Anti-disturbance control method for tilting mechanism of tilt-rotor unmanned aerial vehicle based on parameter self-tuning of RBF neural network

Abstract

The application discloses a tilt mechanism anti-disturbance control method for tilt-rotor unmanned aerial vehicle based on RBF neural network parameter self-adjustment, and belongs to the technical field of unmanned aerial vehicle.The joint motor is equivalent to a second-order position loop model, and internal unmodeled dynamics and external disturbance of the system are unified and merged into total disturbance; a third-order extended state observer is designed to realize real-time estimation and compensation of the total disturbance; an RBF neural network is established, tracking error and differential error signals are utilized, Jacobian information is combined, and key gains in an incremental control law of an active disturbance rejection controller are modified online; control increments are calculated and output according to the modified gains, and the joint motor is driven to drive the tilt mechanism to move.The application does not need to establish an accurate mathematical model of the joint motor, can automatically adjust control parameters when the working condition of the tilt mechanism changes, effectively suppresses reciprocating jitter near the target angle, and has the characteristics of strong adaptive capacity, good anti-disturbance performance and easy engineering implementation.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) technology, specifically relating to a disturbance rejection control method for the tilt mechanism of a tilt rotor UAV based on RBF neural network parameter self-tuning. Background Technology

[0002] When tiltrotor drones switch between vertical takeoff and landing, hovering, and cruise, a tilt mechanism is needed to drive the rotor or power unit to complete the angle change. The joint motor in the tilt mechanism is usually composed of a power drive module, motor body, reduction transmission mechanism, position, speed, and torque feedback unit, and mechanical limit structure. Its control performance directly affects the smoothness, response speed, and attitude transition accuracy of the tilt process.

[0003] Existing joint control methods for tilting mechanisms mostly employ classical PID, fuzzy PID, model feedforward compensation, traditional ADRC, or offline optimized ADRC. Their main advantages and disadvantages are: PID control is simple in structure and easy to implement, but its adaptability to parameter variations and nonlinear disturbances is limited; fuzzy PID can adjust control parameters to a certain extent, but rule design relies on human experience; model feedforward compensation has good control performance when the model is relatively accurate, but it requires high accuracy of the motor and transmission mechanism models; traditional ADRC can unify unmodeled dynamics and external disturbances into a total disturbance and perform observation compensation, but its observer gain, state error feedback gain, and equivalent input gain usually need to be manually tuned, resulting in insufficient online adaptive capability.

[0004] The existing technology still has the following main problems and shortcomings:

[0005] 1) The controller parameters rely on manual tuning and lack online adaptive capability.

[0006] Traditional PID, traditional ADRC, and offline optimized ADRC control parameters often rely on manual experience or offline debugging. When the load, temperature, friction, backlash, and motor parameters of the tilting mechanism change, fixed parameters are difficult to maintain optimal control performance, and problems such as slow response, increased overshoot, or increased steady-state error are likely to occur.

[0007] 2) Limited adaptability to the nonlinear and time-varying characteristics of articulated motors.

[0008] In actual operation, the tilting mechanism's articulated motor experiences nonlinear factors such as reduction gear backlash, backlash reversal, sudden static friction changes, drive dead zone, feedback quantization error, and mechanical limits. Furthermore, the motor's resistance, inductance, equivalent moment of inertia, and damping coefficient change with temperature rise, wear, and load attitude variations. Existing control methods struggle to identify these changes online based on actual input and output data, leading to decreased control performance.

[0009] 3) Insufficient ability to suppress external disturbances and internal uncertainties.

[0010] Tiltrotor unmanned aerial vehicles (UAVs) are susceptible to disturbances such as aerodynamic changes, sudden load changes, mechanical vibrations, and external impacts during tilting. While traditional control methods can reduce errors to some extent, when disturbances occur suddenly or system parameters change rapidly, the controller's recovery speed is slow, and the angle deviation is large, making it difficult to meet the requirements of rapid and smooth switching of the tilting mechanism.

[0011] 4) Small back-and-forth shaking is likely to occur near the target angle.

[0012] When the articulated motor approaches the target angle, it is prone to slight left-right back-and-forth rotation due to limited feedback resolution, minute changes in speed command, backlash reversal, and static friction. Existing control methods typically only focus on reducing tracking error and lack soft control, dead-zone holding, and position holding strategies to address low-speed jitter near the target, making it difficult to guarantee the stability of the articulated motor after it has reached its position. Summary of the Invention

[0013] To address the aforementioned problems, this invention proposes a disturbance rejection control method for the tilt mechanism of a tilt-rotor UAV based on RBF neural network parameter self-tuning. This method uses the joint motor position servo system as the controlled object, introduces an RBF neural network into the active disturbance rejection controller, and performs online learning of the joint motor's input-output characteristics through the neural network. Furthermore, it performs online self-tuning of the key parameters of the active disturbance rejection controller based on the system's operating state, thereby improving the joint motor's position tracking accuracy, disturbance rejection capability, and operational stability under conditions of load variation, friction variation, backlash influence, and parameter perturbation.

[0014] The technical solution provided by this invention is: a disturbance rejection control method for the tilt mechanism of a tilt-rotor UAV based on RBF neural network parameter self-tuning, comprising the following steps:

[0015] S1: Establish an equivalent position loop model for the articulated motor, and convert the dynamic characteristics of the articulated motor into a second-order position loop model:

[0016]

[0017] in, This represents the actual output angle of the joint. To control the input, For equivalent input gain, The total disturbance includes unmodeled dynamics, parameter perturbations, and nonlinear terms within the system, as well as external load disturbances.

[0018] S2: Expand the total disturbance into a new state variable, design a third-order expanded state observer to estimate the joint angle, angular velocity and total disturbance in real time, and obtain the angle estimate, angular velocity estimate and total disturbance estimate respectively;

[0019] S3: Joint target angle input from the outside. and its target angular velocity As the command signal, based on the estimated angle and angular velocity, a basic state error feedback control quantity is constructed. The estimated total disturbance is then incorporated into this basic control quantity for compensation, yielding the actual control quantity.

[0020] S4: Construct a three-input, multi-hidden-layer, single-output RBF neural network. Within each control cycle, calculate the outputs of each hidden-layer node and the network output. Use the partial derivatives of the RBF network output with respect to the control input as equivalent Jacobian information to represent the input-output sensitivity of the current system.

[0021] S5: Based on the deviation between the actual output and the RBF network output, the weights, basis width, and center vector of the RBF network are updated online using a combination of gradient descent and momentum term.

[0022] S6: Construct a differential error signal based on the tracking error sequence, and correct the key gain in the incremental control law of the active disturbance rejection controller online based on the current error, equivalent Jacobian information and differential error signal;

[0023] S7: Calculate the current control increment based on the corrected critical gain: superimpose the control output of the previous cycle to obtain the current control output, and compensate the control output in combination with the total disturbance estimate to drive the joint motor to drive the tilting mechanism to move.

[0024] Preferably, step S1 specifically includes:

[0025] exist In the coordinate system, the electrical equations are expressed as:

[0026]

[0027] in, , For dq axis voltage, , For dq axis current, For stator resistance, , For dq axis inductance, The d-axis current change rate, The q-axis current change rate is... Electric angular velocity, t is the permanent magnet flux linkage, d is time, d is the direct axis aligned with the direction of the rotor magnetic field, and q is the quadrature axis.

[0028] The equations of electromagnetic torque and mechanical motion are expressed as follows:

[0029]

[0030] in, For electromagnetic torque, For extreme logarithms, For the equivalent moment of inertia, For mechanical angular velocity, For mechanical angular acceleration, The viscous damping coefficient is... For external load torque, This refers to the equivalent disturbance caused by friction and backlash. For the joint output angle, The rate of change of angle;

[0031] The electrical components of the tilting mechanism, transmission mechanism, driver limiting, friction, backlash, and load disturbance in actual operation are uniformly equivalent to a second-order position loop model:

[0032]

[0033] in, This refers to the actual angle of the joint. Angular velocity, Joint angular acceleration, This is the second state variable of the system. To control the input, For equivalent input gain, This indicates unmodeled internal dynamics, parametric perturbations, and nonlinear terms. Indicates external load disturbance;

[0034] Let the total disturbance be:

[0035] The final equivalent position loop model of the joint motor can be obtained:

[0036]

[0037] Preferably, step S2 includes:

[0038] make: The total disturbance is expanded into new state variables, where, Indicates the actual angle of the joint. Indicates joint angular velocity, The extended system can be represented as follows: (The original text contains several grammatical errors and inconsistencies. A more accurate translation would require the full context.)

[0039]

[0040] in, This represents the total rate of change of disturbance;

[0041] Design a third-order extended state observer to estimate the angle, angular velocity, and total disturbance:

[0042]

[0043] in, This is the actual output of the system. , , These are the estimated values ​​for angle, angular velocity, and total disturbance, respectively. For observation error, , , For observer gain, It is a nonlinear error function. , , where are the exponential parameters of the fal function. The threshold for the linear interval of the fal function. This is the equivalent input gain.

[0044] Preferably, the third-order extended state observer in step S2 employs a nonlinear error function. The observation error is processed in segments:

[0045]

[0046] in, For error, It is a non-linear exponent. For linear interval thresholds, For symbolic functions, This is a formula for handling small errors.

[0047] Preferably, step S3 is expressed as:

[0048]

[0049] in, Based on the control quantity, For the final control input, For position error feedback gain, For speed error feedback gain, From the perspective of the target, For the target angular velocity, , , These are the estimated values ​​for angle, angular velocity, and total disturbance, respectively. For equivalent input gain, For positional error, For speed error, This represents the total disturbance.

[0050] Preferably, in S4, a three-input, multi-hidden-layer, single-output RBF neural network is established: the network input vector consists of the control increment of the previous cycle, the current feedback angle, and the feedback angle of the previous cycle.

[0051]

[0052] in, For the first The network input vector for each control cycle For the current discrete control cycle, For the previous control cycle, To control the increment in the previous cycle, To control the quantity, From the current feedback perspective, This is the feedback angle from the previous cycle.

[0053] Preferably, in step S4, the calculation of the outputs of each hidden layer node and the network output of the RBF neural network, and the partial derivatives of the RBF network output with respect to the control input, are used as equivalent Jacobian information to represent the input-output sensitivity of the current system.

[0054] No. Each hidden layer node uses a Gaussian radial basis function:

[0055]

[0056] in, For the first Output of hidden layer nodes Number the hidden layer nodes. It is an exponential function. For the first Hidden layer node center vector, For the first The base width of each hidden layer node. The base width is square. It is the Euclidean norm;

[0057] The network output is:

[0058]

[0059] in, For the output of the RBF neural network, For the current control cycle, Number the hidden layer nodes. The total number of hidden layer nodes, n=6. For the first The weights of each hidden layer node, For the first Output of each hidden layer node;

[0060] The partial derivative of the RBF network output with respect to the control input is used as the equivalent Jacobian information:

[0061]

[0062] in, For the first Jacobian information for each control cycle, This represents the partial derivative of the network output with respect to the control input. For RBF network output, To control the input, For the current control cycle, Number the hidden layer nodes. This represents the number of hidden layer nodes. For the first Hidden layer node weights For the first Output of hidden layer nodes For the first The components corresponding to the control increment input in each center vector. The first component of the network input vector. For the first The base width of each hidden layer node. The base width is square. This refers to the component in the network input vector that corresponds to the control increment.

[0063] Preferably, S5: Based on the deviation between the actual output and the RBF network output, the weights, basis width, and center vector of the RBF network are updated online using a combination of gradient descent and momentum terms, specifically including:

[0064] With learning rate and momentum factor The parameter is the network error, which is the deviation between the actual output and the network output. Then the weights are updated as follows:

[0065]

[0066] in, For the first Cycle number The weights of each hidden layer node This is the option value from the previous week. This is the option value from two weeks ago. For the actual output, For network output, For the first Output of each hidden layer node;

[0067] Base width updated to:

[0068]

[0069] in, For the first Cycle number Each node's base width, The base width of the previous period, The base width is the period above. For network error, For network input vectors, For the input vector of the th One portion, For the first The center vector of each node For the current control cycle, Let be the Euclidean distance between the input vector and the center vector;

[0070] The center vector of the first The dimension component is updated as follows:

[0071]

[0072] in, For the first The central vector of the nth center vector dimensional components, The central component of the previous cycle, It is the central component of the previous period.

[0073] Preferably, S6 specifically includes:

[0074] Let the joint angle tracking error be:

[0075]

[0076] in, From the perspective of the current goal, From the current practical perspective, This represents the current tracking error;

[0077] Three differential error signals are constructed based on the error sequence:

[0078]

[0079] in, This is the tracking error from the previous cycle. For the tracking error of the previous cycle, This is a first-order difference error signal. It is a second-order difference error signal. This is the current error signal;

[0080] The RBF network corrects the three key gains in the ADRC incremental control law online based on the current error, equivalent Jacobian information, and differential error signal. , , :

[0081]

[0082] in, , , The ADRC gain learning rate, Represents the saturation constraint function. No. The first ADRC gain of the cycle, No. The third ADRC gain of the cycle, No. The second ADRC gain of the cycle, This is equivalent to Jacobian information.

[0083] This invention also provides a disturbance rejection control system for the tilt mechanism of a tilt-rotor UAV based on RBF neural network parameter self-tuning, comprising:

[0084] The input command terminal is used to input the target angle of the joint motor;

[0085] The RBF-ADRC controller is connected to the input command terminal and the feedback loop respectively, and is used to calculate the tracking error and generate the control quantity based on the target angle and the actual output angle fed back by the feedback loop.

[0086] A drive signal conversion module, connected to the output terminal of the RBF-ADRC controller, is used to convert the control quantity into a drive signal;

[0087] The controlled object is connected to the output terminal of the drive signal conversion module. The controlled object is the tilt mechanism joint motor position servo system of a tilt rotor UAV, which is used to perform angle adjustment under the drive signal.

[0088] The output position monitoring module is connected to the output end of the controlled object and is used to monitor the actual output angle of the joint motor and output the actual angle signal.

[0089] The feedback loop is connected between the output terminal of the output position monitoring module and the feedback input terminal of the RBF-ADRC controller, and is used to feed back the actual angle signal to the RBF-ADRC controller to form a closed-loop anti-disturbance control loop.

[0090] The RBF-ADRC controller includes:

[0091] The tracking error calculation module is connected to the input command terminal and the feedback loop respectively, and is used to calculate the tracking error based on the target angle and the actual output angle.

[0092] An error differential generation module is connected to the output of the tracking error calculation module and is used to generate a differential error signal based on the tracking error.

[0093] An extended state observer, connected to the feedback loop and the control output of the RBF-ADRC controller, is used to estimate the total system disturbance based on the actual output angle and the current control quantity, and obtain the total disturbance estimate.

[0094] The RBF neural network online self-tuning module, connected to the feedback loop, is used to correct the key parameters of the incremental control law online based on system operating data.

[0095] The incremental control law module is connected to the tracking error calculation module, the error difference generation module, the extended state observer, and the RBF neural network online self-tuning module, respectively, and is used to calculate the control quantity by integrating the tracking error, the difference error signal, the total disturbance estimate, and the key parameters corrected by the RBF neural network.

[0096] The output limiting and smoothing module is connected to the output of the incremental control law module and is used to limit and smooth the control quantity before outputting the final control quantity.

[0097] The beneficial effects of this invention are as follows:

[0098] This invention provides a disturbance rejection control method for the tilt mechanism of a tilt-rotor UAV based on RBF neural network parameter self-tuning. This method uses an RBF neural network to learn the actual input and output data of the joint motor online, identify changes in system characteristics in real time, and perform online self-tuning of the key gain of the active disturbance rejection controller accordingly. This enables the controller to adapt to parameter perturbations caused by changes in load, temperature, and friction characteristics during the tilting process, overcoming the shortcomings of fixed parameter control methods in terms of control performance degradation under changing operating conditions, and significantly enhancing the environmental adaptability and robustness of the control system.

[0099] Meanwhile, this invention unifies motor parameter variations, frictional nonlinearity, backlash, load disturbances, and unmodeled dynamics into a single total disturbance. This disturbance is estimated in real time using an extended state observer and compensated for in the control law. This eliminates the need for a precise mathematical model of the joint motor, simplifying the controller design process and reducing engineering complexity. When the tilting mechanism is subjected to disturbances such as sudden load changes, sudden friction changes, backlash reversal, or external impacts, the extended state observer can quickly estimate the disturbance and adjust control parameters online, effectively suppressing angle deviations, significantly improving the recovery speed after disturbances, and ensuring the system converges quickly to the target position, achieving a balance between fast response and low overshoot.

[0100] Furthermore, by introducing target smoothing, feedback filtering, softening control, and position holding strategies, this invention effectively reduces the minute reciprocating corrections of the joint motor near the target angle caused by nonlinear factors such as feedback resolution limitations, static friction, and backlash, thereby improving position stability and control accuracy. By limiting the amplitude and rate of change of the control output, it effectively avoids mechanical shocks and mechanism vibrations caused by sudden changes in control quantities. Moreover, the RBF neural network has a simple structure and low computational load, making it easy to run in real time in digital controllers and possessing good engineering promotion value. Attached Figure Description

[0101] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0102] Figure 1 This is a diagram showing the overall structure of the controlled object and the RBF-ADRC disturbance rejection control in this invention.

[0103] Figure 2 This is a block diagram of the internal structure of the RBF-ADRC controller of the present invention;

[0104] Figure 3 This is a flowchart of the RBF-ADRC control algorithm software of the present invention. Detailed Implementation

[0105] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0106] The existing technology has the following problems: Traditional control methods rely on manual experience or offline debugging for parameter tuning, resulting in insufficient online adaptive capability and difficulty in maintaining optimal control performance under varying operating conditions such as load, temperature, friction, and backlash of the tilting mechanism; nonlinear factors such as reduction mechanism backlash, backlash reversal, static friction abrupt changes, drive dead zone, and feedback quantization errors during joint motor operation, as well as the time-varying characteristics of parameters such as resistance, inductance, equivalent moment of inertia, and damping coefficient caused by temperature rise, wear, and load attitude changes, limit the adaptability of existing control methods and degrade control performance; during tilting... Disturbances such as aerodynamic changes, sudden load changes, mechanism vibrations, and external shocks, as well as uncertainties such as unmodeled dynamics and parameter perturbations within the system, render existing control methods inadequate in their disturbance suppression capabilities. They exhibit slow recovery speeds and large angle deviations after disturbances occur, making it difficult to meet the requirements for rapid and smooth switching of tilting mechanisms. Limited feedback resolution, minute changes in speed commands, backlash reversal, and static friction effects cause the joint motor to exhibit slight reciprocating jitter near the target angle. Existing control methods lack targeted softening control, dead-zone holding, and position holding strategies. Fixed-parameter controllers struggle to balance rapid response and low overshoot.

[0107] To address the aforementioned technical problems, this invention provides a disturbance rejection control method for the tilt mechanism of a tilt-rotor unmanned aerial vehicle (UAV) based on RBF neural network parameter self-tuning, such as... Figure 1 As shown, the overall structure of the controlled object and RBF-ADRC disturbance rejection control of this invention includes: input, RBF-ADRC controller, calculated drive signal, controlled object, disturbance, output, output position monitoring, and feedback loop. Its working principle is as follows: the input command provides the target angle of the joint motor, and the feedback loop feeds back the actual output angle of the controlled object to the RBF-ADRC controller. The RBF-ADRC controller internally calculates the tracking error based on the target angle and the feedback angle, generates a control quantity, and converts the control quantity into a drive signal, which is applied to the controlled object to complete the angle adjustment. The disturbance is applied to the controlled object, and the output is the actual angle. The output position monitoring is used to monitor the actual angle, and the feedback loop feeds the output signal back to the controller, forming a closed-loop disturbance rejection control.

[0108] like Figure 2 As shown in the diagram, the internal structure of the RBF-ADRC controller includes: input command, system feedback, calculation of tracking error, error differential generation, incremental control law, RBF neural network online self-tuning, extended state observer (ESO), output limiting and smoothing processing, and control output.

[0109] Its working principle is as follows: The tracking error is obtained by comparing the input command with the system feedback. Error differential generation generates an error signal based on the tracking error. The RBF neural network performs online self-tuning based on system operating data to correct key parameters in the incremental control law. The extended state observer (ESO) estimates the total system disturbance based on system feedback and control output, obtaining... The total disturbance estimate is fed into an incremental control law for compensation. The incremental control law combines the error signal, the RBF online self-tuning result, and the total disturbance estimate to calculate the control quantity. After output limiting and smoothing, the final control output is obtained.

[0110] 1) Establish the equivalent position loop model of the joint motor:

[0111] exist In the coordinate system, the electrical equations can be expressed as:

[0112] (1)

[0113] in, , For dq axis voltage, , For dq axis current, For stator resistance, , For dq axis inductance, The d-axis current change rate, The q-axis current change rate is... Electric angular velocity, t represents the permanent magnet flux linkage, d represents time, d represents the direct axis (the axis aligned with the direction of the rotor magnetic field), and q represents the quadrature axis.

[0114] The equations of electromagnetic torque and mechanical motion can be expressed as follows:

[0115] (2)

[0116] in, For electromagnetic torque, For extreme logarithms, For the equivalent moment of inertia, For mechanical angular velocity, For mechanical angular acceleration, The viscous damping coefficient is... For external load torque, This refers to the equivalent disturbance caused by friction and backlash. For the joint output angle, The angle change rate is denoted as .

[0117] In the actual operation of the tilting mechanism, it is difficult to accurately model the motor electrical components, transmission mechanism, actuator limiting, friction, backlash, and load disturbances. To facilitate controller design, these are uniformly represented as a second-order position loop model:

[0118] (3)

[0119] in, This refers to the actual angle of the joint. Angular velocity, Joint angular acceleration, This is the second state variable of the system. To control the input, For equivalent input gain, This indicates unmodeled internal dynamics, parametric perturbations, and nonlinear terms. This represents external load disturbance. Let the total disturbance be:

[0120] We can obtain:

[0121] (4)

[0122] 2) ADRC extended state observation and base compensation

[0123] make: Expand the total disturbance into new state variables, where... Indicates the actual angle of the joint. Indicates joint angular velocity, This represents the total disturbance comprised of unmodeled internal dynamics, parametric perturbations, nonlinear factors, and external disturbances. The extended system can then be represented as:

[0124] (5)

[0125] in, This represents the total rate of change of disturbance.

[0126] Design a third-order extended state observer to estimate the angle, angular velocity, and total disturbance:

[0127] (6)

[0128] in, This is the actual output of the system. , , These are the estimated values ​​for angle, angular velocity, and total disturbance, respectively. For observation error, , , For observer gain, It is a nonlinear error function. , , where are the exponential parameters of the fal function. The threshold for the linear interval of the fal function. This is the equivalent input gain.

[0129] To improve the estimation performance of the extended state observer within different error ranges, a nonlinear error function is employed. The observation error is processed in segments. When the observation error is small, an approximately linear form is used to smooth the error and reduce the impact of measurement noise on the observer. When the observation error is large, a nonlinear form is used to enhance the error correction capability, enabling the observer to converge faster.

[0130] (7)

[0131] in, For error, It is a non-linear exponent. For linear interval thresholds, For symbolic functions, This is a formula for handling small errors.

[0132] The basic state error feedback control quantity is constructed based on the observed state, and the total disturbance estimate is incorporated into the compensation:

[0133] (8)

[0134] in, Based on the control quantity, For the final control input, For position error feedback gain, For speed error feedback gain, From the perspective of the target, For the target angular velocity, , , These are the estimated values ​​for angle, angular velocity, and total disturbance, respectively. For equivalent input gain, For positional error, For speed error, This represents the total disturbance.

[0135] 3) RBF Neural Network Structure and Online Identification:

[0136] The network input vector consists of the control increment from the previous cycle, the current feedback angle, and the feedback angle from the previous cycle.

[0137] (9)

[0138] in, For the first The network input vector for each control cycle For the current discrete control cycle, For the previous control cycle, To control the increment in the previous cycle, To control the quantity, From the current feedback perspective, This is the feedback angle from the previous cycle.

[0139] No. Each hidden layer node uses a Gaussian radial basis function:

[0140] (10)

[0141] in, For the first Output of hidden layer nodes Number the hidden layer nodes. It is an exponential function. For the first Hidden layer node center vector, For the first The base width of each hidden layer node. The base width is square. It is the Euclidean norm.

[0142] The network output is:

[0143] (11)

[0144] in, For the output of the RBF neural network, For the current control cycle, Number the hidden layer nodes. This represents the total number of hidden layer nodes. For the first The weights of each hidden layer node, For the first Output of hidden layer nodes.

[0145] The RBF network is used to approximate the input-output relationship of a joint motor under its current operating state online, enabling the ADRC parameters to be adjusted online according to the actual response of the controlled object. The partial derivative of the RBF network output with respect to the control input is used as equivalent Jacobian information to characterize the current system input-output sensitivity, i.e., the direction and intensity of the influence of changes in the control input on changes in the output angle. Its expression is:

[0146] (12)

[0147] in, For the first Jacobian information for each control cycle, This represents the partial derivative of the network output with respect to the control input. For RBF network output, To control the input, For the current control cycle, Number the hidden layer nodes. This represents the number of hidden layer nodes. For the first Hidden layer node weights For the first Output of hidden layer nodes For the first The components corresponding to the control increment input in each center vector. The first component of the network input vector. For the first The base width of each hidden layer node. The base width is square. This represents the component in the network input vector corresponding to the control increment. This Jacobian information reflects the direction and intensity of the effect of the current control input change on the output angle change, and is used for subsequent ADRC gain self-tuning.

[0148] 4) RBF network parameter learning law:

[0149] The RBF network weights, basis width, and center vector are updated online using a combination of gradient descent and momentum terms. The learning rate is used as the basis for these updates. and momentum factor The parameter is the network error, which is the deviation between the actual output and the network output. Then the weights are updated as follows:

[0150] (13)

[0151] in, For the first Cycle number The weights of each hidden layer node This is the option value from the previous week. This is the option value from two weeks ago. For the actual output, For network output, For the first Output of hidden layer nodes.

[0152] Base width updated to:

[0153] (14)

[0154] in, For the first Cycle number Each node's base width, The base width of the previous period, The base width is the period above. For network error, For network input vectors, For the input vector of the th One portion, For the first The center vector of each node For the current control cycle, Let be the Euclidean distance between the input vector and the center vector.

[0155] The center vector of the first The dimension component is updated as follows:

[0156] (15)

[0157] in, For the first The central vector of the nth center vector dimensional components, The central component of the previous cycle, It is the central component of the previous period.

[0158] In practical engineering, , , In addition, Jacobian estimates are set with upper and lower limits to prevent numerical divergence of network parameters during online learning, thus ensuring the stable operation of the RBF-ADRC controller.

[0159] 5) Online self-tuning of key gain in ADRC

[0160] Let the joint angle tracking error be:

[0161] (16)

[0162] in, From the perspective of the current goal, From the current practical perspective, This represents the current tracking error.

[0163] Three differential error signals are constructed based on the error sequence:

[0164] (17)

[0165] in, This is the tracking error from the previous cycle. For the tracking error of the previous cycle, This is a first-order difference error signal. It is a second-order difference error signal. This is the current error signal.

[0166] The RBF network corrects the three key gains in the ADRC incremental control law online based on the current error, equivalent Jacobian information, and differential error signal. , , :

[0167] (18)

[0168] in, , , The ADRC gain learning rate, Represents the saturation constraint function. No. The first ADRC gain of the cycle, No. The third ADRC gain of the cycle, No. The second ADRC gain of the cycle, This is equivalent to Jacobian information. By adjusting three parameters online, the controller can automatically change the control intensity based on the characteristics of the real-time object.

[0169] The incremental RBF-ADRC control law is:

[0170] (19)

[0171] in, For the current control increment, This is the current control output. This is the control output from the previous cycle. In the actual discrete implementation, the total disturbance estimate output by the extended state observer is... As a compensation quantity, it participates in the control output correction, enabling the controller to offset the total disturbance effect during the control quantity calculation process.

[0172] 6) Target ramp, filtering, position holding and safety constraints

[0173] To improve the stability of the joint motor near the target angle and reduce the slight jitter caused by feedback quantization, backlash reversal switching, and small, repeated corrections of the control quantity, engineering constraints such as target smoothing, feedback filtering, output limiting, and position holding are set in addition to the RBF-ADRC control output.

[0174] Target smoothing: When the target angle changes, the rate of change of the target angle is limited so that the joint motor moves along a smooth reference trajectory, avoiding control shock caused by sudden changes in the target.

[0175] Feedback filtering: First-order low-pass filtering is applied to the feedback angle to reduce the impact of measurement noise and feedback quantization error on the controller.

[0176] Target-area softening control: When the angle error is less than the set softening threshold, the control output is gradually reduced according to the magnitude of the error to avoid the joint motor from generating reverse correction after passing the target angle.

[0177] Position holding control: When both the angle error and the feedback speed are less than the set threshold, it is determined that the joint motor has reached the target position, enters the stationary holding state, and stops outputting small reciprocating correction control quantities.

[0178] Control output amplitude and rate of change limit: Limit the magnitude of the control output and the amount of change in the control output within adjacent control cycles to prevent sudden changes in the control quantity from causing motor impact, mechanism vibration or mechanical limit collision.

[0179] 7) Discrete Implementation

[0180] Let the sampling period be , No. The discrete execution process of the RBF-ADRC controller within each control cycle is as follows.

[0181] Feedback angle filtering:

[0182] (20)

[0183] Target slope generation:

[0184] (twenty one)

[0185] RBF network input:

[0186] (twenty two)

[0187] Hidden layer output:

[0188] (twenty three)

[0189] Network output:

[0190] (twenty four)

[0191] Jacobian estimates:

[0192] (25)

[0193] Tracking error:

[0194] (26)

[0195] Error difference term:

[0196] (27)

[0197] ADRC key gain online update:

[0198] (28)

[0199] Controlling the increment:

[0200] (29)

[0201] Control output:

[0202] (30)

[0203] in, The feedback angle after filtering. For the slope target, These are the filter coefficients. The maximum target change per cycle. This indicates that the rate of change of the control output between adjacent cycles is limited.

[0204] Based on the above control principle, the technical solution of the present invention will be further described in detail below with reference to a specific embodiment.

[0205] Example 1

[0206] This embodiment takes the joint motor of the tilt mechanism of a certain type of tiltrotor UAV as the controlled object and implements the above-mentioned RBF-ADRC disturbance rejection control method in engineering.

[0207] Step 1: Obtain the joint motor operating parameters and establish an equivalent position loop model.

[0208] Obtain the basic operating parameters of the joint motor of the tilt mechanism of the tilt rotor UAV, including rated voltage, rated speed, output angle range, reduction ratio, moment of inertia, damping coefficient, motor resistance, inductance, permanent magnet flux linkage, feedback resolution, maximum allowable control quantity, and mechanical limit range.

[0209] Based on the electrical equations, electromagnetic torque equations, and mechanical motion equations of the motor in the dq coordinate system, the basic dynamic relationship between the control input and output angle of the articulated motor is established. However, due to factors such as changes in motor parameters, load variations, friction, backlash, hysteresis, and external disturbances during the actual operation of the tilting mechanism, it is difficult to establish a completely accurate mathematical model. Therefore, the articulated motor and tilting mechanism are uniformly equivalent to a second-order position loop system.

[0210] ,

[0211] Step 2: Build the total disturbance model and convert it into the ADRC standard form

[0212] Factors that are difficult to model accurately during the operation of the joint motor or that vary with operating conditions are collectively included in the total disturbance term. These factors include:

[0213] (1) Internal disturbances caused by changes in the electrical parameters of the motor;

[0214] (2) Nonlinear disturbances caused by friction, backlash, hysteresis and static friction abrupt changes in the transmission mechanism;

[0215] (3) External disturbances caused by changes in the load of the tilting mechanism, external impacts, and changes in aerodynamic forces;

[0216] (4) Equivalent disturbances caused by drive limiting, feedback quantization error and nonlinearity near mechanical limit.

[0217] Let the total disturbance be:

[0218] The joint motor position loop model can then be simplified to:

[0219] The complex joint motor position control problem is transformed into a problem of total disturbance. The problem of estimating, compensating, and adjusting control parameters online.

[0220] Step 3: Design the extended state observer and estimate the total disturbance.

[0221] In order to estimate the angle, angular velocity and total disturbance during the operation of the joint motor in real time, the total disturbance is expanded into a new state variable.

[0222] make:

[0223] The extended system can then be represented as: , , ,

[0224] Design a third-order extended state observer to estimate joint angles, angular velocities, and total disturbances, and obtain angle estimates. Angular velocity estimate The total disturbance estimate The observer continuously corrects its internal state based on the observation error between the actual feedback angle and the estimated angle, so that... Approximately realistic angle Approximately the actual angular velocity, Approaching the total system disturbance.

[0225] Step 4: Construct the basic state error feedback control quantity and perform disturbance compensation.

[0226] In obtaining the observer output , , Then, based on the target angle and observation status, the basic state error feedback control quantity is constructed:

[0227] The total disturbance estimated by the extended state observer Introduce a control law for compensation: It can reduce the impact of load changes, friction changes, backlash, and parameter perturbations on the position tracking accuracy of the articulated motor.

[0228] Step 5: Build the RBF neural network and initialize the network parameters

[0229] To achieve online self-tuning of key parameters of the active disturbance rejection controller, an RBF neural network with three inputs, six hidden layer nodes, and one output, i.e., a 3-6-1 structure, is established.

[0230] The network input vector is selected as follows:

[0231] Initialize the center vector of the RBF neural network , base width Weight At the same time, learning rate, momentum factor, upper and lower limits of parameters, and upper and lower limits of Jacobian estimates are set to avoid parameter divergence during online learning.

[0232] Step 6: Perform online RBF network identification and Jacobian estimation.

[0233] Within each control cycle, the current network input vector is... Input the RBF neural network and calculate the output of each hidden layer node:

[0234]

[0235] Then calculate the network output:

[0236] Based on the local variation relationship between the RBF network output and the control input, calculate the equivalent Jacobian information: This enables the controller to obtain the input and output sensitivity of the joint motor under the current operating state, and uses this information for subsequent ADRC key gain online self-tuning, so that the controller can automatically adjust the control strength according to the actual object characteristics.

[0237] Step 7: Update RBF network parameters

[0238] Based on actual output With RBF network output The deviation between the parameters is addressed by updating the network parameters using a combination of gradient descent and momentum terms. The network error is:

[0239] Update the weights of the RBF network according to the network error. , base width and center vector This allows the network to continuously adjust its parameters as the joint motor's operating state changes, thereby improving its ability to approximate the current input-output relationship.

[0240] Step 8: Online correction of ADRC key gain

[0241] Let the joint angle tracking error be:

[0242] Three differential error signals are constructed based on the error sequence:

[0243] , ,

[0244] Jacobian information estimated using RBF network By combining the current error and differential error signals, the three key gains in the ADRC incremental control law are corrected online:

[0245] , ,

[0246]

[0247] This enables the controller to automatically adjust the control intensity based on the real-time input and output characteristics of the joint motor.

[0248] Step 9: Calculate the incremental RBF-ADRC control quantity and apply the output constraints.

[0249] According to the online correction , , Calculate the current control increment:

[0250]

[0251] Then, the control increment is added to the control output of the previous cycle to obtain the current control output:

[0252]

[0253] To improve the smoothness of the joint motor's operation, the control output is further constrained, including:

[0254] (1) Target smoothing: Limit the maximum change in target angle in each control cycle;

[0255] (2) Feedback filtering: Perform first-order low-pass filtering on the actual feedback angle;

[0256] (3) Softening control near the target: When the angle error enters the softening zone, the control output is reduced proportionally to the error.

[0257] (4) Position holding control: When both the angle error and the feedback speed are less than the set threshold, the system enters the stationary holding state;

[0258] (5) Control output amplitude and rate of change limit: Limit the control output amplitude and the change of control quantity in adjacent cycles to prevent mechanical shock and oscillation.

[0259] Step 10: Execution flow of the control system software program

[0260] In digital controllers, the RBF-ADRC control algorithm executes cyclically according to a fixed sampling period. Its RBF-ADRC control algorithm software flow is as follows: Figure 3 As shown, the execution flow of the control system software program is as follows:

[0261] (1) Data acquisition and preprocessing

[0262] At the beginning of each control cycle, the target angle command of the tilting mechanism is first read, and the current actual angle of the joint motor is acquired through the position feedback unit. The acquired feedback angle is filtered and outlier-limiting processed to obtain a smooth feedback angle for closed-loop control.

[0263] (2) Target trajectory generation and error calculation

[0264] A smooth reference trajectory is generated based on the current target angle to avoid abrupt changes in the target angle directly affecting the controller. The tracking error between the current target angle and the feedback angle is calculated. And combine the error calculations from the previous cycle and the cycle before that. , , .

[0265] (3) Observation of the extended state and estimation of the total disturbance

[0266] Based on the current control input, feedback angle, and observation error, update the internal state of the extended state observer and calculate the angle estimate in real time. Angular velocity estimate Total disturbance estimate This provides a basis for subsequent disturbance compensation.

[0267] (4) Forward computation of RBF neural network

[0268] Constructing the input vector of an RBF neural network Calculate the output of each hidden layer node. Calculate the RBF network output based on the network weights. Calculate equivalent Jacobian information based on network parameters. It is used to determine the direction and intensity of the influence of the current control input on the output angle.

[0269] (5) Online update of RBF network parameters

[0270] Based on the error between the actual feedback angle and the RBF network output, the weights, basis width, and center vector of the RBF network are updated online, and upper and lower bound constraints are applied to the relevant parameters to ensure the stability of the network learning process.

[0271] (6) Online self-tuning of key gain in ADRC

[0272] Using the current tracking error, differential error signal, and Jacobian information estimated by the RBF network, the three key gains of ADRC are corrected online. , , Furthermore, a saturation limiting function is used to prevent the gain from being too large, too small, or taking an unreasonable value.

[0273] (7) Calculation of control variables and disturbance compensation

[0274] Calculate the control increment based on the updated ADRC key gain. The current control output is obtained by superimposing it with the control output of the previous cycle. Simultaneously, the total disturbance estimated by the extended state observer is used to compensate the control output, enabling the joint motor to stably track the target angle even when disturbances are present.

[0275] (8) Output constraints, softening control and position holding

[0276] The calculated control output is limited in amplitude and rate of change. When the joint motor approaches the target angle, the target near softening control is executed. When both the angle error and the feedback speed are less than the set threshold, the position holding state is entered, and the output of small reciprocating correction control quantity is stopped.

[0277] (9) Drive output and state saving

[0278] The final control input is converted into a drive signal recognizable by the underlying driver, causing the joint motor to drive the tilting mechanism to move towards the target angle. Before the end of the control cycle, the current error, feedback angle, control output, RBF network parameters, and ADRC gain parameters are saved as historical data for the calculation of the next control cycle.

[0279] (10) Enter the next control cycle

[0280] After completing the calculation for this cycle, the control system waits for the next sampling cycle to be triggered and repeats the above process to achieve continuous closed-loop operation of the joint motor position control.

[0281] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0282] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A disturbance rejection control method for the tilt mechanism of a tilt-rotor UAV based on RBF neural network parameter self-tuning, characterized in that, Includes the following steps: S1: Establish an equivalent position loop model for the articulated motor, and convert the dynamic characteristics of the articulated motor into a second-order position loop model: ； in, This represents the actual output angle of the joint. To control the input, For equivalent input gain, The total disturbance includes unmodeled dynamics, parameter perturbations, and nonlinear terms within the system, as well as external load disturbances. S2: Expand the total disturbance into a new state variable, design a third-order expanded state observer to estimate the joint angle, angular velocity and total disturbance in real time, and obtain the angle estimate, angular velocity estimate and total disturbance estimate respectively; S3: Joint target angle input from the outside. and its target angular velocity As the command signal, based on the estimated angle and angular velocity, a basic state error feedback control quantity is constructed. The estimated total disturbance is then incorporated into this basic control quantity for compensation, yielding the actual control quantity. S4: Construct a three-input, multi-hidden-layer, single-output RBF neural network. Within each control cycle, calculate the outputs of each hidden-layer node and the network output. Use the partial derivatives of the RBF network output with respect to the control input as equivalent Jacobian information to represent the input-output sensitivity of the current system. S5: Based on the deviation between the actual output and the RBF network output, the weights, basis width, and center vector of the RBF network are updated online using a combination of gradient descent and momentum term. S6: Construct a differential error signal based on the tracking error sequence, and correct the key gain in the incremental control law of the active disturbance rejection controller online based on the current error, equivalent Jacobian information and differential error signal; S7: Calculate the current control increment based on the corrected critical gain: superimpose the control output of the previous cycle to obtain the current control output, and compensate the control output in combination with the total disturbance estimate to drive the joint motor to drive the tilting mechanism to move.

2. The disturbance rejection control method for the tilt mechanism of a tilt-rotor UAV based on RBF neural network parameter self-tuning according to claim 1, characterized in that, Step S1 specifically includes: exist In the coordinate system, the electrical equations are expressed as: ； in, , For dq axis voltage, , For dq axis current, For stator resistance, , For dq axis inductance, The d-axis current change rate, The q-axis current change rate is... Electric angular velocity, t is the permanent magnet flux linkage, d is time, d is the direct axis aligned with the direction of the rotor magnetic field, and q is the quadrature axis. The equations of electromagnetic torque and mechanical motion are expressed as follows: ； in, For electromagnetic torque, For extreme logarithms, For equivalent rotational inertia, For mechanical angular velocity, For mechanical angular acceleration, The viscous damping coefficient is... For external load torque, This refers to the equivalent disturbance caused by friction and backlash. For the joint output angle, The rate of change of angle; The electrical components of the tilting mechanism, transmission mechanism, driver limiting, friction, backlash, and load disturbance in actual operation are uniformly equivalent to a second-order position loop model: ； in, This refers to the actual angle of the joint. Angular velocity, Joint angular acceleration, This is the second state variable of the system. To control the input, For equivalent input gain, This indicates unmodeled internal dynamics, parametric perturbations, and nonlinear terms. Indicates external load disturbance; Let the total disturbance be: ; The final equivalent position loop model of the joint motor can be obtained: 。 3. The disturbance rejection control method for the tilt mechanism of a tilt-rotor UAV based on RBF neural network parameter self-tuning according to claim 1, characterized in that, Step S2 includes: make: The total disturbance is expanded into new state variables, where, Indicates the actual angle of the joint. Indicates joint angular velocity, The extended system can be represented as follows: (The original text contains several grammatical errors and inconsistencies. A more accurate translation would require the full context.) ； in, This represents the total rate of change of disturbance; Design a third-order extended state observer to estimate the angle, angular velocity, and total disturbance: ； in, This is the actual output of the system. , , These are the estimated values ​​for angle, angular velocity, and total disturbance, respectively. For observation error, , , For observer gain, It is a nonlinear error function. , , where are the exponential parameters of the fal function. The threshold for the linear interval of the fal function. This is the equivalent input gain.

4. The disturbance rejection control method for the tilt mechanism of a tilt-rotor UAV based on RBF neural network parameter self-tuning according to claim 1, characterized in that, The third-order extended state observer described in step S2 employs a nonlinear error function. The observation error is processed in segments: ； in, For error, It is a non-linear exponent. For linear interval thresholds, For symbolic functions, This is a formula for handling small errors.

5. The disturbance rejection control method for the tilt mechanism of a tilt-rotor UAV based on RBF neural network parameter self-tuning according to claim 1, characterized in that, Step S3 is represented as follows: ； in, Based on the control quantity, For the final control input, For position error feedback gain, For speed error feedback gain, From the perspective of the target, For the target angular velocity, , , These are the estimated values ​​for angle, angular velocity, and total disturbance, respectively. For equivalent input gain, For positional error, For speed error, This represents the total disturbance.

6. The disturbance rejection control method for the tilt mechanism of a tilt-rotor UAV based on RBF neural network parameter self-tuning according to claim 1, characterized in that, In S4, a three-input, multi-hidden-layer, single-output RBF neural network is established: the network input vector consists of the control increment from the previous cycle, the current feedback angle, and the feedback angle from the previous cycle. ； in, For the first The network input vector for each control cycle For the current discrete control cycle, For the previous control cycle, To control the increment in the previous cycle, To control the quantity, From the current feedback perspective, This is the feedback angle from the previous cycle.

7. The disturbance rejection control method for the tilt mechanism of a tilt-rotor UAV based on RBF neural network parameter self-tuning according to claim 1, characterized in that, The calculation of the outputs of each hidden layer node and the network output of the RBF neural network described in S4 uses the partial derivatives of the RBF network output with respect to the control input as equivalent Jacobian information to represent the input-output sensitivity of the current system. No. Each hidden layer node uses a Gaussian radial basis function: ； in, For the first Output of hidden layer nodes Number the hidden layer nodes. It is an exponential function. For the first Hidden layer node center vector, For the first The base width of each hidden layer node. The base width is square. It is the Euclidean norm; The network output is: ； in, For the output of the RBF neural network, For the current control cycle, Number the hidden layer nodes. The total number of hidden layer nodes, n=6. For the first The weights of each hidden layer node, For the first Output of each hidden layer node; The partial derivative of the RBF network output with respect to the control input is used as the equivalent Jacobian information: ； in, For the first Jacobian information for each control cycle, This represents the partial derivative of the network output with respect to the control input. For RBF network output, To control the input, For the current control cycle, Number the hidden layer nodes. This represents the number of hidden layer nodes. For the first Hidden layer node weights For the first Output of hidden layer nodes For the first The components corresponding to the control increment input in each center vector. The first component of the network input vector. For the first The base width of each hidden layer node. The base width is square. This refers to the component in the network input vector that corresponds to the control increment.

8. The disturbance rejection control method for the tilt mechanism of a tilt-rotor UAV based on RBF neural network parameter self-tuning according to claim 1, characterized in that, S5: based on the deviation between the actual output and the RBF network output, the weights, basis width, and center vector of the RBF network are updated online using a combination of gradient descent and momentum terms, specifically including: With learning rate and momentum factor The parameter is the network error, which is the deviation between the actual output and the network output. Then the weights are updated as follows: ； in, For the first Cycle number The weights of each hidden layer node This is the option value from the previous week. This is the option value from two weeks ago. For the actual output, For network output, For the first Output of each hidden layer node; Base width updated to: ； in, For the first Cycle number Each node's base width, The base width of the previous period, The base width is the period above. For network error, For network input vectors, For the input vector of the th One portion, For the first The center vector of each node For the current control cycle, Let be the Euclidean distance between the input vector and the center vector; The center vector of the first The dimension component is updated as follows: ； in, For the first The central vector of the nth center vector dimensional components, This is the central component of the previous cycle. It is the central component of the previous period.

9. The disturbance rejection control method for the tilt mechanism of a tilt-rotor UAV based on RBF neural network parameter self-tuning according to claim 1, characterized in that, S6 specifically includes: Let the joint angle tracking error be: ； in, From the perspective of the current goal, From the current practical perspective, This represents the current tracking error. Three differential error signals are constructed based on the error sequence: ； in, This is the tracking error from the previous cycle. For the tracking error of the previous cycle, This is a first-order difference error signal. It is a second-order difference error signal. This is the current error signal; The RBF network corrects the three key gains in the ADRC incremental control law online based on the current error, equivalent Jacobian information, and differential error signal. , , : ； in, , , The ADRC gain learning rate, Represents the saturation constraint function. No. The first ADRC gain of the cycle, No. The third ADRC gain of the cycle, No. The second ADRC gain of the cycle, This is an equivalent Jacobian message.

10. A disturbance rejection control system for the tilt mechanism of a tilt-rotor unmanned aerial vehicle based on RBF neural network parameter self-tuning, characterized in that, include: The input command terminal is used to input the target angle of the joint motor; The RBF-ADRC controller is connected to the input command terminal and the feedback loop respectively, and is used to calculate the tracking error and generate the control quantity based on the target angle and the actual output angle fed back by the feedback loop. A drive signal conversion module, connected to the output terminal of the RBF-ADRC controller, is used to convert the control quantity into a drive signal; The controlled object is connected to the output terminal of the drive signal conversion module. The controlled object is the tilt mechanism joint motor position servo system of a tilt rotor UAV, which is used to perform angle adjustment under the drive signal. The output position monitoring module is connected to the output end of the controlled object and is used to monitor the actual output angle of the joint motor and output the actual angle signal. The feedback loop is connected between the output terminal of the output position monitoring module and the feedback input terminal of the RBF-ADRC controller, and is used to feed back the actual angle signal to the RBF-ADRC controller to form a closed-loop anti-disturbance control loop. The RBF-ADRC controller includes: The tracking error calculation module is connected to the input command terminal and the feedback loop respectively, and is used to calculate the tracking error based on the target angle and the actual output angle. An error differential generation module is connected to the output of the tracking error calculation module and is used to generate a differential error signal based on the tracking error. An extended state observer, connected to the feedback loop and the control output of the RBF-ADRC controller, is used to estimate the total system disturbance based on the actual output angle and the current control quantity, and obtain the total disturbance estimate. The RBF neural network online self-tuning module, connected to the feedback loop, is used to correct the key parameters of the incremental control law online based on system operating data. The incremental control law module is connected to the tracking error calculation module, the error difference generation module, the extended state observer, and the RBF neural network online self-tuning module, respectively, and is used to calculate the control quantity by integrating the tracking error, the difference error signal, the total disturbance estimate, and the key parameters corrected by the RBF neural network. The output limiting and smoothing module is connected to the output of the incremental control law module and is used to limit and smooth the control quantity before outputting the final control quantity.

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