Stable control method and system for robot arm based on fractional order sliding mode adaptive compensation

Abstract

This invention discloses a method and system for stabilizing a robotic arm based on fractional-order sliding mode adaptive compensation. The method includes: constructing a unified dynamic model incorporating time-varying delays, nonlinear disturbances, and neural network approximation errors; defining the sliding mode function using Caputo fractional derivatives, establishing an improved trend law based on the improved Fal function and hyperbolic tangent function, and obtaining a control law based on the error-driven dynamic model and the improved approach law; constructing a dynamic adaptive compensator linked to time-delay gradient information to address the residual errors of the radial basis function and the unknown nonlinear terms in the neural network approximation, and dynamically adjusting the compensation gain based on the dynamic adaptive compensator; constructing a Lyapunov functional adapted to the fractional-order system, deriving the exponential stability criterion for the closed-loop system using Young's inequality and Halany's inequality, and determining the quantitative correlation between the fractional-order order and the convergence rate. This invention solves the problems of imbalance between robustness and smoothness and weak time-delay adaptability in existing technologies, significantly improving control accuracy and reliability.

Description

Technical Field

[0001] This invention relates to the field of industrial robotic arm control technology, and in particular to a robotic arm stabilization control method, system, storage medium, and electronic device based on fractional sliding mode adaptive compensation. Background Technology

[0002] Industrial robotic arms are core equipment in automated production, and their control precision and operational stability directly determine production efficiency and product quality. In practical applications, robotic arms exhibit time-varying characteristics such as joint transmission lag and sensor sampling lag. They also face problems such as nonlinear dynamic coupling, external load disturbances, parameter perturbations, and residual errors in neural network approximation, which can easily lead to increased trajectory tracking errors, joint tremors, and decreased system stability, thus hindering the implementation of high-precision operations.

[0003] In existing technologies, fractional-mode sliding mode control is widely used in robotic arm control due to its strong robustness. Adaptive compensation techniques can offset the effects of approximation errors and disturbances, but these two technologies are often designed independently and lack a collaborative optimization mechanism. Traditional sliding mode reaching laws are poorly designed, resulting in limited jitter suppression. Stability criteria are mostly based on fixed operating conditions, making them less adaptable to complex operating conditions such as sudden load changes and time delay changes. Existing methods focus on algorithm design and fail to fully consider practicality for engineering applications, making it difficult to meet the high-precision and stable control requirements of robotic arms under complex operating conditions. Summary of the Invention

[0004] This invention provides a robotic arm stabilization control method, system, storage medium, and electronic device based on fractional sliding mode adaptive compensation, which can achieve synergistic optimization of time delay suppression, error convergence, and jitter reduction, thereby improving the control performance and engineering applicability of the robotic arm under complex working conditions.

[0005] This invention provides a robotic arm stabilization control method based on fractional sliding mode adaptive compensation, comprising: Based on the time scale theory, a unified dynamic model is constructed that integrates the continuous time domain and the discrete sampling domain, including time-varying time delay, nonlinear disturbance and neural network approximation error. The sliding mode function is defined using the Caputo fractional derivative. A composite reaching term is constructed based on the improved fal function and the hyperbolic tangent function. Time-varying reaching coefficients are designed. An improved trend law is constructed based on the composite reaching term and the time-varying reaching coefficients. The control law is obtained based on the error-driven dynamic model and the improved reaching law. To address the residual errors of radial basis functions and neural network approximation of unknown nonlinear terms, a dynamic adaptive compensator linked to time-delay gradient information is constructed. Based on the dynamic adaptive compensator, the compensation gain is dynamically adjusted to obtain the corrected control law. We construct a Lyapunov functional adapted to fractional-order systems, derive the exponential stability criterion for closed-loop systems by combining Young's inequality and Halany's inequality, and determine the quantitative relationship between fractional order and convergence rate.

[0006] Furthermore, based on the above-mentioned robotic arm stabilization control method based on fractional sliding mode adaptive compensation, the derivative on the time scale is defined by the following formula to unify the continuous time domain and the discrete sampling domain:

[0007] in, This is the joint angular displacement vector. Indicates taking the derivative. The joint angular velocity vector. The sampling period is For the set of real numbers, It is a set of integers.

[0008] Furthermore, based on the above-mentioned robotic arm stabilization control method based on fractional sliding mode adaptive compensation, an RBF neural network is used to approximate the unknown nonlinear term. , The approximation result is residual error Construct a unified dynamic model:

[0009] in, To approximate unknown nonlinear terms using an RBF neural network, For residual error, The inertia matrix, The matrix of Coriolis force and centrifugal force. For gravity, External disturbances For time-varying and time-delayed, For ideal control input, For the corrected control input, For the actual trajectory, To track the desired trajectory; Define the error vector as The first derivative of the error vector is defined as: The second derivative of the error vector is defined as: ; The unified dynamic model is then rearranged to obtain an error-driven dynamic model:

[0010] in, This is a comprehensive disturbance term that includes all non-ideal factors.

[0011] Furthermore, based on the above-mentioned robotic arm stabilization control method based on fractional sliding mode adaptive compensation, the sliding mode function is defined using the Caputo fractional derivative, a composite reaching term is constructed based on the improved fal function and the hyperbolic tangent function, time-varying reaching coefficients are designed, and an improved trend law is constructed based on the composite reaching term and the time-varying reaching coefficients, including: The sliding mode function is defined as follows:

[0012] in, This is the error adjustment coefficient. This is the trajectory tracking error vector. The Caputo fractional derivative is defined as: ,in Gamma function ; Build Improvement function:

[0013] in, for function, For the sliding mode function Each joint component The boundary layer threshold, For power-order parameters; Combining the hyperbolic tangent function with the improved fal function, a composite approach term is formed:

[0014] in, For composite trend terms, The smoothing coefficient of the hyperbolic tangent function; The time-varying approach coefficient for design is:

[0015] in, For time-varying approach coefficients, Based on the convergence coefficient, For adjustment coefficients, The attenuation coefficient; An improved reaching law is constructed by combining the composite reaching term and the dynamic reaching coefficient: .

[0016] Furthermore, based on the above-mentioned robotic arm stabilization control method based on fractional sliding mode adaptive compensation, the control law is obtained based on the error-driven dynamic model and the improved reaching law, including: Differentiating the sliding mode function, we get:

[0017] Based on the error-driven dynamics model and the improved reaching law, the control law is derived. :

[0018] The control law is rearranged to obtain:

[0019] The core parameters are tuned using the particle swarm optimization algorithm, and the objective function is:

[0020] in, These are the weighting coefficients.

[0021] Furthermore, based on the above-mentioned robotic arm stabilization control method based on fractional sliding mode adaptive compensation, a dynamic adaptive compensator linked to time-delay gradient information is constructed to address the residual errors of the radial basis function and the unknown nonlinear term approximation by the neural network. The compensation gain is dynamically adjusted based on the dynamic adaptive compensator to obtain the corrected control law, including: Residual error in radial basis function neural network approximation of unknown nonlinear terms Combined with time-varying time delay External disturbances Define the integrated coupling perturbation term:

[0022] in, For the combined coupled disturbance term, This is the control input after time delay compensation. The gradient is a time-delay gradient; A dynamic adaptive compensator linked to the time-delay gradient is constructed, expressed by the following equation:

[0023] in, For dynamic adaptive compensators, For adaptive learning rate, Forgetting factor, The time-delay gradient linkage coefficient; Based on adaptive gain compensation Construct error compensation term :

[0024] The compensation term is embedded in the control law to achieve control over the combined coupled disturbance. The real-time cancellation, i.e., the corrected control law, is: .

[0025] Furthermore, based on the above-mentioned robotic arm stabilization control method based on fractional sliding mode adaptive compensation, a Lyapunov functional adapted to the fractional-order system is constructed, and the exponential stability criterion of the closed-loop system is derived by combining Young's inequality and Halany's inequality. The quantitative correlation between the fractional-order order and the convergence rate is determined, including: For the characteristics of fractional sliding mode systems, a Lyapunov functional is constructed that includes sliding mode variables and compensation for gain estimation errors:

[0026] in, For Lyapunov functionals, , The optimal value for compensating for the gain; right Taking the time derivative and combining it with the aforementioned error-driven dynamics model, improved reaching law, and adaptive law, we can simplify to obtain:

[0027] Utilizing the properties of robotic arm dynamics, the result can be further simplified to:

[0028] For any ,have ,Pick Scaling the coupling perturbation term, we get:

[0029] Will Substitute, combine Optimality, Simplifying, we get:

[0030] in, The convergence coefficient; Using Halany's inequality, combined with The boundedness of the closed-loop system leads to the following exponential stability criterion: ; Determine the order of fractions With convergence rate Quantitative correlation: when the fractional order At that time, convergence rate satisfy: ,Right now The closer to 1, the faster the convergence rate. The larger the value, the faster the system error converges.

[0031] The present invention also provides a robotic arm stability control system based on fractional sliding mode adaptive compensation, comprising: The unified dynamics model construction module is used to unify the continuous time domain and the discrete sampling domain based on the time scale theory, and to construct a unified dynamics model containing time-varying time delays, nonlinear perturbations and neural network approximation errors. The control law calculation module is used to define the sliding mode function using the Caputo fractional derivative, construct a composite reaching term based on the improved fal function and the hyperbolic tangent function, design time-varying reaching coefficients, construct an improved trend law based on the composite reaching term and the time-varying reaching coefficients, and obtain the control law based on the error-driven dynamic model and the improved reaching law. The control law correction module is used to construct a dynamic adaptive compensator linked with time-delay gradient information for the residual error of the radial basis function and the unknown nonlinear term of the neural network approximation. Based on the dynamic adaptive compensator, the compensation gain is dynamically adjusted to obtain the corrected control law. The quantization correlation determination module is used to construct a Lyapunov functional adapted to the fractional-order system, derive the exponential stability criterion of the closed-loop system by combining Young's inequality and Halany's inequality, and determine the quantization correlation between the fractional-order order and the convergence rate.

[0032] The present invention also provides a computer-readable storage medium storing a plurality of instructions adapted for loading by a processor to execute any of the above-described robotic arm stabilization control methods based on fractional sliding mode adaptive compensation.

[0033] The present invention also provides an electronic device, including a processor and a memory, wherein the processor is electrically connected to the memory, the memory is used to store instructions and data, and the processor is used in the steps of the robotic arm stabilization control method based on fractional sliding mode adaptive compensation described in any of the preceding claims.

[0034] This invention provides a robotic arm stabilization control method, system, storage medium, and electronic device based on fractional sliding mode adaptive compensation. Based on time-scale theory, this invention is compatible with continuous robotic arm motion and discrete sampled signals. It constructs a unified dynamic model incorporating time-varying delays, nonlinear disturbances, and neural network approximation errors, clarifying the correlation between each parameter and the control objective. A third-order composite Caputo-type fractional sliding mode function is employed to construct an improved reaching law. An improved fal function and a hyperbolic tangent function composite term are introduced to dynamically adjust the reaching coefficient and suppress sliding mode chatter. By combining the joint constraints of the robotic arm to optimize the control law parameters, the control output is ensured to adapt to the mechanical characteristics. For the residual error in the approximation of unknown nonlinear terms by the radial basis function (RBF) neural network, a dynamic adaptive compensator linked to time-delay gradient information is designed to identify the time-varying time delay and error variation patterns in real time, dynamically adjust the compensation gain, and construct an error closed-loop suppression link to stably control the approximation error within the order of magnitude, thus offsetting the synergistic effect of time delay and disturbance. A Lyapunov functional adapted to the fractional-order system is constructed, and by combining Young's inequality and Halany's inequality, the exponential stability criterion of the closed-loop system is rigorously derived, clarifying the quantitative correlation between the fractional order and the convergence rate. This invention has the following beneficial effects: (1) The robustness is significantly improved. The fractional sliding mode and adaptive compensation are deeply coupled, which can resist ±20% rated load change and 0-0.5s time delay change. The control error fluctuation range is reduced by more than 40%, which is suitable for complex working conditions.

[0035] (2) Improved approach law design reduces sliding mold vibration amplitude by 60%, avoids joint mechanical wear, and extends equipment service life.

[0036] (3) The error decays at a preset exponential rate, the neural network approximation error is controlled within the order of magnitude, and the trajectory tracking accuracy is greatly improved.

[0037] (4) The control method does not require major modifications to the existing robotic arm hardware, and can be directly integrated and deployed. The modification cost is low and the practicality is strong. Attached Figure Description

[0038] The technical solution and other beneficial effects of the present invention will become apparent from the following detailed description of specific embodiments of the invention, in conjunction with the accompanying drawings.

[0039] Figure 1 A flowchart of a robotic arm stabilization control method based on fractional sliding mode adaptive compensation provided in an embodiment of the present invention.

[0040] Figure 2 The sliding mode variable convergence curve is provided for an embodiment of the present invention.

[0041] Figure 3 This is a schematic diagram of the disturbance adaptive compensation gain following characteristic provided in an embodiment of the present invention.

[0042] Figure 4 The control error comparison curve under experimental conditions is provided for the embodiments of the present invention.

[0043] Figure 5 The stability verification curves under different time-delay conditions are provided for embodiments of the present invention.

[0044] Figure 6 This is a schematic diagram of the structure of a robotic arm stability control system based on fractional sliding mode adaptive compensation, provided in an embodiment of the present invention. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] To address the aforementioned problems, embodiments of the present invention provide a robotic arm stabilization control method, system, storage medium, and electronic device based on fractional-order sliding mode adaptive compensation. The robotic arm stabilization control system based on fractional-order sliding mode adaptive compensation provided by embodiments of the present invention can be integrated into an electronic device, which can be a terminal, server, or other device. The terminal can include a tablet computer, laptop computer, personal computer (PC), microprocessor box, or other devices.

[0047] Please see Figure 1 , Figure 1 The flowchart illustrates a robotic arm stabilization control method based on fractional sliding mode adaptive compensation, provided in an embodiment of the present invention. This method, applied in electronic devices, includes the following steps: S1, based on the time scale theory, unifies the continuous time domain and the discrete sampling domain, and constructs a unified dynamic model containing time-varying time delays, nonlinear disturbances and neural network approximation errors.

[0048] By unifying the continuous time domain and the discrete sampling domain through time scale theory, specifically by defining the time scale using the following formula... Derivative:

[0049] in, This is the joint angular displacement vector. Indicates taking the derivative. The joint angular velocity vector. The sampling period is For the set of real numbers, It is a set of integers.

[0050] pass The derivative is compatible with both continuous motion and discrete sampling characteristics, avoiding the errors of the "continuous-discrete" conversion in traditional modeling.

[0051] Based on the Lagrange equations, an ideal dynamic model of the robotic arm without disturbance or time delay is constructed:

[0052] in, for Second derivative, For ideal control input.

[0053] Considering the time delay of control signal transmission and sensor sampling, the control input is corrected to... External load mutations, friction fluctuations, and other disturbances are uniformly represented as... An RBF neural network is used to approximate the unknown nonlinear term. The approximation result is residual error Construct a unified dynamic model:

[0054] in, To approximate unknown nonlinear terms using an RBF neural network, For residual error, The inertia matrix, The matrix of Coriolis force and centrifugal force. For gravity, External disturbances For time-varying and time-delayed, For ideal control input, For the corrected control input, For the actual trajectory, To track the desired trajectory; The control objective is to make the actual trajectory Tracking the desired trajectory The error vector is defined as The first derivative of the error vector is defined as: The second derivative of the error vector is defined as: ; The unified dynamic model is rearranged to obtain the error-driven dynamic model:

[0055] in, This is a comprehensive disturbance term that includes all non-ideal factors.

[0056] Control input Combined disturbances need to be offset driving error The convergence to the target range provides a direct model basis for the subsequent design of control laws and compensators.

[0057] S2 uses the Caputo fractional derivative to define the sliding mode function, constructs a composite reaching term based on the improved fal function and the hyperbolic tangent function, designs time-varying reaching coefficients, constructs an improved trend law based on the composite reaching term and the time-varying reaching coefficients, and obtains the control law based on the error-driven dynamic model and the improved reaching law.

[0058] Using Caputo fractional derivatives, the sliding mode function is defined as follows:

[0059] in, This is the error adjustment coefficient. This is the trajectory tracking error vector. The Caputo fractional derivative is defined as: ,in Gamma function .

[0060] This sliding mode function integrates the fractional derivative, instantaneous value, and integral term of the error, which can enhance the tracking ability of time-varying errors.

[0061] To address the issue of insufficient smoothness of the linear segment in the traditional fal function within the small error region, an improved fal function is constructed. The function is:

[0062] in, for function, For the sliding mode function Each joint component The boundary layer threshold determines the width of the segmented interval. The power parameter controls the degree of nonlinearity of the function.

[0063] Introducing the hyperbolic tangent function into the small error region can further reduce jitter.

[0064] Combining the hyperbolic tangent function and the improved fal function, a composite approach term is formed:

[0065] in, For composite trend terms, The smoothing coefficients of the hyperbolic tangent function (in one specific embodiment) =0.005), ensure The transition is slow near the sliding surface.

[0066] To achieve "rapid convergence in the distant domain and smooth convergence in the near domain", the time-varying convergence coefficient is designed as follows:

[0067] in, For time-varying approach coefficients, Based on the convergence coefficient, For adjustment coefficients, This is the attenuation coefficient.

[0068] In one specific embodiment, the basic convergence coefficient adjustment coefficient attenuation coefficient .when When the range is large (far range), , rapidly approaching; when When the range is small (near-range), Smooth convergence.

[0069] An improved reaching law is constructed by combining the composite reaching term and the dynamic reaching coefficient: .

[0070] This approach law, through the synergy of time-varying coefficients and composite functions, fundamentally suppresses sliding mode chatter.

[0071] Taking the derivative of the sliding mode function, we get:

[0072] Based on the error-driven dynamics model and the improved reaching law, the control law is derived. :

[0073] The control law is rearranged to obtain:

[0074] The core parameters are tuned using the Particle Swarm Optimization (PSO) algorithm, and the objective function is:

[0075] in, These are the weighting coefficients.

[0076] In one specific embodiment, , , It is used to constrain and control torque and joint angular velocity to ensure they do not exceed limits.

[0077] S3. To address the residual error of the radial basis function and the unknown nonlinear term approximation by the neural network, a dynamic adaptive compensator linked with the time-delay gradient information is constructed. Based on the dynamic adaptive compensator, the compensation gain is dynamically adjusted to obtain the corrected control law.

[0078] By using a dynamic adaptive compensator, the time-varying delay and error variation patterns are identified in real time, and the compensation gain is dynamically adjusted to construct an error closed-loop suppression link, thereby stabilizing and controlling the approximation error within a certain range. Within a certain order of magnitude, it offsets the combined effects of time delay and disturbance.

[0079] Residual error for approximating unknown nonlinear terms using radial basis function (RBF) neural networks Combined with time-varying time delay External disturbances Define the integrated coupling perturbation term:

[0080] in, For the combined coupled disturbance term, This is the control input after time delay compensation. The time-delay gradient represents the rate of change of the time-varying time delay.

[0081] Constructing a dynamic adaptive compensator linked to the time-delay gradient, the core of which is to compensate for the gain. The online update law is expressed by the following formula:

[0082] in, For dynamic adaptive compensators, For adaptive learning rate, Forgetting factor, The time-delay gradient linkage coefficient; Based on adaptive gain compensation Construct error compensation term :

[0083] By embedding the compensation term into the control law, the combined coupled disturbance can be controlled. The real-time cancellation, i.e., the corrected control law, is:

[0084] By adjusting the parameters of the adaptive law, the residual error of the RBF neural network can be reduced. Stable control at Within the order of magnitude, that is: .

[0085] S4. Construct a Lyapunov functional adapted to the fractional-order system, and derive the exponential stability criterion for the closed-loop system by combining Young's inequality and Halany's inequality, thus determining the quantitative relationship between the fractional order and the convergence rate.

[0086] For the characteristics of fractional sliding mode systems, a Lyapunov functional is constructed that includes sliding mode variables and compensation for gain estimation errors:

[0087] in, For Lyapunov functionals, , The optimal value for compensating for the gain; right By taking the time derivative and combining it with the error-driven dynamics model, the improved reaching law, and the adaptive law, we can simplify to obtain:

[0088] Utilizing the properties of robotic arm dynamics, the result can be further simplified to:

[0089] For any ,have ,Pick Scaling the coupling perturbation term, we get:

[0090] Will Substitute, combine Optimality, Simplifying, we get:

[0091] in, The convergence coefficient; Using Halany's inequality, combined with The boundedness of the closed-loop system leads to the following exponential stability criterion: ; Determine the order of fractions With convergence rate Quantitative correlation: when the fractional order At that time, convergence rate satisfy: ,Right now The closer to 1, the faster the convergence rate. The larger the value, the faster the system error converges.

[0092] The present invention will now be described in further detail with reference to specific embodiments.

[0093] Using a 6-joint serial industrial robotic arm as the controlled object, and applying it to a precision assembly scenario for automotive parts, high-precision tracking of joint trajectories (tracking error) is required. Furthermore, it must withstand complex operating conditions such as ±20% load fluctuations and 0~0.5s time-varying communication delays during assembly. The specific implementation is as follows: The inertia matrix, Coriolis force coefficients, and gravity term for each joint were identified using the least squares method, with a model fit ≥95%. The order of the Caputo-type fractional derivative is also considered. Error scaling factor of sliding mode function Error integral coefficient The approach gain of the improved approach law , tremor inhibitory factor Improve the nonlinear exponent of the fal function The adaptive learning rate of the dynamic adaptive compensator Forgetting factor Time-delay gradient linkage coefficient The parameters work together to achieve a balance between robustness and control smoothness.

[0094] The expected trajectory is: Time-varying and time-delayed External disturbances .

[0095] Robotic arm zero-homing calibration, sensor calibration, initialization of compensation gain and sliding mode variables The accuracy of the identification model was verified through experimental data, ensuring a fit of ≥95%. The control law was compiled and downloaded to the DSP. The controller acquired signals in real time at a 1ms cycle, calculated errors and sliding mode variables, updated compensation gains, and output control commands. Three sets of experiments were set up: ideal operating condition + traditional control, complex operating condition + traditional control, and complex operating condition + the method of this invention. Each set was repeated 3 times, and the experimental results were averaged. Data such as angle, torque, and error were acquired in real time, and the tracking error RMSE, jitter amplitude, and response time were calculated offline.

[0096] Under complex operating conditions, the tracking error RMSE of the method of this invention is: Compared with the traditional method (5.2×10), - The error decreased by 40.4% (³ rad), the steady-state error decreased by 42.9%, and the residual error stabilized at... Order of magnitude. The method of this invention reduces the amplitude of joint tremors from 0.008~0.020 rad to 0.003~0.008 rad, with an average suppression rate of 60.3%. Fractional order. At that time, convergence rate Lyapunov functionals The system exhibits exponential decay and shows no instability during sudden time delays, thus validating the criterion's effectiveness.

[0097] This embodiment uses a 6-joint industrial robotic arm as the controlled object. Through multi-condition comparative experiments, the effectiveness and superiority of the fractional-order sliding mode adaptive compensation robotic arm stability control method of the present invention are verified. Figure 2 The sliding mode variable convergence curve provided in the embodiment of the present invention, Figure 3 This is a schematic diagram of the disturbance adaptive compensation gain following characteristic provided in an embodiment of the present invention. Figure 4 The control error comparison curve under experimental conditions provided in the embodiments of the present invention is shown. Figure 5 The figures provided in this invention are stability verification curves under different time-delay conditions. Experimental results show that the method of this invention, through deep coupling of fractional sliding mode control and adaptive error compensation, reduces trajectory tracking error by more than 40% compared to the traditional fractional sliding mode control method under complex conditions involving time-varying time delays, nonlinear load disturbances, and neural network approximation residual error coupling. The improved fractional sliding mode reaching law effectively suppresses sliding mode chatter, reducing the average joint chatter amplitude by 60%, balancing control accuracy and mechanical smoothness. The dynamic adaptive compensator linked to the time-delay gradient can identify the time-varying time delay and error variation patterns in real time, stabilizing the residual error within a certain range. The magnitude effectively offsets the combined effects of time delay and disturbance. By constructing a Lyapunov functional adapted to the fractional-order system and combining the exponential stability criterion derived from Young's inequality and Halany's inequality, the global stability of the closed-loop system is ensured, and the quantitative correlation between the fractional order and the convergence rate can precisely control the system response speed.

[0098] Based on the method described in the above embodiments, this embodiment will further describe the robotic arm stability control system from the perspective of a fractional sliding mode adaptive compensation system. The robotic arm stability control system based on fractional sliding mode adaptive compensation can be implemented as an independent entity or integrated into an electronic device. The electronic device can be a terminal, server, or other devices. The terminal can include a tablet computer, a laptop computer, a personal computer (PC), a microprocessor box, or other devices.

[0099] Please see Figure 6 , Figure 6 This invention specifically describes a robotic arm stabilization control system based on fractional sliding mode adaptive compensation, which is applied in electronic devices. The robotic arm stabilization control system based on fractional sliding mode adaptive compensation may include: The unified dynamics model construction module is used to unify the continuous time domain and the discrete sampling domain based on the time scale theory, and to construct a unified dynamics model containing time-varying time delays, nonlinear perturbations and neural network approximation errors. The control law calculation module is used to define the sliding mode function using the Caputo fractional derivative, construct a composite reaching term based on the improved fal function and the hyperbolic tangent function, design time-varying reaching coefficients, construct an improved trend law based on the composite reaching term and the time-varying reaching coefficients, and obtain the control law based on the error-driven dynamic model and the improved reaching law. The control law correction module is used to construct a dynamic adaptive compensator linked with time-delay gradient information for the residual error of the radial basis function and the unknown nonlinear term of the neural network approximation. Based on the dynamic adaptive compensator, the compensation gain is dynamically adjusted to obtain the corrected control law. The quantization correlation determination module is used to construct a Lyapunov functional adapted to the fractional-order system, derive the exponential stability criterion of the closed-loop system by combining Young's inequality and Halany's inequality, and determine the quantization correlation between the fractional-order order and the convergence rate.

[0100] In specific implementation, the above modules and / or units can be implemented as independent entities, or they can be arbitrarily combined and implemented as the same or several entities. For the specific implementation of the above modules and / or units, please refer to the previous method embodiments. For the specific beneficial effects that can be achieved, please also refer to the beneficial effects in the previous method embodiments, which will not be repeated here.

[0101] In addition, this embodiment of the invention also provides an electronic device, which may be a computer, tablet computer, or other similar device. This electronic device can implement the steps of any embodiment of the robotic arm stabilization control method based on fractional-order sliding mode adaptive compensation provided in this embodiment of the invention. Therefore, it can achieve the beneficial effects achievable by any robotic arm stabilization control method based on fractional-order sliding mode adaptive compensation provided in this embodiment of the invention, as detailed in the preceding embodiments, and will not be repeated here.

[0102] This electronic device can be used to implement the robotic arm stabilization control method based on fractional sliding mode adaptive compensation provided in the above embodiments. The electronic device 500 can be a terminal, server, or other device. The terminal can include a tablet computer, laptop computer, personal computer (PC), microprocessor box, or other devices.

[0103] Specifically, in this embodiment, the mobile terminal further includes a memory and one or more programs, wherein one or more programs are stored in the memory and configured to be executed by one or more processors. One or more programs contain instructions for performing the following operations: Based on the time scale theory, a unified dynamic model is constructed that integrates the continuous time domain and the discrete sampling domain, including time-varying time delay, nonlinear disturbance and neural network approximation error. The sliding mode function is defined using the Caputo fractional derivative. A composite reaching term is constructed based on the improved fal function and the hyperbolic tangent function. Time-varying reaching coefficients are designed. An improved trend law is constructed based on the composite reaching term and the time-varying reaching coefficients. The control law is obtained based on the error-driven dynamic model and the improved reaching law. To address the residual errors of radial basis functions and neural network approximation of unknown nonlinear terms, a dynamic adaptive compensator linked to time-delay gradient information is constructed. Based on the dynamic adaptive compensator, the compensation gain is dynamically adjusted to obtain the corrected control law. We construct a Lyapunov functional adapted to fractional-order systems, derive the exponential stability criterion for closed-loop systems by combining Young's inequality and Halany's inequality, and determine the quantitative relationship between fractional order and convergence rate.

[0104] In practice, the above modules can be implemented as independent entities or combined in any way to be implemented as the same or several entities. For the specific implementation of the above modules, please refer to the previous method implementation examples, which will not be repeated here.

[0105] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by instructions, or by instructions controlling related hardware. These instructions can be stored in a computer-readable storage medium and loaded and executed by a processor. Therefore, embodiments of the present invention provide a storage medium storing multiple instructions that can be loaded by a processor to execute the steps of any embodiment of the robotic arm stabilization control method based on fractional-order sliding mode adaptive compensation provided by the present invention.

[0106] The computer-readable storage medium may include: read-only memory (ROM), random access memory (RAM), disk or optical disk, etc.

[0107] Since the instructions stored in the storage medium can execute the steps in any embodiment of the robotic arm stabilization control method based on fractional sliding mode adaptive compensation provided in the embodiments of the present invention, the beneficial effects that any robotic arm stabilization control method based on fractional sliding mode adaptive compensation provided in the embodiments of the present invention can achieve can be realized. For details, please refer to the previous embodiments, which will not be repeated here.

[0108] The foregoing has provided a detailed description of a robotic arm stabilization control method, system, storage medium, and electronic device based on fractional sliding mode adaptive compensation provided by embodiments of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A machine arm stable control method based on fractional order sliding mode adaptive compensation, characterized in that, The method includes: Based on the time scale theory, a unified dynamic model is constructed that integrates the continuous time domain and the discrete sampling domain, including time-varying time delay, nonlinear disturbance and neural network approximation error. The sliding mode function is defined using the Caputo fractional derivative. A composite reaching term is constructed based on the improved fal function and the hyperbolic tangent function. Time-varying reaching coefficients are designed. An improved trend law is constructed based on the composite reaching term and the time-varying reaching coefficients. The control law is obtained based on the error-driven dynamic model and the improved reaching law. To address the residual errors of radial basis functions and neural network approximation of unknown nonlinear terms, a dynamic adaptive compensator linked to time-delay gradient information is constructed. Based on the dynamic adaptive compensator, the compensation gain is dynamically adjusted to obtain the corrected control law. We construct a Lyapunov functional adapted to fractional-order systems, derive the exponential stability criterion for closed-loop systems by combining Young's inequality and Halany's inequality, and determine the quantitative relationship between fractional order and convergence rate.

2. The robotic arm stabilization control method based on fractional sliding mode adaptive compensation according to claim 1, characterized in that, The derivative over the time scale is defined by the following formula to unify the continuous time domain and the discrete sampling domain: in, This is the joint angular displacement vector. Indicates taking the derivative. The joint angular velocity vector. The sampling period is For the set of real numbers, It is a set of integers.

3. The robotic arm stabilization control method based on fractional sliding mode adaptive compensation according to claim 1, characterized in that, Using RBF neural networks to approximate unknown nonlinear terms , The approximation result is residual error Construct a unified dynamic model: in, To approximate unknown nonlinear terms using an RBF neural network, For residual error, The inertia matrix, The matrix of Coriolis force and centrifugal force. For gravity, External disturbances For time-varying and time-delayed, For ideal control input, For the corrected control input, For the actual trajectory, To track the desired trajectory; Define the error vector as The first derivative of the error vector is defined as: The second derivative of the error vector is defined as: ; The unified dynamic model is then rearranged to obtain an error-driven dynamic model: wherein is the comprehensive disturbance term, containing all non-ideal factors.

4. The robotic arm stabilization control method based on fractional sliding mode adaptive compensation according to claim 1, characterized in that, The sliding mode function is defined using the Caputo fractional derivative. A composite reaching term is constructed based on the improved Fal function and the hyperbolic tangent function. Time-varying reaching coefficients are designed. An improved trend law is constructed based on the composite reaching term and the time-varying reaching coefficients, including: The sliding mode function is defined as follows: in, This is the error adjustment coefficient. This is the trajectory tracking error vector. The Caputo fractional derivative is defined as: ,in Gamma function ; Construction improvements Function: in, for function, For the sliding mode function Each joint component The boundary layer threshold, For power-order parameters; Combining the hyperbolic tangent function with the improved fal function, a composite approach term is formed: wherein, is a complex trend term, is a hyperbolic tangent function smoothing coefficient; The time-varying approach coefficient for design is: in, For time-varying approach coefficients, Based on the convergence coefficient, For adjustment coefficients, The attenuation coefficient; An improved reaching law is constructed by combining the composite reaching term and the dynamic reaching coefficient: 。 5. The robotic arm stabilization control method based on fractional sliding mode adaptive compensation according to claim 4, characterized in that, Based on the error-driven dynamic model and the improved reaching law, the control law is obtained, including: Differentiating the sliding mode function, we get: Based on the error-driven dynamics model and the improved reaching law, the control law is derived. : The control law is rearranged to obtain: The core parameters are tuned using the particle swarm optimization algorithm, and the objective function is: in, These are the weighting coefficients.

6. The robotic arm stabilization control method based on fractional sliding mode adaptive compensation according to claim 5, characterized in that, To address the residual errors of the radial basis function and the neural network approximation of unknown nonlinear terms, a dynamic adaptive compensator linked to time-delay gradient information is constructed. Based on this dynamic adaptive compensator, the compensation gain is dynamically adjusted to obtain the corrected control law, including: Residual error in radial basis function neural network approximation of unknown nonlinear terms Combined with time-varying time delay External disturbances Define the integrated coupling perturbation term: in, For the combined coupled disturbance term, This is the control input after time delay compensation. The gradient is a time-delay gradient; A dynamic adaptive compensator linked to the time-delay gradient is constructed, expressed by the following equation: in, For dynamic adaptive compensators, For adaptive learning rate, Forgetting factor, The time-delay gradient linkage coefficient; Based on adaptive gain compensation Construct error compensation term : The compensation term is embedded in the control law to achieve control over the combined coupled disturbance. The real-time cancellation, i.e., the corrected control law, is: 。 7. The method of claim 1, wherein, A Lyapunov functional adapted to fractional-order systems is constructed, and the exponential stability criterion for closed-loop systems is derived by combining Young's inequality and Halany's inequality. The quantitative relationship between fractional order and convergence rate is determined, including: For the characteristics of fractional sliding mode systems, a Lyapunov functional is constructed that includes sliding mode variables and compensation for gain estimation errors: wherein is a Lyapunov function, , is the optimal value of the compensation gain; For Taking time derivative and combining with the error-driven dynamics model, improved reaching law and adaptive law, we have Utilizing the properties of robotic arm dynamics, the result can be further simplified to: For any , there , take , the coupling perturbation term is reduced to: Will Substitute, combine Optimality, Simplifying, we get: in, The convergence coefficient; Using Halany's inequality, combined with The boundedness of the closed-loop system leads to the following exponential stability criterion: ; Determine the order of fractions With convergence rate Quantitative correlation: when the fractional order At that time, convergence rate satisfy: ,Right now The closer to 1, the faster the convergence rate. The larger the value, the faster the system error converges.

8. A robotic arm stability control system based on fractional sliding mode adaptive compensation, characterized in that, include: The unified dynamics model construction module is used to unify the continuous time domain and the discrete sampling domain based on the time scale theory, and to construct a unified dynamics model containing time-varying time delays, nonlinear perturbations and neural network approximation errors. The control law calculation module is used to define the sliding mode function using the Caputo fractional derivative, construct a composite reaching term based on the improved fal function and the hyperbolic tangent function, design time-varying reaching coefficients, construct an improved trend law based on the composite reaching term and the time-varying reaching coefficients, and obtain the control law based on the error-driven dynamic model and the improved reaching law. The control law correction module is used to construct a dynamic adaptive compensator linked with time-delay gradient information for the residual error of the radial basis function and the unknown nonlinear term of the neural network approximation. Based on the dynamic adaptive compensator, the compensation gain is dynamically adjusted to obtain the corrected control law. The quantization correlation determination module is used to construct a Lyapunov functional adapted to the fractional-order system, derive the exponential stability criterion of the closed-loop system by combining Young's inequality and Halany's inequality, and determine the quantization correlation between the fractional-order order and the convergence rate.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a plurality of instructions adapted for loading by a processor to execute the robotic arm stabilization control method based on fractional sliding mode adaptive compensation as described in any one of claims 1 to 7.

10. An electronic device, characterized in that, The system includes a processor and a memory, the processor being electrically connected to the memory, the memory being used to store instructions and data, and the processor being used to execute the steps in the robotic arm stabilization control method based on fractional sliding mode adaptive compensation as described in any one of claims 1 to 7.

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