A method for compensating the dead-zone nonlinearity of actuators in industrial control systems based on digital twins

Abstract

This invention discloses a method for nonlinear compensation of actuator dead zone in industrial control systems based on digital twins. The method involves real-time acquisition of actuator vibration, control commands, and operating condition data; extraction of dimensionality-reduced vibration features using wavelet packet transform and stacked autoencoders; inputting these features along with the operating condition time series into a GRU with an integrated attention mechanism to dynamically infer asymmetric positive and negative dead zone boundaries; and then applying an exponential smooth inverse model to flexibly reconstruct the original commands, generating smooth compensation commands. Simultaneously, a digital twin base is constructed, and unscented Kalman filtering combined with actual feedback errors is used to correct the twin parameters online. This invention breaks the static assumption of dead zone, eliminates severe chattering at zero crossings, and achieves high-fidelity, self-evolving, and smooth, hysteresis-free control of traditional industrial equipment throughout its entire lifecycle under complex disturbances.

Description

Technical Field

[0001] This invention relates to the field of industrial automation control technology, and in particular to a method for compensating for the dead zone nonlinearity of actuators in industrial control systems based on digital twins. Background Technology

[0002] With the continuous evolution of modern industrial automation technology, distributed control systems and programmable logic controllers (PLCs) are widely used in large-scale energy equipment such as steam turbines and hydro turbines. As core components of industrial control systems, actuators such as servo valves and hydraulic actuators inevitably experience nonlinear dead-zone effects due to the coupling effects of mechanical wear, static friction, and hydraulic dynamics during long-term operation. This can easily lead to control signal truncation, system response hysteresis, increased steady-state error, and even limit cycle oscillations, directly affecting the control accuracy and operational stability of industrial equipment.

[0003] CN110673472A discloses an adaptive robust control method based on neural network compensation for dead zone inversion error. This scheme constructs an approximate inverse transformation of the dead zone using a smooth, continuous mathematical model, designs a single-hidden-layer neural network to compensate for inversion errors online, and derives an adaptive parameter law to handle system uncertainties. It also incorporates a nonlinear robust feedback term to suppress modeling errors and external disturbances. However, this scheme does not consider the dynamic disturbances to the dead zone boundary caused by complex operating conditions such as high-frequency vibrations and oil temperature and pressure fluctuations in industrial settings, and cannot capture dead zone softening and boundary drift phenomena under strong vibration environments. Furthermore, it fails to explore the temporal dependence of dead zone evolution and the long-term degradation trend of equipment, lacking full lifecycle adaptive capability. It also does not construct a digital twin virtual mapping of the actuator and an online model correction mechanism, resulting in significant limitations in compensation accuracy and adaptability under harsh operating conditions of large industrial equipment.

[0004] CN120143775A discloses a method and system for real-time transmission of IoT sensing data in a digital twin scenario. This solution collects multi-source sensing data from industrial equipment, constructs a timestamp alignment mechanism to achieve data temporal matching, builds a digital twin based on equipment topology and process constraints, and achieves multi-device collaborative control and transmission chain gap compensation through a dynamic parameter correction loop. However, this solution mainly focuses on IoT sensing data transmission and multi-device collaborative control in industrial production lines, without addressing the compensation algorithm for actuator dead-zone nonlinearity, nor integrating digital twin technology into the high-frequency dead-zone compensation stage. Furthermore, it lacks a dedicated timing prediction model and smooth transition compensation mechanism designed for dead-zone characteristics, failing to solve problems such as control hysteresis and command jump chatter caused by dead-zone effects, and thus struggling to meet the millisecond-level high-precision control requirements of actuators.

[0005] In summary, existing actuator dead-zone compensation technologies mostly employ fixed-parameter static inverse models or simple adaptive gain adjustment, generally treating the dead-zone boundary as a constant or slowly varying scalar. This severely ignores the dynamic disturbances to dead-zone characteristics caused by complex industrial conditions. Furthermore, due to the lack of exploration into the temporal dependence of dead-zone evolution, as well as the absence of online correction of digital twin models and full lifecycle adaptive optimization mechanisms, it is difficult to achieve dynamic and accurate compensation of the dead zone under complex conditions. Consequently, these technologies fail to meet the high-precision, high-fidelity, and smooth, disturbance-free control requirements of high-end industrial equipment, which remains a pressing technical problem to be solved in the current field. Summary of the Invention

[0006] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0007] In view of the aforementioned existing problems, this invention is proposed. Therefore, this invention provides a method for compensating for the dead-zone nonlinearity of actuators in industrial control systems based on digital twins, to solve the problems mentioned in the background art.

[0008] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for compensating the dead-zone nonlinearity of actuators in industrial control systems based on digital twins, comprising: The system acquires in real time the vibration signal of the actuator, the original control commands output by the main controller, and the operating condition data characterizing the operating status of the actuator. The vibration signal is processed to extract and fuse vibration features that characterize the changes in the dead zone characteristics of the actuator; Using the vibration characteristics, original control commands, and operating data as input, a pre-trained time-series prediction model dynamically predicts the current positive dead zone boundary and negative dead zone boundary of the actuator. Based on the dynamically predicted positive dead zone boundary and negative dead zone boundary, the original control command is adjusted to generate a compensated control command, and the compensated control command is applied to the actuator.

[0009] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention introduces high-frequency vibration signals into the dead zone evaluation dimension. By extracting and fusing multi-dimensional time-frequency features through wavelet packet transform and stacked encoder, it can keenly capture the changes in mechanical clearance state and dead zone softening phenomenon caused by mechanical resonance or harsh working conditions, thus solving the problem of severe distortion of traditional scalar dead zone models under strong disturbance environments.

[0010] 2. This invention employs a GRU timing prediction model that integrates an attention mechanism, fully exploring the timing dependence of the physical properties of fluid hindrance and mechanical friction. By dynamically weighting and focusing on key historical abrupt changes, it can infer the asymmetric dynamic dead zone boundary of the actuator during forward and reverse movements in real time and accurately, providing reliable data support for underlying high-frequency control.

[0011] 3. Furthermore, this invention abandons the traditional hard-switching inverse model and applies a smooth inverse model with an exponential smooth transition slope factor. This model achieves flexible reconstruction compensation from discontinuous to continuous near the dead zone boundary, enabling the control command to smoothly transition at the zero crossing point, effectively avoiding high-frequency jumps in the valve core and oil pressure resonance, and achieving smooth, lag-free drive. Attached Figure Description

[0012] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart illustrating the overall process of a digital twin-based method for compensating the dead-zone nonlinearity of actuators in an industrial control system, as described in one embodiment of the present invention. Detailed Implementation

[0013] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0014] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0015] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0016] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Example 1

[0017] Reference Figure 1 This is the first embodiment of the present invention, which provides a method for compensating for the dead-zone nonlinearity of actuators in an industrial control system based on digital twins, including: S1. Real-time acquisition of the actuator's vibration signal, the original control commands output by the main controller, and operating condition data characterizing the actuator's operating status.

[0018] Specifically, in this embodiment, the premise of constructing a high-fidelity digital twin model for dead zone nonlinear compensation is to acquire multi-source heterogeneous data that can reflect the coupling state of multiple physics fields. These data include vibration signals, original control commands, and operating condition data.

[0019] It should be noted that in the harsh actual operating conditions of large energy equipment (such as steam turbines and water turbines), the mechanical dead zone of actuators (such as electro-hydraulic servo valves and hydraulic actuators) is not a static constant. High-frequency mechanical vibrations can change the microscopic contact state and friction coefficient between the valve core and valve sleeve, thereby causing dead zone softening or boundary drift phenomena in physics. Therefore, in the present invention, the vibration signals acquired specifically include high-frequency vibration signals collected by a turbine shaft inlet monitoring device (such as the TSI rotating machinery safety monitoring and protection system) and a piezoelectric accelerometer or eddy current sensor installed on the actuator housing.

[0020] Furthermore, assume the number of acquisition channels is... In discrete time The collected vibration signal vector Represented as: in, Indicates the first One vibration monitoring channel The vibration amplitude at any given moment (e.g., acceleration or displacement). This is represented as a transpose operation.

[0021] It should be explained that introducing this vibration signal can break the limitation of the traditional control theory that assumes the dead zone width is a fixed mechanical clearance, and provide a reference for capturing the dynamic dead zone changes excited by vibration.

[0022] Furthermore, the acquired raw control commands are ideal drive signals calculated by the main controller (e.g., DCS distributed control system, DEH digital electro-hydraulic control system, or PLC) based on process setpoints and control logic such as PID, denoted as... This signal represents the desired action command without considering any mechanical or hydraulic hysteresis. It serves as a benchmark for calculating compensation amounts, driving the digital twin, and comparing the actual output to solve for model errors.

[0023] Furthermore, the nonlinear dead zone of the actuator is affected not only by mechanical clearance but also by the coupled influence of fluid dynamics and thermodynamics. For example, changes in the temperature of fire-resistant oil or turbine oil significantly alter the dynamic viscosity of the fluid, thereby affecting hydraulic damping and the starting pressure differential of the hydraulic actuator, resulting in an asymmetric change in the dead zone during valve opening and closing. Therefore, in this embodiment, the real-time acquired operating data mainly includes the hydraulic system's oil temperature, supply pressure, and the actual feedback displacement of the actuator. Taking these data as an example, in... Operating condition data vector at time point It can be represented as: in, It indicates the real-time temperature of the hydraulic oil, used to characterize the effect of the oil's viscosity-temperature characteristics on hydraulic resistance. This indicates the real-time oil supply pressure of the system, serving as the boundary of the available power source used to overcome dead zone static friction. This represents the actual displacement feedback of the actuator acquired through a linearly variable differential transformer, used to characterize the actuator's current spatial position within the nonlinear hysteresis loop.

[0024] In addition, in order for the vibration signals, original control commands and operating condition data obtained above to be effectively processed by subsequent models, these data must be normalized, and then the temporal correlation between these data and their historical states must be established to reflect the memory effect and degradation trend of dead zone evolution.

[0025] Specifically, this normalization method uses traditional Z-score standardization to accommodate the uneven distribution of the aforementioned data. It is important to emphasize that the mean and standard deviation of each feature dimension calculated during offline training will be fixed and stored in the parameter library of the digital twin model. During online real-time operation, the stored mean and standard deviation must be strictly used to perform the same standardization processing on the real-time acquired data.

[0026] Meanwhile, in order to eliminate the differences in sampling rates among these data, downsampling or interpolation algorithms can be used to align the collected high-frequency vibration signals, original control commands, and operating condition data to the single operation cycle (e.g., 20ms) time base of the underlying control system, thereby providing an aligned data foundation for subsequent feature extraction and time series prediction.

[0027] S2. Process the vibration signal, extract and fuse the vibration features that characterize the changes in the dead zone of the actuator.

[0028] It should be noted that the original high-frequency vibration signal usually contains a large amount of environmental background noise and the rotor's own power frequency interference. Directly inputting this into the prediction model will lead to an explosion of feature dimensions and is highly likely to cause the curse of dimensionality and model overfitting. Furthermore, since the vibration energy of a specific frequency band (e.g., the inherent resonant frequency of the actuator housing or valve core) is the fundamental physical cause of the change in the mechanical clearance contact separation state (i.e., dead zone softening), it is necessary to extract multi-dimensional features from the perspectives of the time and frequency domains and use unsupervised learning networks for nonlinear dimensionality reduction to extract the essential features that best characterize the dead zone evolution law.

[0029] Furthermore, wavelet packet transform (WPT) is used to perform multi-scale time-frequency decomposition of the vibration signal, and the energy distribution characteristics of each decomposed frequency band are calculated to form a preliminary time-frequency feature vector.

[0030] Specifically, let the discrete sequence of a single-channel vibration signal after time truncation be... Define the number of wavelet packet decomposition layers as Unlike traditional discrete wavelet transform, which only decomposes the low-frequency components, the wavelet packet transform in this invention performs orthogonal decomposition on both the low-frequency and high-frequency components simultaneously. The decomposition algorithm is as follows: in, Indicates the first The first layer of decomposition Wavelet packet coefficients of each node ( ,and ); and These represent the low-pass and high-pass filter coefficients that are conjugate or orthogonal to the selected wavelet basis (e.g., the orthogonal Daubechies wavelet).

[0031] Furthermore, in obtaining the first Layer After calculating the frequency band coefficients, the vibration energy within each independent frequency band is calculated. : In addition, to eliminate the fluctuations in absolute amplitude caused by different unit operating conditions, it is necessary to normalize the energy of each frequency band and calculate the normalized energy distribution characteristics. ,get: It should be noted that, after the above processing, the present invention converts the high-frequency vibration signal into a signal with a length of [missing information]. The initial time-frequency eigenvector is denoted as... This vector primarily depicts the energy spectrum of the actuator when it is excited by vibration, thus highly sensitively reflecting the frequency distribution shift caused by microscopic jamming or wear of the valve's internal components.

[0032] Furthermore, based on the above processing, relying solely on wavelet packet band energy can easily overlook the global impact and wear levels. Therefore, it is necessary to combine the obtained preliminary time-frequency feature vector with other time-domain or frequency-domain features extracted from the vibration signal.

[0033] Specifically, the root mean square value (representing the overall intensity of vibration) and kurtosis index (representing the transient impact intensity caused by mechanical jamming) in the time domain are extracted. In this embodiment, the kurtosis index is used. For example, the processing formula is as follows: in, The number of sampling points. This represents the signal mean.

[0034] Furthermore, by concatenating the aforementioned time-domain features with the preliminary time-frequency feature vector, a multi-dimensional hybrid feature vector can be constructed, denoted as... .

[0035] Furthermore, due to the redundancy and collinearity issues in the mixed feature vectors, directly feeding them into subsequent models would severely slow down the real-time computing speed of the digital twin system. Therefore, this scheme constructs a pre-trained stacked autoencoder (SAE) for the fusion and dimensionality reduction of nonlinear features. Specifically, the stacked autoencoder consists of multiple stacked autoencoders, and its network topology is symmetrical hourglass-shaped. This network structure includes an input layer, an encoder composed of multiple hidden layers, a bottleneck layer with a minimum number of neurons, and a symmetrical decoder.

[0036] Specifically, the encoding process of this stacked encoder can be represented by the following formula: in, For the first The output of the hidden layer ( ), and The first The weight matrix and bias vector of the layer, It is a non-linear activation function (e.g., ReLU or Sigmoid).

[0037] It should be noted that through the layer-by-layer mapping of the above encoding process, the intermediate bottleneck layer can be reached for output.

[0038] In one possible implementation of this embodiment, the training and application steps of the stacked encoder are described as follows: First, a training set is constructed by collecting a large number of hybrid feature vectors of actuator vibrations in both healthy and degraded states throughout history. The hierarchical structure of the SAE is set as follows: [Input dimension → 64 → 32 → 16 → 32 → 64 → Output dimension], where the bottleneck layer has a dimension of 16. Then, to avoid getting trapped in local optima, each individual autoencoder is pre-trained layer by layer to minimize the error between a single layer's input and its reconstructed output. After stacking all layers, the global reconstruction error (i.e., the mean squared error (MSE) between the hybrid feature vector of the input and the hybrid feature vector of the decoder's final predicted output) is used as the loss function. in, Indicates the first... A mixed feature vector; Similarly.

[0039] Next, the Adam optimization algorithm is used to update the weight parameters of all layers until the network converges. Finally, in the online real-time execution phase, the trained decoder is discarded, and the real-time extracted hybrid feature vector is input into the stacked encoder. Forward propagation is performed only to the bottleneck layer, and the output of the bottleneck layer is taken as the final vibration feature, denoted as . .

[0040] It should be explained that the effect of using this stacked encoder to extract bottleneck layer features is that, through an unsupervised self-reconstruction mechanism, the encoder can automatically filter out white noise and unrelated redundant components in the vibration signal, and map the high-dimensional heterogeneous engineering signal into a low-dimensional and dense latent space. In this space, the final output vibration features integrate the physical interference intensity of the vibration on the dead zone nonlinearity, and therefore can be used as a standardized context input.

[0041] S3. Using vibration characteristics, original control commands, and operating condition data as input, a pre-trained time-series prediction model is used to dynamically predict the current positive and negative dead zone boundaries of the actuator.

[0042] It should be noted that the nonlinear dead zone of an actuator is not only a transient phenomenon, but also exhibits a strong memory effect and asymmetric hysteresis characteristics. For example, when a valve is continuously opened in the forward direction and suddenly closed in the reverse direction, its dead zone boundary is drastically different due to internal oil compression, elastic deformation of mechanical components, and the conversion of static / dynamic friction. Therefore, it is impossible to accurately locate the dead zone boundary based solely on the data at the current moment. Based on this, the present invention employs a network model containing a gated recurrent unit (GRU) as a time-series prediction model, primarily used to handle the time-series dependencies of the input data.

[0043] Furthermore, in constructing the input data, this invention concatenates the extracted final vibration features with the aligned original control commands and operating condition data. Specifically, for each historical time step within the sliding window... ( , (where the time sliding window length is used) to construct a comprehensive input vector. : Furthermore, a complete time series input matrix can be formed based on this integrated input vector, denoted as... And then feed it into a pre-trained GRU network.

[0044] It should be explained that the GRU network was chosen instead of the traditional recurrent neural network (RNN) or long short-term memory network (LSTM) because GRU can effectively overcome the problem of vanishing gradients in long sequences while simplifying the gating structure (i.e., retaining only update gates and reset gates), which greatly reduces the number of network parameters. This has a crucial real-time advantage for industrial control underlying digital twin systems that require millisecond-level response.

[0045] Furthermore, the GRU in this embodiment includes classic update gates, reset gates, candidate hidden states, and the current hidden state. The forward propagation physical calculation process for each time step is as follows: Update Gate This is used to control how much of the physical state information from the previous moment is retained in the current state: Reset door Used to control the degree to which previous state information is ignored in order to cope with sudden changes in operating conditions: Candidate hidden state and current hidden state The calculation is as follows: in, It is the Sigmoid activation function. It is the hyperbolic tangent function. This represents matrix element-wise multiplication. This is the previous hidden state; , , and , , These are all weight matrices learned by the GRU during training; similarly, , , Both are bias terms.

[0046] It should be noted that in the above calculations, the hidden state represents the implicit hysteresis memory accumulated by the actuator up to this point (e.g., accumulated frictional heat, deformation potential energy, etc.).

[0047] Furthermore, in harsh industrial environments, actuators may be subjected to transient vibration shocks or oil pressure surges. These sudden events at historical moments have a decisive impact on the evolution of the current dead zone boundary. To accurately capture these critical moments, the timing prediction model of this invention also integrates an attention mechanism.

[0048] Specifically, attention mechanisms are used to predict the current moment. When the dead zone boundary is reached, the hidden states of all historical time steps output by the GRU are dynamically weighted. The calculation logic is as follows: First, calculate each historical time step. Attention score : in, , This is the weight matrix in the attention mechanism. This is the bias term in the attention mechanism.

[0049] Then, the scores are normalized using the Softmax function to obtain the dynamic weight coefficients. : Finally, all historical hidden states are weighted and summed to generate a context vector focusing on key historical information. : It should be noted that the advantage of introducing an attention mechanism is that it enables the digital twin model to prioritize tasks during deployment. When the digital twin model detects a surge in high-frequency vibrations at a certain historical moment (reflected in the final vibration characteristics of the integrated input vector), the attention mechanism automatically amplifies the dynamic weight coefficients at that moment, thereby simulating the dead zone softening and contraction phenomenon caused by forced vibration of mechanical clearances.

[0050] Furthermore, at the output of the temporal prediction model of this invention, the context vector is concatenated with the hidden state at the current time step, and after mapping through a fully connected layer, the current positive dead zone boundary of the actuator is dynamically predicted. (That is, overcoming the threshold of static friction and fluid force to begin positive action) and negative dead zone boundary. (That is, the threshold at which the reverse action begins), resulting in: Among them, symbols This represents concatenating the context vector with the current hidden state in a dimensional manner; This represents the weight matrix of the output layer; This represents the bias vector of the output layer.

[0051] It should be explained that, in the above formula, the bias vector of the output layer can be physically understood as the inherent static dead zone reference value of the actuator under conditions of no external dynamic disturbances (e.g., no vibration, constant oil temperature, steady-state maintenance). It represents the basic dead zone width determined at the time of manufacture by machining clearances, valve core overlap, or inherent static friction. By calculating the dynamic incremental change through series splicing and then superimposing it onto the inherent static dead zone reference value, the final dynamic boundary can be obtained.

[0052] In one possible implementation of this embodiment, the offline construction and training steps of the time-series prediction model (including GRU and attention mechanism) are described as follows: The first step is to collect multi-condition operating data of the equipment throughout its entire lifecycle. Using high-precision offline system identification algorithms (e.g., hysteresis loop identification based on high-frequency test excitation) or multiphysics simulation software, the true positive and negative dead zone boundaries at each moment are extracted and used as true labels for supervised learning, denoted as... .

[0053] The second step is to set the length of the sliding window. (For example, set to 50, corresponding to a temporal memory depth of 1 second), set the number of GRU hidden layer nodes (for example, 64), and similarly to the previous stacked encoder, use mean squared error (MSE) as the loss function: in, This is the training batch size.

[0054] The third step is to use the Adam optimizer to perform backpropagation to update the network parameters (including the weight matrix in the GRU and the attention mechanism). , as well as The initial learning rate is set to 0.001, and a learning rate decay strategy is used until the loss function on the validation set tends to converge.

[0055] The fourth step is to encapsulate the trained time series prediction model into an inference engine module for the digital twin model. When running online, the time series prediction model no longer performs backpropagation, but instead uses a lightweight forward computation method and continuously outputs dynamically predicted positive and negative dead zone boundaries at the same period (e.g., 20ms) as the control system, based on a real-time sliding input matrix.

[0056] S4. Based on the dynamically predicted positive dead zone boundary and negative dead zone boundary, adjust the original control command to generate a compensated control command, and apply the compensated control command to the actuator.

[0057] Furthermore, after obtaining the positive and negative dead zone boundaries at the current moment output by the time-series prediction model, the control command needs to be reconstructed. In traditional control theory, the commonly used dead zone compensation method typically employs a hard-switching exact inverse model: when the control command is greater than 0, the positive dead zone value is directly added; when it is less than 0, the negative dead zone value is directly subtracted (the negative dead zone value is usually negative, referring to numerical superposition). However, this approach has a fatal flaw in industrial settings: when the original control command fluctuates slightly near zero, the compensation command will undergo a drastic jump between the positive and negative dead zone boundaries. This high-frequency jump not only causes strong chattering in the execution system (e.g., servo valve spool) but also accelerates fatigue wear of mechanical components, and in severe cases, may even trigger resonance in the hydraulic system, leading to control system instability. Therefore, this embodiment applies a smooth inverse model based on dynamically predicted dead zone boundaries to perform a nonlinear transformation from discontinuous to continuous for the original control command. This smooth inverse model introduces an exponential smooth transition function to generate a smooth transition compensation amount near the dead zone boundary, thus forming the compensated control command, denoted as . .

[0058] Furthermore, the formula for calculating the nonlinear transformation of this smooth inverse model is as follows: Among them, nonlinear compensation amount The calculation logic is as follows: in, It is a natural constant; For smooth transition slope factor (and This factor is primarily used to define the smoothness of the nonlinear compensation region. When the smooth transition slope factor is large, the exponential term... Rapid decay and a compensation model that approximates the traditional hard-switching inverse model result in a fast response but are prone to slight chattering. When the smooth transition slope factor is small, the compensation curve transitions more smoothly near the zero-crossing point, completely eliminating chattering, but causing a slight lag in compensation intervention. It is important to emphasize that in actual engineering deployments, the value of the smooth transition slope factor can be calibrated or tuned offline based on the actuator's natural frequency and the bulk modulus of the hydraulic oil.

[0059] It should be noted that the advantage of using this smooth inverse model is that when the original control command is extremely small (within the dead zone), the smooth inverse model provides sufficient initial driving force through nonlinear amplification to help the valve core overcome static friction and achieve immediate response of the micro-command; while when the original control command is large (leaving the dead zone and entering the linear working zone), the exponential term approaches 0, and the compensation amount smoothly transitions to equal the dynamic dead zone boundary value, thereby offsetting the command loss caused by mechanical backlash and realizing the linearization of the input and output of the overall control loop.

[0060] Furthermore, the calculated high-precision, smooth and continuous compensated control commands are output as standard electrical signals (e.g., 4~20mA analog signals or servo drive current) through a digital-to-analog converter (D / A) module and applied to the actuator's drive coil or servo motor.

[0061] It should be noted that by deploying on a digital twin model and leveraging the dynamic boundary prediction capability and the flexible reconstruction capability of the smooth inverse model provided by the digital twin model, the actuator can still maintain a smooth, hysteresis-free, and steady-state error-free high-fidelity action response when facing mechanical aging, oil pressure fluctuations, or even high-frequency vibration interference.

[0062] S5. Build and run a digital twin model of an actuator, and synchronously input the compensated control commands into the digital twin model to obtain a twin output.

[0063] Specifically, based on the aforementioned feedforward dead zone compensation (i.e., S1~S4), in order to overcome the problem of the virtual model becoming disconnected from the physical entity due to long-term operation of the equipment, this embodiment constructs a digital twin model based on the actuator in parallel within the control system. This digital twin model is a hybrid fidelity model that integrates fluid dynamics mechanism equations and data-driven algorithms, used to simulate the dynamic displacement response of the actuator in real time in virtual space.

[0064] Furthermore, in each operation cycle of the control system, the generated compensated control commands are applied to the actual actuators, and simultaneously input into the digital twin model without delay. Within the digital twin model, the theoretical predicted displacement of the actuators in the virtual space is calculated based on the current boundary state, serving as the twin output.

[0065] In one feasible implementation of this embodiment, the core mechanism equation of the digital twin model is derived from the lumped parameter dynamics of the actuator, and its basic kinematic equation can be expressed as: in, The equivalent mass of the moving parts of the actuator; The time-varying viscous friction coefficient to be corrected; The equivalent spring stiffness to be corrected; The effective piston area; The hydraulic chamber pressure differential driving force is obtained by converting the compensated control command. The theoretical displacement calculated for the digital twin model; This is a nonlinear frictional resistance model mapped from the dynamic dead zone boundary output by the time-series prediction model. In each operational cycle of the control system, by combining the above equations and using the fourth-order Runge-Kutta method for numerical integration, the theoretical predicted displacement of the actuator in the virtual space can be calculated in real time, yielding a twin output.

[0066] S6. Compare the twin output with the actual output obtained from the actuator in real time to generate a twin error. Use the twin error to correct the model parameters in the digital twin model online through a state estimation algorithm and maintain high fidelity between the digital twin model and the actuator.

[0067] Furthermore, due to hydraulic oil contamination, seal aging, or irreversible mechanical wear, the time-series prediction model and digital twin model of this invention will inevitably experience cumulative drift after several months of operation. Therefore, this step aims to achieve online self-healing of model parameters through a feedback mechanism.

[0068] Furthermore, firstly, the real-time actual output displacement of the displacement sensor (e.g., LVDT) installed on the actuator is acquired. And calculate twin error : in, This is represented as twin output.

[0069] Furthermore, in order to extract effective model degradation information from twin errors mixed with measurement noise, this embodiment also employs an unscented Kalman filter (UKF) as the state estimation algorithm.

[0070] Specifically, the online correction logic of the UKF algorithm is as follows: Define the twin parameter state vector to be corrected as follows: (For example, this includes the time-varying viscous friction coefficient of the actuator, the equivalent spring stiffness, and the drift of the bias term in the output layer mentioned above). The UKF generates a set of Sigma points near the current state estimate through an unscented transformation. These Sigma points are then substituted into the digital twin model for time and measurement updates, calculating the predicted measurement mean. Covariance Matrix and the cross-covariance matrix of state and measurement. Finally, the Kalman gain is calculated. And the twin parameters are physically updated online based on the real-time twin error: It should be noted that the UKF-based online correction mechanism is introduced because the algorithm can endow the system with self-awareness. When the actuator's inherent dead zone reference is permanently changed due to mechanical wear, UKF can keenly detect the continuous twin error and correct it in reverse as an equivalent parameter drift into the digital twin model, ensuring that the industrial equipment maintains a high-fidelity mapping with the real physical entity throughout its entire life cycle.

[0071] S7. Periodically use vibration signals, operating condition data, and dead zone boundary labels obtained through other identification methods accumulated during online operation as new samples to incrementally learn or fine-tune the time series prediction model, thereby improving the time series prediction model's adaptability to unseen operating conditions or degradation modes.

[0072] Specifically, when the digital twin model detects that the Kalman gain frequently exceeds the set threshold, or the unit has undergone major maintenance (leading to a sudden change in mechanical characteristics), it indicates that the current time-series predictive model (GRU) can no longer fully cover the current degradation mode. At this time, the control system will automatically trigger the incremental learning mechanism.

[0073] Furthermore, the control system extracts cached data of severe operating conditions that cause large errors during online operation (i.e., data of unseen operating conditions), and combines this with the latest true labels of dead zone boundaries identified periodically by the offline system to construct an incremental fine-tuning dataset. Moreover, in the model fine-tuning training, to prevent catastrophic forgetting (i.e., learning new operating conditions but forgetting the patterns of healthy states), this scheme employs an experience replay combined with a local freeze strategy: (i) The core samples of health status in the historical training set are mixed with newly collected degraded samples in a specific ratio (e.g., 3:1) to form a playback pool.

[0074] (ii) During backpropagation updates, freeze the feature extraction layers of the stacked encoder and the weight matrices of the first few layers of the GRU for extracting general temporal features, and only release the attention mechanism layer and the fully connected output layer (i.e. The parameters are updated using gradients.

[0075] (iii) Use a very small fine-tuning learning rate (e.g., 1×10⁻⁶). -5 This allows the dead zone boundary decision plane of the model to smoothly migrate to a new wear state while ensuring that the original nonlinear feature mapping capability is not destroyed.

[0076] It should be noted that, through the above processing (i.e. S5~S7), the present invention achieves transient high-frequency prediction and smooth compensation of dead zone, and also establishes an adaptive evolutionary control architecture for the entire life cycle of industrial equipment, solving the problems of easy aging and poor robustness of traditional industrial control models.

[0077] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for compensating the dead-zone nonlinearity of actuators in industrial control systems based on digital twins, characterized in that, include: The system acquires in real time the vibration signal of the actuator, the original control commands output by the main controller, and the operating condition data characterizing the operating status of the actuator. The vibration signal is processed to extract and fuse vibration features that characterize the changes in the dead zone characteristics of the actuator; Using the vibration characteristics, original control commands, and operating data as input, a pre-trained time-series prediction model dynamically predicts the current positive dead zone boundary and negative dead zone boundary of the actuator. The pre-trained time-series prediction model is a network model containing gated recurrent units, used to handle the time-series dependencies of the input data; The network model of the gated recurrent unit also integrates an attention mechanism, which is used to dynamically weight the input data of historical time steps when predicting the current dead zone boundary and focus on historical information that has an influence on the current prediction task. Based on the dynamically predicted positive dead zone boundary and negative dead zone boundary, the original control command is adjusted to generate a compensated control command, and the compensated control command is applied to the actuator. Adjusting the original control commands includes: A smooth inverse model based on the dynamically predicted dead zone boundary is applied to perform a nonlinear transformation on the original control command, and a smooth transition compensation quantity is generated near the dead zone boundary to form the compensated control command. The method further includes: Build and run a digital twin model of the actuator; The compensated control commands are synchronously input into the digital twin model to obtain a twin output; The twin output is compared with the actual output obtained from the actuator in real time to generate a twin error; Using the twin error, a state estimation algorithm is used to correct the model parameters in the digital twin model online and maintain high fidelity between the digital twin model and the actuator.

2. The method for compensating the dead-zone nonlinearity of actuators in industrial control systems based on digital twins as described in claim 1, characterized in that, The acquired vibration signals include those collected by the turbine shaft inlet monitoring device.

3. The method for compensating the dead-zone nonlinearity of actuators in industrial control systems based on digital twins as described in claim 1, characterized in that, The extraction and fusion of vibration features characterizing the changes in the dead zone properties of the actuator includes: The vibration signal is decomposed into multiple time-frequency components using wavelet packet transform, and the energy distribution characteristics of each decomposed frequency band are calculated to form a preliminary time-frequency feature vector.

4. The method for compensating the dead-zone nonlinearity of actuators in industrial control systems based on digital twins as described in claim 3, characterized in that, Also includes: The preliminary time-frequency feature vector is combined with other time-domain or frequency-domain features extracted from the vibration signal to form a hybrid feature vector; The hybrid feature vector is input into a pre-trained stacked encoder, and the output of the encoder bottleneck layer is taken as the vibration feature.

5. The method for compensating the dead-zone nonlinearity of actuators in industrial control systems based on digital twins as described in claim 1, characterized in that, Also includes: Periodically, vibration signals, operating condition data, and dead zone boundary labels obtained through other identification methods accumulated during online operation are used as new samples to incrementally learn or fine-tune the time series prediction model, thereby improving the time series prediction model's adaptability to unseen operating conditions or degradation modes.

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