to obtain NARX displacement prediction values ​​based on DEA real-time voltage, DEA resampling current, DEA real-time ground true displacement and a preset NARX prediction model. The error calculation module is used to obtain the real-time trajectory tracking error based on the preset DEA displacement trajectory and NARX displacement prediction value; The control quantity generation module is used to obtain the feedback correction quantity based on the real-time trajectory tracking error and the pre-trained MPC feedback control model, and to obtain the total DEA trajectory control quantity based on the feedback correction quantity and the preset ILC feedforward control quantity. The construction process of the pre-trained MPC feedback control model includes: Based on the preset first excitation conditions, preset constraints and pre-calibrated DEA, several first DEA calibration voltages and several MPC predicted displacements are obtained, and based on the several MPC predicted displacements and the preset benchmark MPC displacement trajectory, several training trajectory tracking errors are obtained. An MPC optimization objective function is constructed based on several first DEA calibration voltages and several training trajectory tracking errors. The initial model of MPC feedback control is trained with the goal of minimizing the MPC optimization objective function until the first preset convergence condition is met, thus obtaining the pre-trained MPC feedback control model.

[0022] This invention provides a DEA trajectory tracking control system that, in practical applications, only requires a NARX displacement prediction module. By inputting the real-time DEA voltage, DEA resampling current, and real-time ground true displacement of the DEA into a preset NARX prediction model, it can sense the DEA displacement in real time without external displacement sensors and obtain the NARX displacement prediction value, thus providing a basis for calculating the real-time trajectory tracking error. Next, an error calculation module is used to obtain the real-time trajectory tracking error using the preset DEA displacement trajectory and the NARX displacement prediction value, providing a reference for subsequent feedback control correction. Then, by constructing an MPC optimization objective function and training a preset MPC feedback control initial model with the goal of minimizing the MPC optimization objective function, a pre-trained MPC feedback control model can be obtained when a preset first convergence condition is met, which is used to optimize the DEA control quantity. Finally, a control quantity generation module is used to input the real-time trajectory tracking error into the pre-trained MPC feedback control model to obtain the feedback correction quantity. The feedback correction quantity is then fused with the preset ILC feedforward control quantity to obtain the total control quantity of the DEA trajectory. This allows for precise compensation of the nonlinear characteristics of the DEA through feedforward control, while effectively suppressing unknown disturbances in the DEA with the help of feedback control, ultimately achieving high-precision trajectory tracking control of the DEA.

[0023] Furthermore, the data acquisition module is used to acquire the real-time voltage of the DEA, the DEA resampling current, and the real-time ground true displacement of the DEA based on the DEA to be controlled, including: Based on the DEA to be controlled, obtain the real-time voltage, real-time current and real-time ground true displacement of the DEA; Median filtering is applied to the real-time DEA current to obtain a smoothed DEA current; The smoothed DEA current is resampled based on a preset control period to obtain the DEA resampled current.

[0024] In the above scheme, by collecting the real-time voltage, real-time current, and real-time ground true displacement of the DEA to be controlled, raw electrical parameters and displacement reference data can be provided for subsequent current processing and displacement error calculation. Next, by performing median filtering on the real-time DEA current, spike noise and random interference during the current acquisition process can be effectively eliminated to obtain a smoothed DEA current, ensuring the accuracy and stability of the current parameters and avoiding noise affecting the accuracy of subsequent displacement prediction. Then, by resampling the smoothed DEA current through a preset control cycle, the sampling time axis of the current data can be strictly aligned with the preset control cycle to obtain the resampled DEA current, ensuring the consistency of the timing of the electrical parameters input to the NARX prediction model and improving the accuracy of displacement prediction. Attached Figure Description

[0025] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0026] Figure 1 A flowchart of a DEA trajectory tracking control method provided in an embodiment of the present invention; Figure 2 This is an architecture diagram of a DEA trajectory tracking control system provided in an embodiment of the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0028] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains; the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the application; the terms “comprising” and “having”, and any variations thereof, in the specification, claims, and foregoing description of the drawings are intended to cover non-exclusive inclusion.

[0029] In the description of the embodiments of this application, technical terms such as "first" and "second" are used only to distinguish different objects and should not be construed as indicating or implying relative importance or implicitly specifying the number, specific order, or primary and secondary relationship of the indicated technical features. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly defined.

[0030] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0031] In the description of the embodiments in this application, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this document generally indicates that the preceding and following related objects have an "or" relationship.

[0032] In the description of the embodiments of this application, the term "multiple" refers to two or more (including two), similarly, "multiple sets" refers to two or more (including two sets), and "multiple pieces" refers to two or more (including two pieces).

[0033] In the description of the embodiments of this application, unless otherwise expressly specified and limited, technical terms such as "installation," "connection," "joining," and "fixing" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. For those skilled in the art, the specific meaning of the above terms in the embodiments of this application can be understood according to the specific circumstances.

[0034] See Figure 1 To avoid limitations in control scenarios due to DEA's reliance on external displacement sensors and to achieve high-precision trajectory tracking control of the DEA, this embodiment provides a DEA trajectory tracking control method. The flowchart of this method can be found in [link to flowchart]. Figure 1 ,include: Step S1: Based on the DEA to be controlled, obtain the real-time voltage of the DEA, the resampling current of the DEA, and the real-time ground true displacement of the DEA; Step S2: Obtain the NARX displacement prediction value based on the DEA real-time voltage, DEA resampling current, DEA real-time ground true displacement, and the preset NARX prediction model; Step S3: Obtain the real-time trajectory tracking error based on the preset DEA displacement trajectory and NARX displacement prediction value; Step S4: Obtain the feedback correction amount based on the real-time trajectory tracking error and the pre-trained MPC feedback control model, and obtain the DEA trajectory total control amount based on the feedback correction amount and the preset ILC feedforward control amount; The construction process of the pre-trained MPC feedback control model includes: Based on the preset first excitation conditions, preset constraints and pre-calibrated DEA, several first DEA calibration voltages and several MPC predicted displacements are obtained, and based on the several MPC predicted displacements and the preset benchmark MPC displacement trajectory, several training trajectory tracking errors are obtained. An MPC optimization objective function is constructed based on several first DEA calibration voltages and several training trajectory tracking errors. The initial model of MPC feedback control is trained with the goal of minimizing the MPC optimization objective function until the first preset convergence condition is met, thus obtaining the pre-trained MPC feedback control model.

[0035] In this embodiment, the DEA to be controlled is a conical DEA, which serves as the rotational drive source for the hip joint of the cable inspection robot dog. The mechanical load end of the DEA is fixedly connected to the thigh linkage of the cable inspection robot dog. The membrane material of the DEA is polydimethylsiloxane (PDMS), which is pre-stretched before installation. The initial joint angle corresponding to the DEA to be controlled is 0°. Then, based on the DEA to be controlled, the real-time voltage, resampling current, and real-time ground true displacement of the DEA are acquired. By inputting the real-time voltage, resampling current, and real-time ground true displacement of the DEA into a preset NARX prediction model (Nonlinear AutoRegressive eXogenous model with external input), the DEA displacement can be sensed in real time without external displacement sensors, and the NARX displacement prediction value can be obtained, thus providing a basis for the calculation of the real-time trajectory tracking error. Next, the real-time trajectory tracking error is obtained through the preset DEA displacement trajectory and the NARX displacement prediction value, which can provide a reference for the correction of subsequent feedback control. Then, the objective function is optimized by constructing MPC (Model Predictive Control), specifically as follows: in, To preset the DEA displacement trajectory, This is the predicted NARX displacement value. Ensure that the DEA joint to be controlled can follow the preset DEA displacement trajectory. and They are respectively The preset lower and upper bounds are defined as follows: N is the MPC prediction time domain length, representing the MPC controller's prediction of the DEA displacement over the next N sampling times, which is the time range of the model prediction; k is the time index within the prediction time domain, and t is the current control time. To control the incremental term, the real-time voltage change amplitude of the DEA at adjacent sampling times is penalized, ensuring that the input energy is enveloped and constrained, preventing electrical breakdown or mechanical fatigue under severe high voltage fluctuations. Safe operation is achieved by limiting the increment. Given the current control time t, the MPC predicts the real-time DEA voltage at the k-th step in the time domain. At the current control time t, the MPC predicts the real-time DEA voltage at step k+1 in the time domain; Q and R are preset weight matrices. A preset MPC feedback control initial model is trained with the goal of minimizing the MPC optimization objective function. A pre-trained MPC feedback control model is obtained when a preset first convergence condition is met, which is used to optimize the DEA control quantity. The preset first convergence condition is that training stops when the MPC optimization objective function is less than or equal to a preset MPC optimization function threshold. Finally, the real-time trajectory tracking error is input into the pre-trained MPC feedback control model to obtain the feedback correction quantity. This feedback correction quantity is then fused with a preset ILC (Iterative Learning Control) feedforward control quantity to obtain the total DEA trajectory control quantity. After D / A conversion, this is output to the high-voltage amplifier. This allows for precise compensation of the DEA's nonlinear characteristics through feedforward control, while effectively suppressing unknown disturbances in the DEA through feedback control, ultimately achieving high-precision trajectory tracking control of the DEA. The above process integrates physical-driven dynamic modeling and under-perception modeling, utilizing both the interpretability of the physical model to generate high-quality feedforward and the ability of neural networks to handle complex nonlinearities. Furthermore, through transfer learning, each model can quickly adapt to different specifications of DEA, demonstrating good versatility.

[0036] Furthermore, the step of acquiring the real-time voltage of the DEA, the resampling current of the DEA, and the real-time ground true displacement of the DEA based on the DEA to be controlled includes: Based on the DEA to be controlled, obtain the real-time voltage, real-time current and real-time ground true displacement of the DEA; Median filtering is applied to the real-time DEA current to obtain a smoothed DEA current; The smoothed DEA current is resampled based on a preset control period to obtain the DEA resampled current.

[0037] In this embodiment, the output of a high-voltage amplifier (such as a TREK model) is connected to the DEA electrode, and the input of the high-voltage amplifier receives an analog voltage signal from the real-time controller. The voltage V, amplified 1000 times, is applied to the DEA to be controlled. Subsequently, the real-time voltage of the DEA is directly output through the real-time controller. The real-time current of the DEA is indirectly obtained by measuring the voltage across a high-precision sampling resistor connected in series in the grounding loop of the DEA using a high-resolution digital multimeter (sampling rate set to 0.08 seconds) or a dedicated current acquisition device. On the experimental platform, a high-precision laser displacement sensor (such as the Keyence IL series) is used to illuminate the mechanical load or joint of the DEA to measure the real-time ground displacement y of the DEA. The acquired real-time voltage, real-time current, and real-time ground displacement of the DEA provide raw electrical parameters and displacement reference data for subsequent current processing and displacement error calculation. Next, median filtering is applied to the real-time current of the DEA, with a sliding window length set to 5, effectively eliminating spike noise and random interference during the current acquisition process, obtaining a smooth DEA ​​current, ensuring the accuracy and stability of the current parameters, and avoiding noise affecting the accuracy of subsequent displacement prediction. Then, since the current sampling rate is inconsistent with the preset control period T (T=0.02s), the smoothed DEA current is resampled through the preset control period. This ensures that the sampling time axis of the current data is strictly aligned with the preset control period, obtains the DEA resampled current, ensures that the timing of the electrical parameters input to the NARX prediction model is consistent, and improves the accuracy of displacement prediction.

[0038] Furthermore, in obtaining the predicted NARX displacement value based on DEA real-time voltage, DEA resampling current, DEA real-time ground true displacement, and a preset NARX prediction model, the construction process of the preset NARX prediction model includes: The pre-calibrated DEA is excited based on the preset second excitation condition to obtain several second DEA calibration voltages, several DEA calibration resampling currents, several DEA calibration current integrals, and several first DEA ground true displacements. A NARX training set is constructed based on several second DEA calibration voltages, several DEA calibration resampling currents, and several DEA calibration current integrals. Several NARX displacement prediction values ​​are obtained based on the NARX training set and the preset NARX initial prediction model. The NARX performance function is constructed based on several NARX displacement prediction values ​​and several first DEA ground true displacement values. The preset NARX prediction initial model is trained with the goal of minimizing the NARX performance function until the preset second convergence condition is met, and the preset NARX prediction model is obtained.

[0039] In this embodiment, by stimulating the pre-calibrated DEA with a preset second excitation condition and collecting several second DEA calibration voltages, several DEA calibration resampling currents, several DEA calibration current integrals, and several first DEA ground true displacements, a NARX training set and actual ground displacements that conform to the actual characteristics of the DEA can be provided for training the preset NARX initial prediction model. Specifically: Where x is the NARX training set, The second DEA calibration voltage, To calibrate the DEA resampling current, The DEA calibration current integral is obtained by numerically integrating several DEA calibration resampled currents, specifically as follows: ,in, For integration time variable, For at any time The collected DEA calibration resampling current, The DEA calibration current is integrated, and t is the sampling time interval. The preset second excitation condition is: using a preset frequency / amplitude combination, the pre-calibrated DEA is periodically swept to excite it, and the first five cycles are taken as the training set. Then, by inputting the constructed NARX training set into the preset NARX initial prediction model, several NARX displacement prediction values ​​are obtained, specifically: The expanded expression is: in, = =1, =2, The preset current delay constant is... The preset voltage delay constant, As the output delay constant, therefore , , =10, To pre-determine the hidden layer neurons in the NARX initial prediction model, , and The weighting coefficients to be determined are... For the linear function of the output layer, For the hidden layer tansig function, and To obtain the bias, The NARX displacement prediction values ​​are then used. Next, the initial NARX prediction model is trained using the nonlinear least squares LM algorithm (Levenberg-Marquardt algorithm), and a NARX performance function is constructed based on several NARX displacement prediction values ​​and several first DEA ground truth displacement values. ,in, The mean square error of NARX performance. The total number of training data in the training set. Let be the NARX displacement prediction value for the i-th training data. Let be the ground truth displacement of the first DEA for the i-th training data. The preset NARX initial prediction model is trained with the goal of minimizing this performance function, iteratively optimizing the NARX model parameters until a preset second convergence condition is met. The current NARX model parameters are then obtained and stored in the controller memory. The preset NARX prediction model is then obtained, and can be used based on real-time measurements... , and Calculate the predicted displacement of the current joint. The above process directly establishes a mapping from electrical parameters to displacement, eliminating reliance on physical sensors and ensuring accurate self-sensing prediction of DEA displacement. The preset second convergence condition refers to stopping training when the NARX performance function is less than or equal to a preset NARX performance threshold.

[0040] Furthermore, in obtaining the feedback correction amount based on the real-time trajectory tracking error and the pre-trained MPC feedback control model, and obtaining the total DEA trajectory control amount based on the feedback correction amount and the preset ILC feedforward control amount, the process of obtaining the preset ILC feedforward control amount includes: Excite the pre-calibrated DEA based on the preset third excitation condition, obtain several third DEA voltages and several second DEA ground true displacements, and train the preset asymmetric hysteresis initial model and the preset creep initial model based on the several third DEA voltages and several second DEA ground true displacements respectively to obtain the asymmetric hysteresis model and the creep model, and construct a static nonlinear model based on the asymmetric hysteresis model and the creep model. Based on the preset second excitation condition and the static nonlinear model, several static DEA ground true displacements are obtained, and based on the several static DEA ground true displacements, the preset dynamic linear initial model is trained to obtain the dynamic linear model. A Hammerstein dynamic model is constructed based on static nonlinear models and dynamic linear models; Preset ILC feedforward control values ​​are obtained based on preset control parameters and the Hammerstein dynamic model.

[0041] In this embodiment, a pre-calibrated DEA is excited by a preset third excitation condition to obtain several third DEA voltages and several second DEA ground truth displacements. Based on these third DEA voltages and second DEA ground truth displacements, a preset asymmetric hysteresis initial model and a preset creep initial model are trained respectively, resulting in the asymmetric hysteresis model and creep model. This constructs a static nonlinear model that accurately fits the asymmetric hysteresis and creep characteristics in the static nonlinear characteristics of the DEA, laying the static characteristic foundation for the subsequent construction of the Hammerstein dynamic model (a nonlinear dynamic model). Next, several static DEA ground truth displacements are obtained using the preset second excitation condition and the static nonlinear model. Based on these static DEA ground truth displacements, a preset dynamic linear initial model is trained to obtain the dynamic linear model, which can fit the dynamic response characteristics of the DEA, achieving accurate characterization of the DEA's dynamic characteristics. Then, by cascading the static nonlinear model and the dynamic linear model, the Hammerstein dynamic model is constructed, which can completely reproduce the static nonlinear characteristics and dynamic linear characteristics of the DEA from electrical input to mechanical output, providing an accurate model for solving the ILC feedforward control quantity. Finally, the known nonlinearity of the DEA is accurately compensated by preset control parameters and the Hammerstein dynamic model to obtain the preset ILC feedforward control quantity, which can provide a basis for the fusion of subsequent feedback correction quantity and preset ILC feedforward control quantity.

[0042] Further, the pre-calibrated DEA is excited based on a preset third excitation condition to obtain several third DEA voltages and several second DEA ground true displacements. Based on these third DEA voltages and second DEA ground true displacements, a preset asymmetric hysteresis initial model and a preset creep initial model are trained respectively to obtain an asymmetric hysteresis model and a creep model. A static nonlinear model is then constructed based on the asymmetric hysteresis model and the creep model, including: The pre-calibrated DEA is excited based on the preset third excitation condition to obtain several third DEA voltages and several second DEA ground true displacements. A nonlinear training set is constructed based on several third DEA voltages; Several asymmetric hysteresis displacement prediction values ​​were obtained based on a nonlinear training set and a pre-set asymmetric hysteresis initial model. Several predicted creep displacement values ​​were obtained based on a nonlinear training set and a preset creep initial model. An asymmetric hysteresis performance function is constructed based on several asymmetric hysteresis displacement predictions and several second DEA ground true displacements. The preset asymmetric hysteresis initial model is trained with the goal of minimizing the asymmetric hysteresis performance function until the preset third convergence condition is met, and the asymmetric hysteresis model is obtained. A creep performance function is constructed based on several predicted creep displacement values ​​and several second DEA ground true displacement values. The creep performance function is minimized to train the preset creep initial model until the preset fourth convergence condition is met, and the creep model is obtained. A static nonlinear model is constructed based on the asymmetric hysteresis model and the creep model.

[0043] In this embodiment, a pre-calibrated DEA is excited by a preset third excitation condition to obtain several third DEA voltages and several second DEA ground true displacements, which can provide calibration data that fits the actual working state for modeling the static nonlinear characteristics of the DEA. The preset third excitation condition is: using a combination of low frequency (e.g., 0.2Hz) and multiple amplitude voltages to periodically sweep the pre-calibrated DEA to excite it. Then, the nonlinear training set is input into a preset asymmetric hysteresis initial model and a preset creep initial model, respectively, specifically: The preset asymmetric hysteresis initial model is: Where t is time, This is the predicted value for asymmetric hysteresis displacement. The coefficients of the polynomial to be determined are i = 1, 2, 3, 4. The third DEA voltage, To preset the total number of hysteresis operators, for density coefficient, The hysteresis operator is shown below: ; Where T is the preset control period. express The switching threshold .

[0044] The preset creep initial model is: ; in, The creep displacement prediction value is output by the creep model. Here is the weighting constant. This represents the total number of creep operators. The creep operator can be calculated using the following formula: ; in, To preset creep characteristic parameters, T represents the preset control period. The obtained asymmetric hysteresis displacement prediction values ​​can provide a reference for the performance optimization of the asymmetric hysteresis model, and the obtained creep displacement prediction values ​​can provide a reference for the performance optimization of the creep model. Then, an asymmetric hysteresis performance function is constructed using several asymmetric hysteresis displacement prediction values ​​and several second DEA ground truth displacements. The preset asymmetric hysteresis initial model is trained with the goal of minimizing this function until the preset third convergence condition is met. This allows for iterative optimization of the model parameters, resulting in an asymmetric hysteresis model that accurately fits the DEA asymmetric hysteresis characteristics. The preset third convergence condition refers to stopping training when the asymmetric hysteresis performance function is less than or equal to a preset asymmetric hysteresis performance threshold. Subsequently, a creep performance function is constructed using several creep displacement prediction values ​​and several second DEA ground truth displacements. The preset creep initial model is trained with the goal of minimizing this function until the preset fourth convergence condition is met. This allows for iterative optimization of the model parameters, resulting in a creep model that accurately fits the DEA creep characteristics. The preset fourth convergence condition refers to stopping training when the creep performance function is less than or equal to a preset creep performance threshold. Finally, by constructing a static nonlinear model using an asymmetric hysteresis model and a creep model, the static nonlinear characteristics of DEA can be integrated to form a static nonlinear model, providing static characteristic support for the subsequent construction of the Hammerstein dynamic model.

[0045] Further, the step of obtaining several static DEA ground truth displacements based on a preset second excitation condition and a static nonlinear model, and training a preset dynamic linear initial model based on these several static DEA ground truth displacements to obtain a dynamic linear model includes: Several static DEA ground true displacements are obtained based on the preset second excitation condition and the static nonlinear model. A dynamic linear training set is constructed based on several static DEA ground truth displacements; Several predicted dynamic linear displacement values ​​are obtained based on the dynamic linear training set and the preset dynamic linear initial model; A dynamic linear performance function is constructed based on several predicted dynamic linear displacements and several static DEA ground truth displacements. The preset dynamic linear initial model is trained with the goal of minimizing the dynamic linear performance function until the preset fifth convergence condition is met, and the dynamic linear model is obtained.

[0046] In this embodiment, by presetting the second excitation condition and the static nonlinear model, several static DEA ground truth displacements that only reflect the dynamic response can be obtained, thus providing a foundation for subsequent training of the preset dynamic linear initial model. Next, by inputting the dynamic linear training set into the preset dynamic linear initial model, several predicted dynamic linear displacement values ​​are obtained, specifically: in, is the predicted value of dynamic linear displacement, and are constants to be obtained, s is the Laplace operator, m and n are positive integers, m < n. When m = 0 and n = 3, . A number of predicted values of dynamic linear displacement can provide a reference basis for optimizing the performance of the dynamic linear model and support for the preliminary fitting of the dynamic characteristics of DEA. Then, a dynamic linear performance function is constructed by a number of predicted values of dynamic linear displacement and a number of static DEA ground truth displacements, and the preset dynamic linear initial model is trained until the preset fifth convergence condition is satisfied with the minimization of the dynamic linear performance function, so as to iteratively optimize the model parameters and obtain a dynamic linear model that can accurately characterize the dynamic response characteristics of DEA, providing support for the dynamic characteristics for the subsequent construction of a complete Hammerstein dynamic model. The preset fifth convergence condition means that when the dynamic linear performance function is less than or equal to the preset dynamic linear performance threshold, the training stops.

[0047] Further, obtaining the preset ILC feedforward control quantity based on the preset control parameter and the Hammerstein dynamic model includes: Obtaining a simulation displacement sequence based on the preset control parameter and the Hammerstein dynamic model, and obtaining an initial tracking error sequence based on the simulation displacement sequence and the preset simulation DEA displacement trajectory; Correcting the preset control parameter based on the initial tracking error sequence and the preset ILC evolution model to obtain a corrected control parameter, so as to obtain a first tracking error sequence based on the corrected control parameter, the Hammerstein dynamic model and the preset simulation DEA displacement trajectory. If the first tracking error sequence satisfies the preset fifth convergence condition, the corrected control parameter is used as the preset ILC feedforward control quantity.

[0048] In this embodiment, a simulation displacement sequence is obtained through the preset control parameter and the Hammerstein dynamic model, and the preset joint angle trajectory is , and is mapped to the preset simulation DEA displacement trajectory , and an initial tracking error sequence is obtained by combining the simulation displacement sequence and the preset simulation DEA displacement trajectory. Specifically: taking the Hammerstein dynamic model as the simulated controlled object, a preset ILC feedforward control quantity is generated by adopting a driving instruction cycle evolution method, where<00神仙道最新版下载00277>is the preset ILC feedforward control quantity generated at the (p + 1)-th time, is the preset ILC feedforward control quantity generated at the p-th time, is the preset proportional learning gain coefficient, which can be set to 2, is the preset integral learning gain coefficient, which can be set to 1, This is the initial tracking error sequence for the p-th iteration. The above process can capture the DEA trajectory deviation under preset control parameters, providing an initial basis for the iterative correction of the ILC feedforward control parameters. Next, the preset control parameters are corrected using the initial tracking error sequence and the preset ILC evolution model to obtain the corrected control parameters. Then, the first tracking error sequence is obtained by combining the corrected control parameters, the Hammerstein dynamic model, and the preset simulated DEA displacement trajectory. It is then determined whether the first tracking error sequence satisfies the preset fifth convergence condition. If it does, the corrected control parameter that meets the preset fifth convergence condition is determined as the preset ILC feedforward control quantity, ensuring that the obtained preset ILC feedforward control quantity can compensate for the nonlinear characteristics of the DEA, providing a precise and effective basic control quantity for subsequently obtaining the total DEA trajectory control quantity. The preset fifth convergence condition is that all values ​​in the first tracking error sequence are less than or equal to 0.01. The control input sequence of the last evolution is recorded as the final preset ILC feedforward control quantity. .

[0049] Further, the step of obtaining several first DEA calibration voltages and several MPC predicted displacements based on preset first excitation conditions, preset constraints, and pre-calibrated DEA, and obtaining several training trajectory tracking errors based on the several MPC predicted displacements and preset reference MPC displacement trajectories, includes: The pre-calibrated DEA is excited based on the preset first excitation conditions and preset constraints to obtain several first DEA calibration voltages; Several MPC predicted displacements are obtained based on a preset MPC feedback control initial model and several first DEA calibration voltages. Based on several MPC predicted displacements and preset benchmark MPC displacement trajectories, several training trajectory tracking errors are obtained.

[0050] In this embodiment, the trained dynamic linear model is used as the initial model for preset MPC feedback control, and the initial model is exported as C code and deployed to the dSPACE controller. By exciting the pre-calibrated DEA with preset first excitation conditions and preset constraints, several first DEA calibration voltages that conform to the DEA hardware characteristics and actual control constraints can be provided for the training of the initial MPC feedback control model. The preset sampling time is 0.01s, the preset prediction time domain is 15, and the preset control time domain is 5. Considering the positive excitation characteristics of the DEA and the input limitations of the high-voltage amplifier, the preset constraints for the preset feedback correction amount are as follows: The preset feedback correction control weight is 0, the feedback correction rate of change weight is 0.7, and the output weight is 0.13. The preset first excitation condition involves periodically sweeping the pre-calibrated DEA using a preset frequency / amplitude combination to excite the pre-calibrated DEA. Next, by inputting several first DEA calibration voltages into the preset MPC feedback control initial model, several MPC predicted displacements are obtained, enabling preliminary prediction of the DEA displacement and providing a reference for subsequent trajectory tracking error calculation. Then, by comparing several MPC predicted displacements with the preset baseline MPC displacement trajectory, several training trajectory tracking errors are obtained, capturing the deviation between the predicted value and the desired trajectory of the preset MPC feedback control initial model, providing a basis for subsequent iterative optimization of the model.

[0051] This embodiment provides a DEA trajectory tracking control system. Please refer to [link / reference]. Figure 2 It includes a data acquisition module, a NARX displacement prediction module, an error calculation module, and a control quantity generation module, specifically: The data acquisition module is used to acquire the real-time voltage of the DEA, the resampling current of the DEA, and the real-time ground true displacement of the DEA based on the DEA to be controlled. The NARX displacement prediction module is used to obtain NARX displacement prediction values ​​based on DEA real-time voltage, DEA resampling current, DEA real-time ground true displacement and a preset NARX prediction model. The error calculation module is used to obtain the real-time trajectory tracking error based on the preset DEA displacement trajectory and NARX displacement prediction value; The control quantity generation module is used to obtain the feedback correction quantity based on the real-time trajectory tracking error and the pre-trained MPC feedback control model, and to obtain the total DEA trajectory control quantity based on the feedback correction quantity and the preset ILC feedforward control quantity. The construction process of the pre-trained MPC feedback control model includes: Based on the preset first excitation conditions, preset constraints and pre-calibrated DEA, several first DEA calibration voltages and several MPC predicted displacements are obtained, and based on the several MPC predicted displacements and the preset benchmark MPC displacement trajectory, several training trajectory tracking errors are obtained. An MPC optimization objective function is constructed based on several first DEA calibration voltages and several training trajectory tracking errors. The initial model of MPC feedback control is trained with the goal of minimizing the MPC optimization objective function until the first preset convergence condition is met, thus obtaining the pre-trained MPC feedback control model.

[0052] This embodiment provides a DEA trajectory tracking control system that, in practical applications, only requires a NARX displacement prediction module. By inputting the real-time DEA voltage, DEA resampling current, and real-time ground true displacement of the DEA into a preset NARX prediction model, the DEA displacement can be sensed in real time without external displacement sensors, and the NARX displacement prediction value can be obtained, thus providing a basis for the calculation of the real-time trajectory tracking error. Next, an error calculation module is used to obtain the real-time trajectory tracking error using the preset DEA displacement trajectory and the NARX displacement prediction value, providing a reference for subsequent feedback control correction. Then, by constructing an MPC optimization objective function and training a preset MPC feedback control initial model with the goal of minimizing the MPC optimization objective function, a pre-trained MPC feedback control model can be obtained when the preset first convergence condition is met, which is used to optimize the DEA control quantity. Finally, a control quantity generation module is used to input the real-time trajectory tracking error into the pre-trained MPC feedback control model to obtain the feedback correction quantity. The feedback correction quantity is then fused with the preset ILC feedforward control quantity to obtain the total control quantity of the DEA trajectory. This allows for precise compensation of the nonlinear characteristics of the DEA through feedforward control, while effectively suppressing unknown disturbances in the DEA with the help of feedback control, ultimately achieving high-precision trajectory tracking control of the DEA.

[0053] Furthermore, the data acquisition module is used to acquire the real-time voltage of the DEA, the DEA resampling current, and the real-time ground true displacement of the DEA based on the DEA to be controlled, including: Based on the DEA to be controlled, obtain the real-time voltage, real-time current and real-time ground true displacement of the DEA; Median filtering is applied to the real-time DEA current to obtain a smoothed DEA current; The smoothed DEA current is resampled based on a preset control period to obtain the DEA resampled current.

[0054] In this embodiment, by acquiring the real-time voltage, real-time current, and real-time ground true displacement of the DEA to be controlled, raw electrical parameters and displacement reference data can be provided for subsequent current processing and displacement error calculation. Next, by performing median filtering on the real-time DEA current, spike noise and random interference during the current acquisition process can be effectively eliminated, obtaining a smoothed DEA current. This ensures the accuracy and stability of the current parameters and avoids noise affecting the accuracy of subsequent displacement prediction. Then, by resampling the smoothed DEA current through a preset control cycle, the sampling time axis of the current data can be strictly aligned with the preset control cycle, obtaining the resampled DEA current. This ensures that the timing of the electrical parameters input to the NARX prediction model is consistent, improving the accuracy of displacement prediction.

[0055] This embodiment also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the functions of the system as described above.

[0056] It is understood that the above system embodiments correspond to the method embodiments of the present invention, and can implement the DEA trajectory tracking control method provided by any of the above method embodiments of the present invention.

[0057] It should be noted that the system embodiments described above are merely illustrative, and some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0058] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A DEA trajectory tracking control method, characterized in that, include: Based on the DEA to be controlled, obtain the real-time voltage of the DEA, the resampled current of the DEA, and the real-time ground true displacement of the DEA. NARX displacement prediction values ​​are obtained based on DEA real-time voltage, DEA resampling current, DEA real-time ground true displacement, and a preset NARX prediction model. Real-time trajectory tracking error is obtained based on preset DEA displacement trajectory and NARX displacement prediction value; The feedback correction amount is obtained based on the real-time trajectory tracking error and the pre-trained MPC feedback control model, and the total DEA trajectory control amount is obtained based on the feedback correction amount and the preset ILC feedforward control amount. The construction process of the pre-trained MPC feedback control model includes: Based on the preset first excitation conditions, preset constraints and pre-calibrated DEA, several first DEA calibration voltages and several MPC predicted displacements are obtained, and based on the several MPC predicted displacements and the preset benchmark MPC displacement trajectory, several training trajectory tracking errors are obtained. An MPC optimization objective function is constructed based on several first DEA calibration voltages and several training trajectory tracking errors. The initial model of MPC feedback control is trained with the goal of minimizing the MPC optimization objective function until the first preset convergence condition is met, thus obtaining the pre-trained MPC feedback control model.

2. The DEA trajectory tracking control method according to claim 1, characterized in that, The process of acquiring the real-time voltage of the DEA, the resampled current of the DEA, and the real-time ground true displacement of the DEA based on the DEA to be controlled includes: Based on the DEA to be controlled, obtain the real-time voltage, real-time current and real-time ground true displacement of the DEA; Median filtering is applied to the real-time DEA current to obtain a smoothed DEA current; The smoothed DEA current is resampled based on a preset control period to obtain the DEA resampled current.

3. The DEA trajectory tracking control method according to claim 1, characterized in that, In obtaining NARX displacement prediction values ​​based on DEA real-time voltage, DEA resampling current, DEA real-time ground true displacement, and a preset NARX prediction model, the construction process of the preset NARX prediction model includes: The pre-calibrated DEA is excited based on the preset second excitation condition to obtain several second DEA calibration voltages, several DEA calibration resampling currents, several DEA calibration current integrals, and several first DEA ground true displacements. A NARX training set is constructed based on several second DEA calibration voltages, several DEA calibration resampling currents, and several DEA calibration current integrals. Several NARX displacement prediction values ​​are obtained based on the NARX training set and the preset NARX initial prediction model. The NARX performance function is constructed based on several NARX displacement prediction values ​​and several first DEA ground true displacement values. The preset NARX prediction initial model is trained with the goal of minimizing the NARX performance function until the preset second convergence condition is met, and the preset NARX prediction model is obtained.

4. The DEA trajectory tracking control method according to claim 1, characterized in that, In obtaining the feedback correction amount based on the real-time trajectory tracking error and the pre-trained MPC feedback control model, and obtaining the total DEA trajectory control amount based on the feedback correction amount and the preset ILC feedforward control amount, the process of obtaining the preset ILC feedforward control amount includes: Excite the pre-calibrated DEA based on the preset third excitation condition, obtain several third DEA voltages and several second DEA ground true displacements, and train the preset asymmetric hysteresis initial model and the preset creep initial model based on the several third DEA voltages and several second DEA ground true displacements respectively to obtain the asymmetric hysteresis model and the creep model, and construct a static nonlinear model based on the asymmetric hysteresis model and the creep model. Based on the preset second excitation condition and the static nonlinear model, several static DEA ground true displacements are obtained, and based on the several static DEA ground true displacements, the preset dynamic linear initial model is trained to obtain the dynamic linear model. A Hammerstein dynamic model is constructed based on static nonlinear models and dynamic linear models; Preset ILC feedforward control values ​​are obtained based on preset control parameters and the Hammerstein dynamic model.

5. The DEA trajectory tracking control method according to claim 4, characterized in that, The process involves exciting a pre-calibrated DEA based on a preset third excitation condition to obtain several third DEA voltages and several second DEA ground true displacements. Based on these third DEA voltages and second DEA ground true displacements, a preset asymmetric hysteresis initial model and a preset creep initial model are trained respectively to obtain an asymmetric hysteresis model and a creep model. A static nonlinear model is then constructed based on the asymmetric hysteresis model and the creep model, including: The pre-calibrated DEA is excited based on the preset third excitation condition to obtain several third DEA voltages and several second DEA ground true displacements. A nonlinear training set is constructed based on several third DEA voltages; Several asymmetric hysteresis displacement prediction values ​​were obtained based on a nonlinear training set and a pre-set asymmetric hysteresis initial model. Several predicted creep displacement values ​​were obtained based on a nonlinear training set and a preset creep initial model. An asymmetric hysteresis performance function is constructed based on several asymmetric hysteresis displacement predictions and several second DEA ground true displacements. The preset asymmetric hysteresis initial model is trained with the goal of minimizing the asymmetric hysteresis performance function until the preset third convergence condition is met, and the asymmetric hysteresis model is obtained. A creep performance function is constructed based on several predicted creep displacement values ​​and several second DEA ground true displacement values. The creep performance function is minimized to train the preset creep initial model until the preset fourth convergence condition is met, and the creep model is obtained. A static nonlinear model is constructed based on the asymmetric hysteresis model and the creep model.

6. The DEA trajectory tracking control method according to claim 4, characterized in that, The process involves obtaining several static DEA ground truth displacements based on a preset second excitation condition and a static nonlinear model, and then training a preset dynamic linear initial model based on these static DEA ground truth displacements to obtain a dynamic linear model, including: Several static DEA ground true displacements are obtained based on the preset second excitation condition and the static nonlinear model. Constructed based on several static DEA ground truth displacements; Several predicted dynamic linear displacement values ​​are obtained based on the dynamic linear training set and the preset dynamic linear initial model; A dynamic linear performance function is constructed based on several predicted dynamic linear displacements and several static DEA ground truth displacements. The preset dynamic linear initial model is trained with the goal of minimizing the dynamic linear performance function until the preset fifth convergence condition is met, and the dynamic linear model is obtained.

7. The DEA trajectory tracking control method according to claim 4, characterized in that, The process of obtaining the preset ILC feedforward control quantity based on preset control parameters and the Hammerstein dynamic model includes: The simulated displacement sequence is obtained based on the preset control parameters and the Hammerstein dynamic model, and the initial tracking error sequence is obtained based on the simulated displacement sequence and the preset simulated DEA displacement trajectory. The preset control parameters are corrected based on the initial tracking error sequence and the preset ILC evolution model to obtain the corrected control parameters. The first tracking error sequence is obtained based on the corrected control parameters, the Hammerstein dynamic model and the preset simulated DEA displacement trajectory. If the first tracking error sequence satisfies the preset fifth convergence condition, the corrected control parameters are used as the preset ILC feedforward control quantity.

8. The DEA trajectory tracking control method according to claim 1, characterized in that, The process involves obtaining several first DEA calibration voltages and several MPC predicted displacements based on preset first excitation conditions, preset constraints, and pre-calibrated DEA, and obtaining several training trajectory tracking errors based on the several MPC predicted displacements and preset benchmark MPC displacement trajectories, including: The pre-calibrated DEA is excited based on the preset first excitation conditions and preset constraints to obtain several first DEA calibration voltages; Several MPC predicted displacements are obtained based on a preset MPC feedback control initial model and several first DEA calibration voltages. Based on several MPC predicted displacements and preset benchmark MPC displacement trajectories, several training trajectory tracking errors are obtained.

9. A DEA trajectory tracking control system, characterized in that, It includes a data acquisition module, a NARX displacement prediction module, an error calculation module, and a control quantity generation module, specifically: The data acquisition module is used to acquire the real-time voltage of the DEA, the resampling current of the DEA, and the real-time ground true displacement of the DEA based on the DEA to be controlled. The NARX displacement prediction module is used to obtain NARX displacement prediction values ​​based on DEA real-time voltage, DEA resampling current, DEA real-time ground true displacement and a preset NARX prediction model. The error calculation module is used to obtain the real-time trajectory tracking error based on the preset DEA displacement trajectory and NARX displacement prediction value; The control quantity generation module is used to obtain the feedback correction quantity based on the real-time trajectory tracking error and the pre-trained MPC feedback control model, and to obtain the total DEA trajectory control quantity based on the feedback correction quantity and the preset ILC feedforward control quantity. The construction process of the pre-trained MPC feedback control model includes: Based on the preset first excitation conditions, preset constraints and pre-calibrated DEA, several first DEA calibration voltages and several MPC predicted displacements are obtained, and based on the several MPC predicted displacements and the preset benchmark MPC displacement trajectory, several training trajectory tracking errors are obtained. An MPC optimization objective function is constructed based on several first DEA calibration voltages and several training trajectory tracking errors. The initial model of MPC feedback control is trained with the goal of minimizing the MPC optimization objective function until the first preset convergence condition is met, thus obtaining the pre-trained MPC feedback control model.

10. A DEA trajectory tracking control system according to claim 9, characterized in that, The data acquisition module is used to acquire the real-time voltage of the DEA, the DEA resampling current, and the real-time ground true displacement of the DEA based on the DEA to be controlled, including: Based on the DEA to be controlled, obtain the real-time voltage, real-time current and real-time ground true displacement of the DEA; Median filtering is applied to the real-time DEA current to obtain a smoothed DEA current; The smoothed DEA current is resampled based on a preset control period to obtain the DEA resampled current.

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