A method for dynamic neural network event-triggered control of motor load frequency

Abstract

This invention discloses a dynamic neural network event-triggered control method for motor load frequency under external disturbances and internal coupling, relating to the field of motor control technology. The method includes the following steps: obtaining the system matrix parameters of the motor system; establishing a motor state-space model to obtain discrete states; based on the discrete states, representing external disturbances and internal coupling in the motor system as a common disturbance term, and estimating the common disturbance term online using a neural network to obtain disturbance estimates; obtaining the trigger update time of the control signal based on the state deviation between the discrete states and their most recent trigger state; constructing a dynamic neural network state feedback controller at the trigger update time; substituting the dynamic neural network state feedback controller into the motor system model, establishing linear matrix inequalities, and implementing dynamic event-triggered control by solving the linear matrix inequalities, which can better cope with unknown disturbances and reduce communication burden.

Description

Technical Field

[0001] This invention relates to the field of motor control technology, and more specifically, to a dynamic neural network event-triggered control method for motor load frequency. Background Technology

[0002] In practical applications of motor systems, motor frequency data detected by sensors is transmitted to the controller via a network. Since data communication resources are often limited, continuous communication increases the computational load and consumes hardware resources. When data from adjacent moments is very close, it is unnecessary to transmit all the data.

[0003] Furthermore, during the operation of traditional motor systems, motors are often subjected to unknown external disturbances. At the same time, the internal coupling between motor subsystems also has an adverse effect, making it difficult for the motor frequency to maintain stable and excellent performance. To resolve these disturbances, it is usually necessary to impose constraints on external disturbances and internal couplings, which leads to increased conservatism in controller design and affects the performance of motor operation.

[0004] The above-disclosed technical solutions have at least the following technical problems: In actual motor operating environments with unknown external load disturbances and uncertainties in internal parameter coupling, traditional control methods based on accurate models and fixed communication mechanisms are difficult to ensure system stability while effectively suppressing unknown disturbances and efficiently utilizing communication resources. This can easily lead to high control conservatism, insufficient robustness, or excessive communication burden. Summary of the Invention

[0005] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a dynamic neural network event-triggered control method for motor load frequency. This method uses a neural network to fit unknown external disturbances and internal couplings, and compensates for their adverse effects in the controller design. This achieves a better control effect for the motor control system in dealing with unknown disturbances and reducing communication burden while ensuring stability.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A dynamic neural network event-triggered control method for motor load frequency includes the following steps: acquiring system matrix parameters of the motor system, establishing a motor state-space model including internal coupling terms, and sampling the system state to obtain discrete states for control and event triggering; based on the discrete states, unifying external disturbances and internal couplings in the motor system into a common disturbance term, and estimating the common disturbance term online using a neural network to obtain a disturbance estimate; based on the state deviation between the discrete state and its most recent triggering state, constructing a dynamic event triggering threshold function that varies with the state error to determine the triggering update time of the control signal, including: during the current control signal holding period, acquiring the system state of the motor system at discrete times, and calculating the state deviation between the discrete state and the state corresponding to the most recent control signal update time; based on the state deviation, combined with a pre-constructed dynamic event triggering threshold function, determining whether the current state deviation reaches or exceeds the corresponding dynamic event triggering threshold; when the state deviation reaches or exceeds the corresponding dynamic event triggering threshold, determining the corresponding time as the triggering update time of the control signal; when the state deviation does not reach the dynamic event triggering threshold, acquiring the dynamic event triggering threshold based on the neural network online estimation... The common disturbance estimate is obtained, and the change of the common disturbance estimate relative to the most recent control signal update time is calculated. When the change of the common disturbance estimate exceeds a preset disturbance change criterion, it is determined that the current control signal can no longer effectively compensate for the system disturbance, and the corresponding time is determined as the trigger update time of the control signal. The specific construction steps of the disturbance change criterion include: obtaining the estimation confidence index of the neural network at the current time based on the neural network model used to estimate the common disturbance; and weighting and fusing the change of the common disturbance estimate according to the estimation confidence index to obtain the confidence-corrected disturbance. The change amount is compared with the confidence-corrected disturbance change amount and the preset disturbance change criterion. When the confidence-corrected disturbance change amount exceeds the disturbance change criterion, it is determined that the current control signal can no longer effectively compensate for the system disturbance. At the trigger update time, a dynamic neural network state feedback controller is constructed, which includes a state feedback term and a disturbance estimation compensation term constructed based on the disturbance estimation value. The dynamic neural network state feedback controller is substituted into the motor system model to establish a linear matrix inequality that simultaneously constrains the state feedback gain matrix and the event trigger matrix, and dynamic event trigger control is implemented by solving the linear matrix inequality.

[0008] In a preferred embodiment, obtaining the discrete state for control and event triggering includes: acquiring system matrix parameters corresponding to each motor subsystem of the motor system; constructing a continuous-time state-space model of the motor containing internal coupling terms based on the system matrix parameters; periodically sampling the system state in the continuous-time state-space model to convert the continuous-time system state into a discrete-time system state.

[0009] In a preferred embodiment, the step of uniformly representing external disturbances and internal couplings in the motor system as a common disturbance term includes: based on the motor state-space model, identifying state change terms in the motor system that are not directly determined by the control input and are not explicitly described by the system matrix, as candidate external disturbance terms; based on the state variables of each motor subsystem in the state-space model, determining the coupling change portion caused by the mutual influence of the states of different motor subsystems, and determining the coupling change portion as candidate internal coupling terms; merging the candidate external disturbance terms and the candidate internal coupling terms to construct a common disturbance term that changes with the state of the motor system, and using the common disturbance term as the target object for subsequent online estimation by the neural network.

[0010] In a preferred embodiment, identifying state change terms in the motor system that are not directly determined by the control input and are not explicitly described by the system matrix, based on the motor state-space model, includes: calculating the nominal state change under the action of a known system matrix and control input based on the motor system state-space model, wherein the nominal state change is jointly determined by the state terms corresponding to the system matrix and the control input; obtaining the actual state change of the motor system at the corresponding time and comparing the actual state change with the nominal state change; and determining the deviation between the actual state change and the nominal state change as state change terms that are not directly determined by the control input and are not explicitly described by the system matrix.

[0011] In a preferred embodiment, the step of constructing a dynamic event triggering threshold function that varies with the state error based on the state deviation between the discrete state and its most recent triggering state includes: acquiring the discrete state of the motor subsystem at the current sampling time and the discrete state at the corresponding most recent event triggering time, and calculating the state deviation between the two; constructing an internal dynamic variable to characterize the trend of the state deviation based on the state deviation; and constructing a dynamic event triggering threshold function based on the internal dynamic variable and in combination with pre-set dynamic event triggering parameters.

[0012] In a preferred embodiment, the step of constructing a dynamic neural network state feedback controller comprising a state feedback term and a disturbance estimation compensation term constructed based on the disturbance estimate at the trigger update time includes: at the trigger update time of the control signal, acquiring the corresponding discrete state of the motor system as the state input of the controller; based on the discrete state, constructing a state feedback term for compensating the nominal dynamic characteristics of the motor system using a state feedback gain matrix obtained by solving linear matrix inequalities; based on the online estimation result of the common disturbance in the discrete state by the neural network, constructing a disturbance compensation term that works in conjunction with the state feedback term to weaken the influence of external disturbances and internal coupling on the system state; and combining the state feedback term and the disturbance compensation term to form a dynamic neural network state feedback controller for the current trigger update time.

[0013] In a preferred embodiment, establishing a linear matrix inequality that simultaneously constrains the state feedback gain matrix and the event triggering matrix includes: constructing a closed-loop model of the motor system containing the event triggering error based on the system state at the most recent control signal triggering time; constructing a Lyapunov function that can simultaneously characterize the system state evolution and the trigger-hold error based on the closed-loop model; analyzing the stability of the closed-loop system based on the Lyapunov function and introducing the event triggering condition into the stability constraints; transforming the stability constraints into a matrix inequality form that simultaneously contains the state feedback gain matrix and the event triggering matrix based on a matrix inequality transformation method; and constructing a linear matrix inequality that can be used to jointly solve the state feedback gain matrix and the event triggering matrix through variable substitution and decoupling processing.

[0014] In a preferred embodiment, the step of implementing dynamic event-triggered control by solving linear matrix inequalities includes: solving the linear matrix inequalities to obtain state feedback control parameters that meet system stability requirements and event triggering parameters for dynamic event triggering determination; substituting the state feedback control parameters into a neural network state feedback control structure to form a dynamic neural network state feedback controller for event-triggered control; determining the dynamic event triggering update time of the control signal based on the event triggering parameters and the evolution process of the discrete state of the motor system; and applying the dynamic neural network state feedback controller to the motor system model based on the dynamic event triggering update time to realize dynamic event-triggered control of the motor system.

[0015] The technical effects and advantages of the dynamic neural network event-triggered control method for motor load frequency of the present invention are as follows:

[0016] This invention establishes a motor state-space model with internal coupling terms within a discrete sampling framework, unifying external disturbances and internal couplings into a common disturbance term, and using a dynamic neural network for online estimation. A disturbance estimation compensation term is introduced into the controller, effectively reducing the impact of unknown disturbances and couplings on the dynamics of the motor load frequency. Simultaneously, an adaptive dynamic event triggering threshold is constructed based on the state deviation between the current state and the most recent triggered state, updating the control signal only when necessary, reducing the control update frequency and computational burden while ensuring system stability. By unifying the state feedback gain and event triggering conditions into a linear matrix inequality for joint design, it achieves a balance between system robustness, adaptability, and control performance without pre-defined upper bounds on the disturbance. Compared to traditional periodic sampling or fixed threshold control methods, this significantly reduces the conservatism of the control design. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating a dynamic neural network event-triggered control method for motor load frequency according to the present invention.

[0018] Figure 2 This is a schematic diagram of the principle architecture of the Markov system of the present invention;

[0019] Figure 3 Add images of external interference to the motor system;

[0020] Figure 4 Add the internal coupling image to the motor system;

[0021] Figure 5 , 6 The state trajectory diagram obtained by adding common interference to the motor system;

[0022] Figure 7 , 8 State diagram of the subsystem;

[0023] Figure 9 , 10 This is a fitting graph of the neural network for common interference;

[0024] Figure 11 , 12 This is a schematic diagram illustrating the dynamic time-triggered state of each motor system. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0026] Example 1, Figure 1 This invention provides a dynamic neural network event-triggered control method for motor load frequency, comprising the following steps:

[0027] S1. Obtain the system matrix parameters of the motor system, establish a motor state-space model including internal coupling terms, and sample the system state to obtain discrete states for control and event triggering.

[0028] like Figure 2 The diagram shown is a schematic of the motor system's architecture. Subsequently, the relevant parameters to be used in the controller design process are determined based on the matrix parameters.

[0029] In this embodiment, the steps of obtaining the system matrix parameters of the motor system, establishing a motor state-space model including internal coupling terms, and sampling the system state to obtain discrete states for control and event triggering include:

[0030] S11. Obtain the matrix parameters of the motor system model. , , , ;

[0031] S12, Based on matrix parameters , The state-space model of the continuous-time system of the motor system is obtained, and the number of motor subsystems is determined. In this embodiment, the state-space model of the continuous-time system is determined by the matrix parameters obtained in step S11, and the expression is:

[0032]

[0033] In the above formula, This is the derivative of the state with respect to time, i.e., the rate of change of the state. The state of a continuous-time system; For control inputs to a continuous-time system subjected to external disturbances; This indicates the coupling terms inside the motor.

[0034] Based on the state-space model of a continuous-time system, and combined with The number of subsystems in the motor system model can then be determined. In this embodiment, the simulation uses the following third-order system to represent the number of motors in the motor system model, namely Motor 1 and Motor 2, as shown below:

[0035] Motor 1:

[0036]

[0037]

[0038] Motor 2:

[0039]

[0040]

[0041] S13. The system state is sampled to obtain the relevant system model parameters required for subsequent controller design. In this embodiment, the system state is continuous, so as... Figure 2 As shown, a separate sampler is set up after each motor subsystem to sample the subsystem state, transforming the continuous state into a discrete state, i.e. Transform into ,in Indicates the number of samples. The sampling interval is This allows us to obtain the discrete system states required for subsequent controller design.

[0042] S2, based on discrete states, external disturbances and internal couplings in the motor system are uniformly represented as a common disturbance term, and the common disturbance term is estimated online through a neural network to obtain the disturbance estimate;

[0043] In this embodiment, the step of uniformly representing external disturbances and internal couplings in the motor system as a common disturbance term includes:

[0044] S21. Based on the motor state-space model, identify state change terms in the motor system that are not directly determined by the control input and are not explicitly described by the system matrix, and use them as candidate external disturbances.

[0045] S22. Based on the state variables of each motor subsystem in the state space model, determine the coupling change part caused by the mutual influence of the states of different motor subsystems, and determine the coupling change part as the internal coupling candidate.

[0046] S23. The external disturbance candidate and the internal coupling candidate are merged to form a common disturbance term that changes with the state of the motor system, and the common disturbance term is used as the target object for subsequent online estimation by the neural network.

[0047] It should be noted that the identification of state change terms in the motor system based on the motor state-space model that are not directly determined by the control input and are not explicitly described by the system matrix includes:

[0048] S211. Based on the state-space model of the motor system, calculate the nominal state change under the action of a known system matrix and control input, wherein the nominal state change is jointly determined by the system matrix and the state terms corresponding to the control input.

[0049] S212. Obtain the actual state change of the motor system at the corresponding time, and compare the actual state change with the nominal state change.

[0050] S213. The deviation between the actual state change and the nominal state change is determined as a state change term that is not directly determined by the control input and is not explicitly described by the system matrix.

[0051] For unknown external disturbances and internal couplings, it is impossible to obtain a specific mathematical model through direct sensor measurements. This makes the motor susceptible to interference during operation, resulting in an inability to maintain a stable motor frequency. To address this issue and maintain the stability of the motor system during operation, this invention leverages the excellent fitting properties of neural networks for unknown nonlinear functions. A neural network is used to fit unknown disturbances, including both external and internal ones. The fitted disturbance results are then incorporated into the controller design, ensuring that the motor system maintains good control performance when facing disturbances.

[0052] The step of estimating the common perturbation term online using a neural network to obtain the perturbation estimate includes:

[0053] The external disturbances and internal couplings experienced by the motor subsystem can be represented as:

[0054]

[0055] in, This indicates the external interference experienced by the motor system; This indicates the internal coupling of the click system; This represents the combined effect of the two interferences. Therefore, the estimated value of the combined interference is expressed as:

[0056]

[0057] In the above formula, This is expressed as an estimate of the external disturbance. This represents an estimate of the internal coupling.

[0058] For unknown common interferences, this invention employs a two-layer neural network to fit their effects. Using the neural network, the common interference can be represented as:

[0059]

[0060] In the above formula, Indicates the first The input to the neural network of each subsystem; and These are the optimal weights from the hidden layer to the output layer and from the input layer to the hidden layer, respectively. The activation function for a neural network is represented by the sigmoid function, i.e. ; The neural network estimation error is represented by the condition that... ; It indicates compactness.

[0061] Since the optimal weights of the neural network are unknown, the estimate of the common interference can be expressed as:

[0062]

[0063] In the above formula, and It is the optimal weight and The estimated value; therefore, the estimation error of the common interference can be expressed as:

[0064]

[0065] In the above formula, The estimation error is due to common interference. The estimated value for common interference. For mutual interference.

[0066] S3. Based on the state deviation between the discrete state and its most recent triggering state, construct a dynamic event triggering threshold function that varies with the state error to determine the triggering update time of the control signal.

[0067] The dynamic event triggering threshold function for each motor subsystem is obtained based on the given dynamic event triggering parameters. The dynamic event triggering parameters are set by the user according to the application scenario. The given parameters can be arbitrary as long as the LMI condition is met; however, different parameter choices will affect the event triggering effect. The triggering matrix needs to be obtained by solving linear matrix inequalities subsequently. The difference between dynamic and static event triggering is that the threshold function becomes dynamic, adaptively adjusting with the error in the system state; therefore, it will not be elaborated further.

[0068] In this embodiment, the step of constructing a dynamic event triggering threshold function that varies with the state error based on the state deviation between the discrete state and its most recent triggering state includes:

[0069] S31. Obtain the discrete state of the motor subsystem at the current sampling time and the discrete state at the corresponding most recent event trigger time, and calculate the state deviation between the two to characterize the degree of deviation of the system state relative to the most recent trigger time.

[0070] S32. Based on the state deviation, construct an internal dynamic variable to characterize the trend of state deviation change, wherein the internal dynamic variable is obtained by nonlinearly mapping the norm of the state deviation to reflect the sensitivity of the state deviation to time evolution.

[0071] S33. Based on the internal dynamic variables and combined with the pre-set dynamic event triggering parameters, construct a dynamic event triggering threshold function so that the dynamic event triggering threshold function adaptively adjusts with the change of state deviation, thereby increasing the triggering sensitivity when the state deviation increases and decreasing the triggering frequency when the state deviation decreases.

[0072] The dynamic event triggering threshold function specifically includes the following steps:

[0073] Acquire sensor number Dynamic event triggering parameters for individual motor systems , , This embodiment has two motor systems, set as follows: , , ; Construct the sensor's first... based on dynamic event triggering parameters Internal dynamic variables triggered by events in a motor system, including internal dynamic variables. The expression is:

[0074]

[0075] In the above formula, exp is an exponential function; These are sensitivity adjustment parameters; For the first The trigger time of each motor system after sampling; Number of triggers; The trigger time; For the first The sampling system state of each motor system at the next moment. .

[0076] The sensor is constructed based on internal dynamic variables. The dynamic event triggering threshold function for a motor system, wherein the dynamic event triggering threshold function The expression is:

[0077]

[0078] In the above formula, and This defines the upper and lower bounds of the adaptive trigger function's range. .

[0079] The determination of the trigger update time for the control signal includes:

[0080] S301. During the current control signal holding period, obtain the system state of the motor system at discrete moments, and calculate the state deviation between the discrete state and the state corresponding to the most recent control signal update moment.

[0081] S302. Based on the state deviation, and combined with the pre-constructed dynamic event triggering threshold function, determine whether the current state deviation reaches or exceeds the corresponding dynamic event triggering threshold.

[0082] S302. If the state deviation does not reach the dynamic event triggering threshold, obtain the common disturbance estimate obtained by online estimation based on neural network, and calculate the change of the common disturbance estimate relative to the most recent control signal update time.

[0083] S303. When the change in the estimated common disturbance exceeds the preset disturbance change criterion, it is determined that the current control signal can no longer effectively compensate for the system disturbance, and an update of the control signal is triggered.

[0084] S304. When any of the following conditions are met, the corresponding time will be determined as the trigger update time for the control signal:

[0085] The state deviation reaches or exceeds the corresponding dynamic event trigger threshold;

[0086] It is determined that the current control signal's ability to compensate for system disturbances has changed significantly.

[0087] It should be noted that the specific construction steps of the disturbance change criterion include:

[0088] Based on the neural network model used to estimate the common perturbation, the estimation confidence index of the neural network at the current time is obtained. The estimation confidence index is used to reflect the stability of the neural network's estimation result of the common perturbation.

[0089] The estimated confidence index includes:

[0090]

[0091] in, To estimate the confidence level, For discrete time intervals, The preceding trigger time is the discrete time. for The estimated disturbance value at time.

[0092] Based on the estimated confidence index, the changes in the common disturbance estimates are weighted and fused to obtain the disturbance change after confidence correction. The lower the estimated confidence index, the lower the weight of the corresponding disturbance change in the control trigger criterion.

[0093] The confidence-corrected disturbance change is compared with a preset disturbance change criterion. When the confidence-corrected disturbance change exceeds the disturbance change criterion, it is determined that the current control signal can no longer effectively compensate for the system disturbance.

[0094] The step of determining whether the current state deviation reaches or exceeds the corresponding dynamic event triggering threshold includes:

[0095] Based on the state deviation, the weighted norm of the state deviation under the preset weight matrix is ​​calculated, and the weighted norm is compared with the threshold value corresponding to the dynamic event triggering threshold function at the current time. When the weighted norm is greater than or equal to the threshold value, it is determined that the current state deviation has reached or exceeded the dynamic event triggering threshold.

[0096] This invention introduces both state deviation and common disturbance estimation changes as the basis for triggering control signal updates. This invention can update the control signal in a timely manner before the system state deteriorates significantly, thereby avoiding performance degradation caused by control lag. While ensuring system stability, it further reduces the frequency of unnecessary control signal updates.

[0097] S4. At the time of triggering the update, construct a dynamic neural network state feedback controller that includes a state feedback term and a disturbance estimation compensation term constructed based on the disturbance estimation value.

[0098] In this embodiment, the step of constructing a dynamic neural network state feedback controller, which includes a state feedback term and a disturbance estimation compensation term constructed based on the disturbance estimation value, at the trigger update time includes:

[0099] After determining that the current time is the trigger update time of the control signal, the discrete state of the motor system corresponding to the trigger update time is extracted, and the discrete state is used as the basic state input for the controller construction.

[0100] Based on the discrete state, a state feedback gain matrix obtained in advance through linear matrix inequalities is introduced, and linear state feedback calculation is performed on the discrete state to obtain a state feedback term used to compensate for the known dynamic characteristics of the motor system.

[0101] Based on the online estimation results of the common disturbances corresponding to the discrete states by the neural network, a disturbance estimation compensation term that works in parallel with the state feedback term is constructed to offset the influence of external disturbances and internal coupling on the system state in the motor system.

[0102] Furthermore, to address the inevitable estimation error in the process of neural network estimation of common disturbances, an estimation error compensation term is constructed based on the upper bound information of the disturbance estimation error. The estimation error compensation term is then combined with the state feedback term and the disturbance estimation compensation term to form a dynamic neural network state feedback controller.

[0103] Construct a neural network state feedback controller, which can be represented in the following form:

[0104]

[0105] Furthermore, the neural network state feedback controller is represented as:

[0106]

[0107] In the above formula, For a continuous-time system subjected to external disturbances, the control input is... This represents the discrete control input calculated at the trigger time and maintained until the next trigger time. Indicates the first The state feedback gain matrix of each motor will be obtained by solving the subsequent linear matrix inequalities; This is a compensation term in the neural network controller, used to compensate for the estimation error when the neural network fits a common disturbance. Its specific form is... ; It is the upper bound of the estimation error. , express The F-norm; To represent a sign function, and to avoid chattering, a method is used. to replace ; These are the parameters used in the subsequent solution of linear matrix inequalities.

[0108] Furthermore, the final expression of the neural network state feedback controller is obtained as follows:

[0109]

[0110] S5. Substitute the dynamic neural network state feedback controller into the motor system model, establish a linear matrix inequality that simultaneously constrains the state feedback gain matrix and the event triggering matrix, and implement dynamic event triggering control by solving the linear matrix inequality.

[0111] In this embodiment, establishing the linear matrix inequality between the simultaneous constraint state feedback gain matrix and the event triggering matrix includes:

[0112] Based on the system state at the moment of the most recent control signal triggering, a closed-loop model of the motor system including event triggering error is constructed;

[0113] Based on the closed-loop system model, a Lyapunov function is constructed that simultaneously characterizes the system state evolution and the effect of trigger-hold error;

[0114] The stability of the closed-loop system is analyzed based on the Lyapunov function, and the event triggering condition is introduced into the stability constraint.

[0115] Based on the matrix inequality transformation method, the stability constraint is transformed into a matrix inequality form that simultaneously includes the state feedback gain matrix and the event triggering matrix;

[0116] By employing variable substitution and decoupling, a linear matrix inequality is constructed that can be used to jointly solve the state feedback gain matrix and the event triggering matrix.

[0117] Obtain the time of the most recent control signal trigger for the i-th motor subsystem. Sampling status Substituting this into the neural network state feedback controller, we obtain the control input expression:

[0118]

[0119] This is a common disturbance term formed by external disturbances and internal coupling. This is a neural network compensation term used to suppress neural network fitting errors;

[0120] This embodiment proves the finite-time stability of the motor closed-loop system using Lyapunov's equations, namely:

[0121]

[0122]

[0123]

[0124] In the above formula, V1(t) is a Lyapunov function; V2(t) is used to characterize the energy evolution of the motor system state over continuous time and sampling intervals, and V2(t) is used to characterize the impact of neural network weight updates and compensation parameter changes on system stability. It is an unknown positive definite matrix; These are the update parameters for the neural network compensation term. Ultimately, we can obtain:

[0125]

[0126] Applying Schur's complement lemma to the braced portion, we obtain:

[0127]

[0128] In the above formula,

[0129]

[0130] -

[0131] Because of the nonlinear component, this invention decouples the matrix inequalities. To this end, new variables are introduced:

[0132]

[0133] in, ;

[0134]

[0135] in,

[0136] Left multiplication and right multiplication of the above matrices and Then, based on the following inequality:

[0137]

[0138] The solvable linear matrix inequality is obtained, and its expression is:

[0139]

[0140] in, For attenuation parameters, ; Intermediate variables required to solve linear matrix inequalities. To solve for the parameters, ;

[0141]

[0142] -

[0143] in, , , .

[0144] The method of implementing dynamic event triggering control by solving linear matrix inequalities includes:

[0145] S501. Based on the closed-loop state model of the motor system and the dynamic event triggering mechanism, a linear matrix inequality is constructed that simultaneously constrains system stability and triggering behavior. After substituting the dynamic neural network state feedback controller into the motor system model, a closed-loop system state equation containing state feedback terms, neural network disturbance compensation terms, and event triggering hold error terms is obtained. Based on the closed-loop system state equation, combined with the constraint effect of the dynamic event triggering threshold function on the state deviation, the finite-time stability condition of the system is uniformly expressed as a linear matrix inequality form that simultaneously contains the state feedback gain matrix, the event triggering matrix, and auxiliary matrix variables.

[0146] S502. By solving the linear matrix inequality, the state feedback control parameters and event triggering parameters are jointly determined; the linear matrix inequality constructed in step S501 is solved using a convex optimization method to obtain the state feedback control gain matrix, event triggering matrix, and intermediate parameter matrix related to the control input channel that satisfy the system stability constraints, so that the controller parameter design and event triggering mechanism are completed collaboratively under the same optimization framework.

[0147] S503. Based on the obtained state feedback control parameters, construct a dynamic neural network state feedback controller; introduce the state feedback control gain matrix obtained in step S502 into the dynamic neural network state feedback controller, so that the control input is composed of the state feedback term, the disturbance compensation term based on the neural network, and the robust compensation term to compensate for the fitting error of the neural network, thereby forming a control signal expression form that is updated only at the triggering time.

[0148] S504. Based on the event trigger matrix, determine the dynamic event trigger update time of the control signal; using the event trigger matrix obtained in step S502, perform a weighted measurement on the state deviation between the current system state and the most recent trigger state, and combine it with the dynamic event trigger threshold function to determine whether the control signal needs to be updated. When the state deviation meets the trigger condition, determine the corresponding time as the trigger update time of the control signal.

[0149] S505. At the control signal trigger update time, the dynamic neural network state feedback controller is applied to the motor system model to realize dynamic event trigger control; at each trigger update time, the control input is calculated according to the current system state and applied to the motor system model, so that the motor system can still maintain stable operation and achieve effective adjustment of load frequency under the event trigger control framework even in the presence of external disturbances and internal coupling uncertainties.

[0150] Solve the linear matrix inequalities to obtain the required state feedback gain matrix. With trigger matrix and the required parameters The result is:

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157] State feedback gain matrix External perturbations in neural network fitting Internal coupling and the given neural network parameter update rate , , The values ​​are then substituted into the dynamic neural network state feedback controller and applied to the motor system model to stabilize the motor load frequency.

[0158] The closed-loop state equation of the motor subsystem is expressed as follows:

[0159]

[0160] In the above formula, ; This is the compensation term for disturbances in the neural network controller; External disturbance and internal coupling The common disturbance is expressed as follows:

[0161]

[0162]

[0163]

[0164]

[0165] Given the relevant parameters of the neural network and the update rate of the weight changes:

[0166]

[0167] In the above formula, for The derivative of is the Jacobian matrix. This simulation example uses 500 neurons and provides the simulation parameters for the neural network. , , .

[0168] The relevant parameters are fed into the neural network dynamic event triggering controller. This step, used to stabilize the motor system model, triggers the controller through neural network dynamic events. Substituting this into a motor system, it forms a mechanism to effectively handle the problem of motors failing to cope well with unknown disturbances during operation, thereby achieving stable frequency control of the motor system. The final expression of the neural network controller is obtained as follows:

[0169]

[0170] in, The intermediate feedback matrix variables obtained from solving linear matrix inequalities are used to eliminate nonlinear coupling relationships in matrix inequalities, and through... Obtain the state feedback gain matrix; It is the core component of the neural network controller, used to counteract the impact of unknown disturbances on system operation; This represents the compensation term in the neural network. The initial states of each motor system are given. .

[0171] Example 2: External interference and internal coupling effects are added to the motor system, as shown in the image. Figure 3 , Figure 4 As shown, when a common disturbance is added to the motor system, the resulting state trajectory is as follows. Figure 5 , Figure 6 As shown, Figure 5 This indicates that the motor system's state trajectory is diverging and in an unstable state, and the motor cannot maintain stable performance after being disturbed; Figure 7 , Figure 8 This indicates that after adding a neural network dynamic event-triggered state feedback controller, the system reached stability within a finite time, and the motor could still maintain good stability under the influence of common disturbances.

[0172] The fitting performance of the neural network to common interference is as follows: Figure 9 , Figure 10 As shown, Figure 9 This demonstrates the fitting performance of the neural network to the common disturbance in motor 1; Figure 10 The figure shows the fitting of the neural network to the common disturbance in motor 2. As can be seen from the figure, the fitting of the neural network to the common disturbance is relatively accurate. The structure of this accurate fitting is used in the controller to perform a compensation for the unknown common disturbance. The biggest advantage is that even if the disturbance is unknown, its adverse effects can be eliminated in the compensation of the implemented neural network controller.

[0173] The dynamic time triggering status of each motor system is as follows: Figure 11 , Figure 12 As shown, the triggering rate of motor system 1 is 6.2%, and the triggering rate of motor system 2 is 6.55%. This indicates that the event triggering does not use all the collected data, but only 6.2% and 6.55% of the data, reducing data transmission volume and saving network resources. Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0174] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0175] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0176] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0177] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0178] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0179] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A motor load frequency dynamic neural network event-triggered control method, characterized in that, Includes the following steps: Obtain the system matrix parameters of the motor system, establish a motor state-space model including internal coupling terms, and sample the system state to obtain discrete states for control and event triggering. Based on discrete states, external disturbances and internal couplings in the motor system are uniformly represented as a common disturbance term, and the common disturbance term is estimated online through a neural network to obtain the disturbance estimate. Based on the state deviation between a discrete state and its most recent triggered state, a dynamic event triggering threshold function that varies with the state error is constructed to determine the triggering update time of the control signal. This includes: during the current control signal holding period, acquiring the system state of the motor system at discrete moments and calculating the state deviation between the discrete state and the state corresponding to the most recent control signal update time; based on the state deviation, combined with the pre-constructed dynamic event triggering threshold function, determining whether the current state deviation reaches or exceeds the corresponding dynamic event triggering threshold; when the state deviation reaches or exceeds the corresponding dynamic event triggering threshold, determining the corresponding time as the triggering update time of the control signal; when the state deviation does not reach the dynamic event triggering threshold, acquiring a common disturbance estimate obtained based on online neural network estimation, and calculating the change of the common disturbance estimate relative to the most recent control signal update time; when the change of the common disturbance estimate exceeds a preset disturbance change criterion, determining that the current control signal can no longer effectively compensate for the system disturbance, and determining the corresponding time as the triggering update time of the control signal. The specific steps for constructing the disturbance change criterion include: obtaining the estimated confidence index of the neural network at the current time based on the neural network model used to estimate the common disturbance; weighting and fusing the changes in the estimated common disturbance values ​​according to the estimated confidence index to obtain the disturbance change amount after confidence correction; comparing the disturbance change amount after confidence correction with the preset disturbance change criterion; and determining that the current control signal can no longer effectively compensate for the system disturbance when the disturbance change amount after confidence correction exceeds the disturbance change criterion. At the time of triggering the update, a dynamic neural network state feedback controller is constructed, which includes a state feedback term and a disturbance estimation compensation term constructed based on the disturbance estimation value. By substituting the dynamic neural network state feedback controller into the motor system model, a linear matrix inequality is established that simultaneously constrains the state feedback gain matrix and the event triggering matrix. Dynamic event triggering control is then implemented by solving the linear matrix inequality.

2. The motor load frequency dynamic neural network event-triggered control method according to claim 1, wherein, The process of obtaining discrete states for control and event triggering includes: Obtain the system matrix parameters corresponding to each motor subsystem of the motor system; A continuous-time state-space model of the motor, including internal coupling terms, is constructed based on the system matrix parameters. The system state in the continuous-time state-space model is periodically sampled to convert the continuous-time system state into a discrete-time system state.

3. The motor load frequency dynamic neural network event-triggered control method according to claim 2, characterized in that, The method of unifying the representation of external disturbances and internal couplings in the motor system as a common disturbance term includes: Based on the motor state-space model, state change terms in the motor system that are not directly determined by the control input and are not explicitly described by the system matrix are identified as candidate external disturbances. Based on the state variables of each motor subsystem in the state space model, the coupling change caused by the mutual influence of the states of different motor subsystems is determined, and the coupling change is identified as an internal coupling candidate. The external disturbance candidate and the internal coupling candidate are merged to construct a common disturbance term that changes with the state of the motor system, and the common disturbance term is used as the target object for subsequent online estimation by the neural network.

4. The motor load frequency dynamic neural network event-triggered control method according to claim 3, characterized in that, The method for identifying state change terms in a motor system based on a motor state-space model that are not directly determined by control inputs and are not explicitly described by the system matrix includes: Based on the state-space model of the motor system, the nominal state change is calculated under the action of a known system matrix and control input, wherein the nominal state change is jointly determined by the system matrix and the state terms corresponding to the control input. Obtain the actual state change of the motor system at the corresponding time, and compare the actual state change with the nominal state change; The deviation between the actual state change and the nominal state change is identified as a state change term that is not directly determined by the control input and is not explicitly described by the system matrix.

5. The motor load frequency dynamic neural network event-triggered control method according to claim 4, characterized in that, The construction of a dynamic event triggering threshold function that varies with state error based on the state deviation between a discrete state and its most recent triggering state includes: Obtain the discrete state of the motor subsystem at the current sampling time and the discrete state at the corresponding most recent event trigger time, and calculate the state deviation between the two. Based on state deviation, an internal dynamic variable is constructed to characterize the trend of state deviation changes. Based on internal dynamic variables and pre-defined dynamic event triggering parameters, a dynamic event triggering threshold function is constructed.

6. The motor load frequency dynamic neural network event-triggered control method according to claim 5, characterized in that, The step of constructing a dynamic neural network state feedback controller, which includes a state feedback term and a perturbation estimation compensation term constructed based on the perturbation estimate, at the trigger update time, includes: At the moment the control signal is triggered and updated, the corresponding discrete state of the motor system is acquired and used as the state input of the controller; Based on the discrete state, a state feedback term for compensating the nominal dynamic characteristics of the motor system is constructed using the state feedback gain matrix obtained by solving linear matrix inequalities. Based on the online estimation results of the common disturbance in the discrete state by the neural network, a disturbance compensation term that works in conjunction with the state feedback term is constructed to weaken the impact of external disturbances and internal coupling on the system state. The state feedback term is combined with the disturbance compensation term to form a dynamic neural network state feedback controller for the current trigger update time.

7. The motor load frequency dynamic neural network event-triggered control method according to claim 6, characterized in that, The establishment of the linear matrix inequality between the simultaneous constraint state feedback gain matrix and the event triggering matrix includes: Based on the system state at the moment of the most recent control signal triggering, a closed-loop model of the motor system including event triggering error is constructed; Based on the closed-loop model, a Lyapunov function is constructed that can simultaneously characterize the system state evolution and the effect of trigger-hold error; The stability of the closed-loop system is analyzed based on the Lyapunov function, and the event triggering condition is introduced into the stability constraint. Based on the matrix inequality transformation method, the stability constraint is transformed into a matrix inequality form that simultaneously includes the state feedback gain matrix and the event triggering matrix; By employing variable substitution and decoupling, a linear matrix inequality is constructed that can be used to jointly solve the state feedback gain matrix and the event triggering matrix.

8. The motor load frequency dynamic neural network event-triggered control method according to claim 7, characterized in that, The method of implementing dynamic event triggering control by solving linear matrix inequalities includes: Solving the linear matrix inequalities yields the state feedback control parameters that satisfy the system stability requirements and the event triggering parameters used for dynamic event triggering determination. Based on the state feedback control parameters, they are substituted into the neural network state feedback control structure to form a dynamic neural network state feedback controller for event-triggered control. Based on the event triggering parameters and the evolution process of the discrete state of the motor system, the dynamic event triggering update time of the control signal is determined. Based on the dynamic event-triggered update time, a dynamic neural network state feedback controller is applied to the motor system model to achieve dynamic event-triggered control of the motor system.

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