Fault-tolerant control method and device for flexible manipulator considering sensor and actuator power failure and storage medium
By establishing a time-varying power fault model and a dynamic self-triggering mechanism, an adaptive fault-tolerant controller was designed, which solved the stability control problem of the flexible robotic arm when both the sensor and actuator experience time-varying power faults, thereby improving the system's stability and resource utilization.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- YANGZHOU UNIV
- Filing Date
- 2026-04-20
- Publication Date
- 2026-06-05
AI Technical Summary
Existing technologies struggle to effectively address the stability control issues of flexible robotic arms when both sensors and actuators experience time-varying power-law failures, and they also consume significant communication and computing resources.
A time-varying power-law fault model for sensors and actuators is established, a dynamic self-triggering mechanism and an adaptive fault-tolerant controller are designed, unknown nonlinear terms are approximated through neural networks, and fault compensation signals are constructed to reduce communication resource consumption.
Stable control of the flexible robotic arm under time-varying idempotent faults of sensors and actuators was achieved, improving system fault tolerance and resource utilization, and reducing communication resource consumption.
Smart Images
Figure CN122143036A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of robotic arm control technology and fault-tolerant control, and in particular to a fault-tolerant control method, apparatus and storage medium for flexible robotic arms that takes into account sensor and actuator idempotency faults. Background Technology
[0002] Compared to rigid robotic arms, flexible robotic arms can adapt to complex unstructured environments through continuous deformation, enabling them to perform delicate maneuvers and are therefore widely used. However, a flexible robotic arm is a highly complex nonlinear system, with numerous unknown nonlinear terms and uncertainties in its dynamic model. In practical engineering applications, key components such as sensors and actuators inevitably experience various failures after prolonged operation. These failures not only affect the system's control performance but can also lead to system instability or even malfunction in severe cases.
[0003] In existing fault-tolerant control research, sensor and actuator faults are typically modeled into two main categories: gain faults and bias faults. Early research primarily focused on constant gain and constant bias faults, but time-varying gain and time-varying bias faults are increasingly being considered. However, these fault models all implicitly assume that the input power of the system signal is fixed at 1, meaning the input-output relationship remains linear. But in practical engineering, due to factors such as actuator aging, spring hardening, and changes in operating conditions, the power of the system input signal may change and no longer remain constant at 1. The input power of the signals measured by sensors and actuators may transform into an unknown time-varying term, known as a time-varying power fault.
[0004] Recently, Shen et al. [QK Shen, P. Shi, CP Lim. Fuzzy Adaptive Fault-Tolerant Stability Control Against Novel Actuator Faults and Its Application to Mechanical Systems. IEEE Transactions on Fuzzy Systems, 2024.] proposed the concept of input power faults and designed an adaptive fault-tolerant control method based on fuzzy logic systems for a class of nonlinear systems, ensuring the asymptotic stability of the system under unknown actuator power faults. However, this study only considered power faults on the actuator side and did not address similar faults that might occur on the sensor side. In practical systems, sensor power faults directly contaminate the feedback signal, distorting the state information obtained by the controller and affecting control performance. Furthermore, this study uses a continuous-time control strategy, requiring the controller to be continuously updated, which can lead to significant resource waste in scenarios with limited communication bandwidth and computational resources.
[0005] To reduce the consumption of communication and computing resources, event-triggered control and self-triggered control methods have received widespread attention. Changchun University of Technology's patent CN120828420A proposes an adaptive dynamic programming self-triggered fault-tolerant control method for a flexible robotic arm, but it mainly addresses non-affine faults and unknown control directions, neglecting input power faults. Summary of the Invention
[0006] Purpose of the invention: The purpose of this invention is to provide a fault-tolerant control method, device and storage medium for flexible robotic arms that considers sensor and actuator idempotent faults, to solve the stable control problem of flexible robotic arms when both sensors and actuators experience time-varying idempotent faults, and to reduce communication resource consumption and improve the fault tolerance and resource utilization of the system.
[0007] Technical Solution: To achieve the above objectives, the present invention provides a fault-tolerant control method for a flexible robotic arm that considers sensor and actuator idempotency faults, comprising the following steps:
[0008] Establish a dynamic model of the flexible robotic arm and perform state transitions on it;
[0009] Establish time-varying power-law fault models for sensors and actuators. The time-varying power-law fault models should include at least the following fault types: unknown time-varying gain fault, unknown time-varying bias fault, and unknown time-varying power-law fault of sensor measurement signals; unknown time-varying gain fault, unknown time-varying bias fault of actuator output signals, and unknown time-varying power-law fault of controller input signals.
[0010] The desired trajectory of the flexible robotic arm is set, the tracking error is defined based on the deviation between the actual output of the flexible robotic arm and the desired trajectory, and a fault compensation signal is constructed based on the time-varying power fault model. The tracking error is reconstructed using the fault compensation signal to obtain the compensated control error.
[0011] A neural network is introduced to approximate the unknown nonlinear terms in the system online, and a dynamic self-triggering mechanism is designed. The dynamic self-triggering mechanism automatically calculates the next trigger time of the control command based on the system operating status, without the need to monitor the triggering conditions in real time.
[0012] A Lyapunov function is constructed, and an adaptive fault-tolerant controller is designed based on the compensated control error and the dynamic self-triggering mechanism. The stability of the closed-loop system is analyzed to ensure that the flexible robotic arm maintains stable operation when time-varying faults occur in the sensors and actuators.
[0013] As a preferred option, the time-varying power-law fault model is as follows:
[0014] Sensor idempotent fault model:
[0015]
[0016] in, This represents the actual measurement state of the sensor. This represents the actual state. The fault is of unknown time-varying gain. The fault is an unknown time-varying bias. The fault is an unknown time-varying input power.
[0017] Actuator idempotent fault model:
[0018]
[0019] in, For the actual output of the actuator, For controller input, The fault is of unknown time-varying gain. The fault is an unknown time-varying bias. The fault is an unknown time-varying input exponentiation.
[0020] As a preferred embodiment, the fault compensation signal is constructed as follows: the difference between the actual measurement state under sensor power failure and the desired trajectory is used as the first compensation signal, and the difference between another actual measurement state under sensor power failure and the corresponding virtual controller is used as the second compensation signal; the original tracking error is subtracted from the first compensation signal to obtain the first unknown compensation error, and the original virtual control error is subtracted from the second compensation signal to obtain the second unknown compensation error. The first and second unknown compensation errors are the reconstructed control error.
[0021] As a preferred embodiment, the dynamic self-triggering mechanism is as follows: the controller output remains constant between two adjacent triggers; the next trigger time is directly determined by a dynamic calculation formula, the numerator of which includes the product of the control signal amplitude and the dynamic parameter at the current trigger time, as well as a dynamic bias term, and the denominator includes the maximum value of the control command change rate; the dynamic parameter changes according to an exponential decay law; and the dynamic bias term is adaptively adjusted according to the magnitude of the tracking error using a hyperbolic tangent function.
[0022] Preferably, in the dynamic self-triggering mechanism, the dynamic parameters satisfy a first-order differential equation. ,in The design constant is such that the dynamic parameters decay exponentially to zero over time; the dynamic bias term is defined as:
[0023]
[0024] in , , For design parameters, This represents the tracking error at the trigger moment.
[0025] As a preferred option, the design of the adaptive fault-tolerant controller includes: designing a virtual controller layer by layer based on the backstepping method, constructing a corresponding Lyapunov function and designing an adaptive law for each layer, which is used to estimate the upper bound of the neural network weights and the upper bound of the approximation error.
[0026] The output of the actual controller consists of the following components: a backstepping feedback term based on the system state, a neural network approximation term, and a compensation term for the residual error after compensation for time-varying power faults; the neural network approximation term is used to approximate the unknown nonlinear function in the system online, and the residual error compensation term is used to handle the nonlinear effects that are not completely eliminated after power fault compensation.
[0027] As a preferred approach, a suitable Lyapunov function and design parameters are selected to prove that all signals in the closed-loop system are bounded and that the output tracking error of the flexible robotic arm converges to the neighborhood near the origin, thereby performing stability analysis.
[0028] Based on the same inventive concept, the present invention also provides a fault-tolerant control device for a flexible robotic arm that considers sensor and actuator idempotent faults, for implementing the aforementioned fault-tolerant control method for a flexible robotic arm that considers sensor and actuator idempotent faults. The device includes:
[0029] The modeling unit is used to establish the dynamic model of the flexible robotic arm and perform coordinate transformations;
[0030] The error reconstruction unit is used to establish the control error based on the desired trajectory and the virtual controller, and to construct a fault compensation signal based on the time-varying power fault model of the sensor and actuator to reconstruct the control error.
[0031] The dynamic triggering unit is used to automatically calculate the triggering time of the next control command based on the dynamic triggering conditions, and dynamically adjust the triggering threshold.
[0032] An adaptive control unit is used to approximate the nonlinear terms in the system using a neural network, design virtual and actual controllers based on the backstepping method, and generate fault-tolerant control commands based on the reconstructed control error.
[0033] The present invention also provides a hardware device, including a memory and a processor coupled to each other, wherein the memory stores computer instructions, and when the instructions are called and executed by the processor, the device implements the aforementioned fault-tolerant control method for a flexible robotic arm that considers sensor and actuator idempotency faults.
[0034] The present invention also provides a computer program product, including a computer-readable storage medium on which a computer program is stored. When the computer program is loaded and executed by a processor, it can realize the aforementioned fault-tolerant control method for a flexible robotic arm that takes into account sensor and actuator idempotency faults.
[0035] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:
[0036] (1) This invention considers both time-varying power faults of sensors and actuators, extends the power fault model to the sensor side, and establishes a unified time-varying power fault model, which is closer to the scenario in actual engineering where both sensors and actuators may undergo nonlinear changes.
[0037] (2) The dynamic self-triggering mechanism of the present invention does not require real-time monitoring of triggering conditions, can automatically calculate the triggering time according to the system status, and considers the coupling between the triggering mechanism and system stability in the controller design, thereby improving the utilization rate of communication resources and the flexibility of the control method.
[0038] (3) A compensation signal for sensor power failure was designed. By performing inverse transformation and compensation on the actual measured value of the sensor, the unmeasurable control error was converted into a measurable compensation signal, thus solving the problem of feedback signal distortion caused by sensor power failure. Attached Figure Description
[0039] Figure 1 This is a schematic flowchart of the fault-tolerant control method according to an embodiment of the present invention;
[0040] Figure 2 The flexible robotic arm outputs y and the desired trajectory in this embodiment of the invention. A schematic diagram of the trajectory;
[0041] Figure 3 Tracking error of the flexible robotic arm in the embodiments of the present invention A schematic diagram of the trajectory;
[0042] Figure 4 This is a schematic diagram of the trajectory of the adaptive law of the flexible robotic arm in an embodiment of the present invention;
[0043] Figure 5 The flexible robotic arm control input in the embodiments of the present invention and A schematic diagram of the trajectory;
[0044] Figure 6 This is a schematic diagram illustrating the number of triggers of the control input under the dynamic self-triggering mechanism in an embodiment of the present invention. Detailed Implementation
[0045] The technical solution of the present invention will be further described below with reference to the accompanying drawings.
[0046] Example 1
[0047] like Figure 1 As shown in the figure, an embodiment of the present invention discloses a fault-tolerant control method for a flexible robotic arm that considers sensor and actuator idempotency faults, which mainly includes the following steps:
[0048] S1. Establish the dynamic model of the flexible robotic arm and perform state transitions.
[0049] The dynamic model of the flexible robotic arm is as follows:
[0050]
[0051] in, These represent the position, velocity, and acceleration of the robotic arm links, respectively. These represent the rotor's angular velocity, velocity, and acceleration, respectively. Indicates the mass of the connecting rod. Represents gravitational acceleration. This represents the distance from the center of mass of the connecting rod to the joint axis. This represents the inertia of the link. Represents the moment of inertia. This represents the spring constant of the joint. This indicates the control input under actuator power failure.
[0052] Based on coordinate transformation, the above model is converted into the following nonlinear system:
[0053]
[0054] in, , , , , This indicates the system output.
[0055] S2. Establish a time-varying power-law fault model for sensors and actuators.
[0056] Sensor idempotent fault model:
[0057]
[0058] Actuator idempotent fault model:
[0059]
[0060] in, This represents the actual measurement state of the sensor. This represents the actual state. For the unknown time-varying gain fault of the sensor (satisfying) ), This is due to an unknown time-varying bias fault in the sensor. For unknown time-varying input exponentiation fault, and ; For the actual output of the actuator, For controller input, The unknown time-varying gain fault of the actuator (satisfying 0 < ρ(t) < 1). The actuator has an unknown time-varying bias fault. For unknown time-varying input power fault (q(t)>0).
[0061] S3. By selecting a suitable desired trajectory, construct control error and fault compensation signals.
[0062] The expression for selecting the ideal trajectory is:
[0063]
[0064] This represents the desired trajectory of the robotic arm.
[0065] Based on the output, state, and desired trajectory of the flexible robotic arm, the control error of the flexible robotic arm is established:
[0066]
[0067] in, This represents the tracking error between the output of the flexible robotic arm and the expected estimate. This represents the virtual control error between the state of the flexible robotic arm and the virtual controller. This refers to the designed virtual controller.
[0068] To compensate for the impact of sensor pluralistic faults on the feedback signal, a fault compensation signal is constructed as follows: the difference between the actual measurement state under a sensor pluralistic fault and the desired trajectory is used as the first compensation signal; the difference between another actual measurement state under a sensor pluralistic fault and the corresponding virtual controller is used as the second compensation signal. The first unknown compensation error is obtained by subtracting the first compensation signal from the original tracking error, and the second unknown compensation error is obtained by subtracting the second compensation signal from the original virtual control error. The first and second unknown compensation errors are the reconstructed control error. In this embodiment, the above compensation signal and compensation error are specifically represented as follows:
[0069]
[0070]
[0071] in, and The compensation signal indicates a sensor pluralistic fault. and This indicates the actual measurement state under sensor power failure. This indicates an unknown compensation error.
[0072] S4. Construct a dynamic self-triggering mechanism to reduce losses and introduce a neural network to approximate the unknown nonlinear terms in the system.
[0073] Construct a mathematical model for a radial basis function neural network, in compact sets. Approximating an unknown smooth function
[0074]
[0075] in, Represents an unknown continuously differentiable function. This represents the input vector of the neural network. This represents the number of nodes in the neural network. This represents the ideal weight vector. This indicates that the approximation error satisfies , Represents an unknown constant; This represents a basis function vector, which is usually composed of Gaussian functions.
[0076] Using the aforementioned neural network model, an unknown smooth function in control design can be approximated online.
[0077] To reduce communication resource waste, a dynamic self-triggering mechanism is designed. The core idea of this mechanism is: the controller outputs... The value remains the same as the value at the time of the previous trigger between two consecutive triggers:
[0078]
[0079] in, Indicates the trigger time of the controller. To trigger at the time The calculated control commands are in the interval Inside, the control signal that actually acts on the actuator remains constant.
[0080] Next trigger time Determined by the following dynamic conditions:
[0081]
[0082] in, Indicates in The dynamic parameters at time t, satisfy Its dynamics are determined by Decide, Design constant;
[0083] The absolute value of the rate of change of the controller is defined as follows: ; This indicates the lower bound of the rate of change of the control input; Indicates in The dynamic bias term at time step is defined as:
[0084]
[0085] In the formula, , , For design parameters, This represents the tracking error at the trigger moment.
[0086] When control commands change drastically, the trigger interval decreases, allowing for more frequent updates to the control signals to cope with rapid changes. When control commands tend to stabilize, the trigger interval increases, reducing the number of updates and conserving communication resources.
[0087] S5. Design the Lyapunov function and the adaptive fault-tolerant controller, and perform stability analysis on the system.
[0088] This step involves constructing Lyapunov functions layer by layer using the backstepping method, designing a virtual controller and an adaptive law, and using the dynamic self-triggering mechanism designed in step 4 to construct an actual controller, ultimately proving the stability of the closed-loop system.
[0089] Construct the first Lyapunov function:
[0090]
[0091] in, Indicates design parameters, , , express The estimated value.
[0092] Design the first virtual controller and the first adaptive law for:
[0093]
[0094]
[0095] in, , Indicates design parameters.
[0096] Construct the second Lyapunov function:
[0097]
[0098] in, Indicates design parameters, , , express The estimated value.
[0099] Design the second virtual controller. and the second adaptive law for:
[0100]
[0101]
[0102] in, , Indicates design parameters.
[0103] Construct the second Lyapunov function:
[0104]
[0105] .
[0106] Design the third virtual controller. And adaptive law for:
[0107]
[0108]
[0109] in, , Indicates design parameters.
[0110] Construct the total Lyapunov function:
[0111]
[0112] in, Indicates design parameters, , , express The estimated value.
[0113] Based on the dynamic self-triggering conditions designed in step 4, the actual controller for the flexible robotic arm is constructed as follows:
[0114]
[0115] in, and Denotes a designable smooth function, for Its satisfaction , , .
[0116] Design the fourth virtual controller. and the 4th adaptive law :
[0117]
[0118]
[0119] in, The first flexible robotic arm There is a virtual controller, where v represents the fourth virtual controller of the flexible robotic arm. The first flexible robotic arm An adaptive law, , , , , , , , , , , These are design parameters.
[0120] We can obtain:
[0121] in, ; ; ;
[0122] ;
[0123] In the formula, , , , , Indicates a positive design parameter. and are unknown constants, representing the upper bound of the ideal weight norm of the neural network and the upper bound of the approximation error, respectively.
[0124] Choose appropriate design parameters, so that , , , , and thus
[0125]
[0126] Therefore, all signals in the closed-loop system are bounded, and the system is stable. By adjusting the design parameters, the tracking error can be made to converge to an arbitrarily small neighborhood around the origin.
[0127] Example 2
[0128] The proposed fault-tolerant control method for a flexible robotic arm, which considers sensor and actuator idempotency faults, was simulated in the Simulink environment to verify its effectiveness and feasibility.
[0129] In the simulation experiment, the parameters of the flexible robotic arm were selected as follows:
[0130] , , , , , .
[0131] The parameters for the dynamic self-triggering mechanism are as follows: , , , , .
[0132] The controller and adaptive law parameters are selected as follows: , , , , , , , , , , , , , , .
[0133] The initial system value is selected as follows: , , , .
[0134] The specific form of sensor and actuator idempotency fault is selected as follows:
[0135] ;
[0136] ;
[0137] ;
[0138] .
[0139] The results of the simulation experiment are as follows Figures 2-6 As shown, Figure 2 The output y and desired trajectory of the flexible robotic arm are shown. The comparison shows that the output can closely track the expected trajectory.
[0140] Figure 3 The tracking error was displayed. The trajectory shows that the error converges quickly and remains within a small neighborhood of the origin.
[0141] Figure 4 The trajectory of the adaptive laws is shown, and all adaptive laws remain bounded.
[0142] Figure 5 Displayed controller output commands and the actual input of the actuator The trajectories of both are bounded and reasonable.
[0143] Figure 6 The results show that, under the dynamic self-triggering mechanism, the controller triggers 199 times within 30 seconds (sampling step size 0.1 seconds). If a traditional time-triggered method is used, the number of triggers would be much higher with the same sampling step size, indicating that this invention can effectively reduce communication resource consumption.
[0144] The simulation results above show that the fault-tolerant control method proposed in this invention can ensure the stability and tracking performance of the flexible robotic arm under the condition that both the sensor and the actuator experience time-varying power-law faults. At the same time, the dynamic self-triggering mechanism effectively saves communication resources.
[0145] Example 3
[0146] The present invention also provides a fault-tolerant control device for a flexible robotic arm that considers sensor and actuator idempotency faults, comprising:
[0147] The modeling unit is used to establish the dynamic model of the flexible robotic arm and perform coordinate transformations. It includes a sensor module and an actuator module. The sensor module collects the state information of the flexible robotic arm in real time, generates residual signals to detect sensor faults, reconstructs state variables, and feeds back the actual measured fault state to the controller. The actuator module monitors the deviation between the actuator output and the controller command in real time, generates the actual driving torque based on the designed fault-tolerant controller input, and drives the flexible robotic arm to move.
[0148] The error reconstruction unit is used to establish the control error based on the desired trajectory and the virtual controller, and to construct a fault compensation signal based on the time-varying power fault model of the sensor and actuator to reconstruct the control error.
[0149] The dynamic triggering unit is used to automatically calculate the triggering time of the next control command based on the dynamic triggering conditions and dynamically adjust the triggering threshold; it performs real-time fault-tolerant control on the flexible robotic arm under fault conditions to ensure the normal operation of the flexible robotic arm under fault conditions.
[0150] An adaptive control unit is used to approximate nonlinear terms in a system using neural networks. It designs virtual and actual controllers based on a backstepping method and generates fault-tolerant control commands based on the reconstructed control error. Specifically, neural network approximation involves using radial basis function neural networks to approximate the nonlinear smooth functions in the control design.
[0151] In addition to the above units, there is also a human-machine interaction module, which is used to record the status information of the flexible robotic arm throughout its entire life cycle, receive fault-tolerant instructions from the operator, and generate a traceable operation log.
[0152] The above-mentioned units work together to realize the method described in this invention.
[0153] This invention also provides a hardware device including a memory and a processor coupled together. The memory stores computer instructions, which, when executed by the processor, enable the device to implement the fault-tolerant control method for a flexible robotic arm that considers sensor and actuator idempotency faults provided by this invention. The hardware device includes, but is not limited to: personal computers, servers, programmable logic controllers, industrial panel PCs, neural network processing units, smart sensors, edge computing gateways, single-board computers, digital signal processors, etc.
[0154] This invention also provides a computer program product, including a computer-readable storage medium on which a computer program is stored. When the computer program is loaded and executed by a processor, it can perform the fault-tolerant control method for a flexible robotic arm that considers sensor and actuator idempotency faults provided by this invention. The storage medium includes, but is not limited to: optical discs, USB flash drives, SD cards, portable hard drives, server solid-state drives, embedded storage chips, network auxiliary storage, cloud storage space, etc.
Claims
1. A fault-tolerant control method for a flexible robotic arm considering sensor and actuator idempotent faults, characterized in that, Includes the following steps: Establish a dynamic model of the flexible robotic arm and perform state transitions on it; Establish a time-varying power fault model for sensors and actuators. The time-varying power fault model includes at least the following fault types: unknown time-varying gain fault, unknown time-varying bias fault, and unknown time-varying power fault of sensor measurement signals; unknown time-varying gain fault, unknown time-varying bias fault of actuator output signals, and unknown time-varying power fault of controller input signals. The desired trajectory of the flexible robotic arm is set, the tracking error is defined based on the deviation between the actual output of the flexible robotic arm and the desired trajectory, and a fault compensation signal is constructed based on the time-varying power fault model. The tracking error is reconstructed using the fault compensation signal to obtain the compensated control error. A neural network is introduced to approximate the unknown nonlinear terms in the system online, and a dynamic self-triggering mechanism is designed. The dynamic self-triggering mechanism automatically calculates the next trigger time of the control command based on the system operating status, without the need to monitor the triggering conditions in real time. A Lyapunov function is constructed, and an adaptive fault-tolerant controller is designed based on the compensated control error and the dynamic self-triggering mechanism. The stability of the closed-loop system is analyzed to ensure that the flexible robotic arm maintains stable operation when time-varying faults occur in the sensors and actuators.
2. The method according to claim 1, characterized in that, The time-varying power fault model is specifically as follows: Sensor idempotent fault model: in, This represents the actual measurement state of the sensor. This represents the actual state. The fault is of unknown time-varying gain. The fault is an unknown time-varying bias. The fault is an unknown time-varying input power. Actuator idempotent fault model: in, For the actual output of the actuator, For controller input, The fault is of unknown time-varying gain. The fault is an unknown time-varying bias. The fault is an unknown time-varying input exponentiation.
3. The method according to claim 1, characterized in that, The fault compensation signal is constructed as follows: the difference between the actual measurement state under sensor power failure and the desired trajectory is used as the first compensation signal, and the difference between another actual measurement state under sensor power failure and the corresponding virtual controller is used as the second compensation signal; the original tracking error is subtracted from the first compensation signal to obtain the first unknown compensation error, and the original virtual control error is subtracted from the second compensation signal to obtain the second unknown compensation error. The first and second unknown compensation errors are the reconstructed control error.
4. The method according to claim 1, characterized in that, The dynamic self-triggering mechanism is as follows: the controller output remains constant between two adjacent triggers; the next trigger time is directly determined by a dynamic calculation formula, the numerator of which includes the product of the control signal amplitude and the dynamic parameter at the current trigger time, as well as a dynamic bias term, and the denominator includes the maximum value of the control command change rate; the dynamic parameter changes according to an exponential decay law; and the dynamic bias term is adaptively adjusted according to the magnitude of the tracking error through a hyperbolic tangent function.
5. The method according to claim 4, characterized in that, In the aforementioned dynamic self-triggering mechanism, the dynamic parameters satisfy a first-order differential equation. ,in The design constant is such that the dynamic parameters decay exponentially to zero over time; the dynamic bias term is defined as: in , , For design parameters, This represents the tracking error at the trigger moment.
6. The method according to claim 1, characterized in that, The design of the adaptive fault-tolerant controller includes: The virtual controller is designed layer by layer based on the backstepping method. Each layer constructs a corresponding Lyapunov function and designs an adaptive law to estimate the upper bound of the neural network weights and the upper bound of the approximation error. The output of the actual controller consists of the following components: a backstepping feedback term based on the system state, a neural network approximation term, and a compensation term for the residual error after compensation for time-varying power faults; the neural network approximation term is used to approximate the unknown nonlinear function in the system online, and the residual error compensation term is used to handle the nonlinear effects that are not completely eliminated after power fault compensation.
7. The method according to claim 1, characterized in that, The stability analysis is as follows: by selecting appropriate Lyapunov functions and design parameters, it is proven that all signals in the closed-loop system are bounded and that the output tracking error of the flexible robotic arm converges to the neighborhood near the origin.
8. A fault-tolerant control device for a flexible robotic arm that considers sensor and actuator idempotency faults, characterized in that, include: The modeling unit is used to establish the dynamic model of the flexible robotic arm and perform coordinate transformations; The error reconstruction unit is used to establish the control error based on the desired trajectory and the virtual controller, and to construct a fault compensation signal based on the time-varying power fault model of the sensor and actuator to reconstruct the control error. The dynamic triggering unit is used to automatically calculate the triggering time of the next control command based on the dynamic triggering conditions, and dynamically adjust the triggering threshold. An adaptive control unit is used to approximate the nonlinear terms in the system using a neural network, design virtual and actual controllers based on the backstepping method, and generate fault-tolerant control commands based on the reconstructed control error.
9. A hardware device, characterized in that, The device includes a coupled memory and a processor, wherein the memory stores computer instructions that, when executed by the processor, enable the device to implement the fault-tolerant control method for a flexible robotic arm that considers sensor and actuator idempotent faults, as described in any one of claims 1 to 7.
10. A computer program product, characterized in that, The invention includes a computer-readable storage medium on which a computer program is stored, which, when loaded and executed by a processor, is capable of performing the fault-tolerant control method for a flexible robotic arm that takes into account sensor and actuator idempotency faults as described in any one of claims 1 to 7.