Industrial robotic arm control method and system based on time-varying time-delay neural network index stabilization

Abstract

The invention discloses an industrial robotic arm control method and system based on time-varying time-delay neural network index stability, and the method comprises the steps: collecting the position, speed and acceleration of each joint of an industrial robotic arm, and constructing a time-delay term-containing dynamic model through a system identification algorithm; a time-varying and time-delay industrial robotic arm control neural network is constructed, an input layer receives state and time-delay information, a hidden layer has neurons with time-varying and time-delay characteristics, and an output layer outputs an estimated value of the uncertainty of a dynamic model. Based on the Lyapunov stability theory, in combination with an expected trajectory generation algorithm, position and speed tracking errors are calculated, a control law based on exponential stability is designed, and a neural network parameter updating algorithm is designed by using a Lyapunov function. According to the method, the dynamic characteristics of the robotic arm can be described more accurately, the control precision and stability are improved, the adaptability of the robotic arm to complex working conditions is enhanced, and a reliable basis is provided for subsequent control design.

Description

Technical Field

[0001] The present invention belongs to the field of industrial robot control, and particularly relates to an industrial robot control method and system based on exponential stability of time-varying delay neural networks. Background Art

[0002] In industrial production, industrial robots are increasingly widely used, and their control accuracy and stability directly affect production efficiency and product quality. With the increasing complexity of the industrial production environment, the robot will inevitably be affected by various interference factors during operation. Among them, the time-varying delay problem is one of the key factors affecting the control performance of the robot. Time-varying delay may lead to system instability, oscillation, or even out-of-control, seriously reducing the control accuracy and reliability of industrial robots.

[0003] Traditional industrial robot control methods, such as those based on PID control, can achieve certain effects for simple control tasks, but their control performance often fails to meet actual requirements when facing complex problems such as time-varying delay. In recent years, neural network technology has been widely studied and applied in the field of industrial robot control due to its strong non-linear mapping ability and self-learning ability. However, existing neural network-based control methods still have some deficiencies in dealing with time-varying delay problems, such as slow network convergence speed and poor stability, resulting in error accumulation and decreased control accuracy during the actual operation of the robot. Summary of the Invention

[0004] Aiming at the problems existing in the prior art, the present invention provides an industrial robot control method based on exponential stability of time-varying delay neural networks, which can solve the problems of low control accuracy and poor stability of existing industrial robot control methods when facing time-varying delay problems, and achieve high-precision and stable control of industrial robots in complex environments, providing a scientific basis in engineering fields such as construction and machinery.

[0005] To solve the above technical problems, the present invention provides the following technical solution: An industrial robot control method based on exponential stability of time-varying delay neural networks, comprising the following steps:

[0006] S1. Collect the position, velocity, and acceleration data of each joint of the industrial robot, measure the time-varying delay of the control signal by combining timestamp technology, and use a system identification algorithm to construct a dynamic model of the industrial robot including time-varying delay terms.

[0007] S2. Construct a neural network for controlling an industrial robotic arm with time-varying time delay, including an input layer, a hidden layer, and an output layer. The input layer receives the output of the dynamic model of the industrial robotic arm with time-varying time delay terms, which includes the state of the robotic arm and time delay information. The hidden layer uses neurons with time-varying time delay characteristics, and the output layer outputs an estimate of the uncertainty of the dynamic model. S3. Train the neural network with time-varying time delay. Based on the Lyapunov stability theory and combined with the desired trajectory generation algorithm, calculate the position and velocity tracking errors, determine the control law parameters using the pole placement method, and design a control law based on exponential stability.

[0008] S4. Design a neural network parameter update algorithm using the Lyapunov function to adjust the connection weights and biases of the neural network, so that the output of the neural network can accurately track the actual uncertainty, and finally obtain a control model for the industrial robotic arm with time-varying time delay.

[0009] S5. Use the control model of the industrial robotic arm with time-varying time delay to achieve tracking control of the industrial robotic arm.

[0010] Further, in the aforementioned step S1, the photoelectric encoder measures the joint position q, and the tachogenerator measures the joint velocity. The accelerometer measures the joint acceleration. At the same time, let the robotic arm operate under different working conditions, including no-load, full-load, different speeds, and angular motion combinations, and collect data in real time.

[0011] Further, in the aforementioned step S1, the least squares method is used for system identification. The measured data is y(t), the model output is The model parameter vector is θ, and the goal is to minimize the error function Adjust the parameter values of the inertia matrix M(q), the Coriolis and centrifugal force matrix The gravity vector G(q) through iterative calculation. For the inertia matrix M(q), its element M ij (q) is continuously optimized through the least squares method in the iteration. t represents time, and N represents the number of measured data.

[0012] Further, in the aforementioned step S1, the timestamp technology and signal transmission delay measurement device are used to measure the time-varying time delay τ(t) from the issuance to the execution of the control signal, and the time-varying time delay model is established as τ(t) = a + bsin(ct), where a, b, and c are constants determined by data fitting. Finally, the dynamic model of the industrial robotic arm including the time-varying time delay term is as follows:

[0013] u represents the control input signal applied to the industrial robotic arm.

[0014] Further, the aforementioned step S2 includes the following sub-steps:

[0015] S2.1. Construct the input layer: Since the number of neurons in the input layer depends on the dimension of the input information, the input vector The dimension of the joint position vector q is n1, and the joint velocity vector has a dimension of n2. The number of neurons in the input layer is n1 + n2 + 1;

[0016] S2.1. Construct the hidden layer: The number of neurons in the hidden layer is determined by the empirical formula where N i is the number of neurons in the input layer, N o is the number of neurons in the output layer, and a is a constant;

[0017] The hidden layer uses time-varying time-delay Sigmoid neurons, and its output is where τ ij (t) is set as a linear time-varying function τ ij (t) = a ij t + b ij , a ij , b ij are determined through experiments or theoretical analysis.

[0018] The connection weight w ij is randomly initialized in the interval [-0.5, 0.5], that is, w ij = rand(-0.5, 0.5); the bias b i is a preset value.

[0019] S2.2. Construct the output layer: The number of neurons in the output layer is the same as the dimension of the uncertainty of the dynamic model.

[0020] Furthermore, the aforementioned step S3 includes the following sub-steps:

[0021] S3.1. Determine the desired joint position trajectory q d and velocity trajectory through the path planning algorithm to obtain the desired motion trajectory of the end effector of the robotic arm, and then obtain the desired trajectory of each joint through inverse kinematics. The desired position trajectory q d (t) = a0 + a1t + a2t 2 + a3t 3 is represented by a cubic spline curve. The coefficients a0, a1, a2, and a3 are determined through boundary conditions; S3.2. Calculate the position tracking error e(t) = q d - q(t) and the velocity tracking error

[0022] S3.3. Use the pole placement method to determine the positive definite proportional and derivative feedback gain matrices K p and K d, let the desired closed-loop poles be λ1, λ2, … λ 2n ,, solve the characteristic equation det(sI - A + BK p - CK d ) = 0 to determine K p and K d , where n is the number of joints, and A, B, and C are the system state-space model matrices;

[0023] S3.4. Substitute the various parameters into the control law formula,

[0024] where is the estimated value of the uncertain term of the dynamic model by the neural network.

[0025] Furthermore, the aforementioned step S4 includes the following steps:

[0026] S4.1. Construct a Lyapunov function where P is a positive definite matrix that satisfies the Lyapunov equation A T P + PA = -Q, where A is the system matrix and Q is a positive definite matrix; is the neural network parameter estimation error, and θ * is the ideal parameter value;

[0027] S4.2. Take the time derivative of V(t) According to the dynamic model and control law of the industrial robot arm, simplify it and analyze its sign to ensure the exponential stability of the system, that is where α is a positive number;

[0028] S4.3. According to the Lyapunov stability theory, derive the neural network parameter update algorithm For the connection weight w ij , the update formula is where Γ ij is the learning rate matrix, and the element corresponding to w ij is

[0029] On the other hand, the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, it implements the steps of any one of the methods of the present invention.

[0030] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of any one of the methods of the present invention.

[0031] Compared with the prior art, the beneficial technical effects of the present invention adopting the above technical solutions are as follows:

[0032] 1. The designed time-varying time-delay neural network can effectively approximate the uncertainties and time-varying time-delay terms in the dynamic model, improving the system's adaptability to complex environments.

[0033] 2. Based on the design of an exponentially stable control law, the industrial robotic arm can still achieve fast and stable tracking control under the influence of time-varying time-delay and external disturbances, significantly improving the control accuracy and stability.

[0034] 3. The neural network parameter update algorithm based on Lyapunov stability theory is adopted to ensure the convergence of neural network parameters and the stability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic diagram of the system flow of the present invention.

[0036] Figure 2 It is a graph showing the variation of joint position, velocity, acceleration and time-varying time-delay with time.

[0037] Figure 3 It is a graph of the time-varying time-delay modeling result.

[0038] Figure 4 It is a graph of the identification result of the dynamic model parameters.

[0039] Figure 5 It is a graph of the desired trajectory and tracking error. DETAILED DESCRIPTION OF THE INVENTION

[0040] To better understand the technical content of the present invention, specific embodiments are given below in conjunction with the accompanying drawings and described as follows.

[0041] In the present invention, various aspects of the present invention are described with reference to the accompanying drawings, in which many illustrative embodiments are shown. The embodiments of the present invention are not limited to those described in the drawings. It should be understood that the present invention can be implemented by any one of the various concepts and embodiments introduced above, as well as the concepts and embodiments described in detail below, because the concepts and embodiments disclosed in the present invention are not limited to any embodiment. In addition, some aspects disclosed in the present invention can be used alone, or in any appropriate combination with other aspects disclosed in the present invention.

[0042] Referring to Figure 1 , the present invention provides a control method for an industrial robotic arm based on the exponential stability of a time-varying time-delay neural network, which is characterized by including the following steps:

[0043] S1. Collect the data of the positions, velocities, and accelerations of the joints of the industrial robotic arm, measure the time-varying time-delay of the control signal in combination with the timestamp technology, and use the system identification algorithm to construct a dynamic model of the industrial robotic arm including the time-varying time-delay term.

[0044] S2. Construct a neural network for controlling an industrial robotic arm with time-varying time delay, including an input layer, a hidden layer, and an output layer. The input layer receives the output of the dynamic model of the industrial robotic arm with time-varying time delay terms to obtain the state of the robotic arm and the time delay information. The hidden layer uses neurons with time-varying time delay characteristics, and the output layer outputs an estimated value of the uncertainty of the dynamic model. S3. Train the neural network with time-varying time delay. Based on the Lyapunov stability theory and combined with the desired trajectory generation algorithm, calculate the position and velocity tracking errors, determine the control law parameters by methods such as pole placement, and design a control law based on exponential stability.

[0045] S4. Design a neural network parameter update algorithm using the Lyapunov function to adjust the connection weights and biases of the neural network, so that the output of the neural network can accurately track the actual uncertainty, and finally obtain a control model for the industrial robotic arm with time-varying time delay.

[0046] S5. Use the control model of the industrial robotic arm with time-varying time delay to achieve tracking control of the industrial robotic arm.

[0047] Further, as a preferred embodiment of the present invention, in step S1, by deploying sensors at each joint of the industrial robotic arm, an optical encoder measures the joint position q, a tachogenerator measures the joint velocity an accelerometer measures the joint acceleration At the same time, let the robotic arm operate under different working conditions, including no-load, full-load, different speed, and angle movement combinations, and collect data in real time.

[0048] Further, as a preferred embodiment of the present invention, in step S1, the least squares method is used for system identification. The measured data is y(t), the model output is the model parameter vector is θ, and the goal is to minimize the error function Adjust the parameter values of the inertia matrix M(q), the Coriolis force and centrifugal force matrix the gravity vector G(q) through iterative calculation. For the inertia matrix M(q), its element M ij (q) is continuously optimized by the least squares method in the iteration. t represents time, and N represents the number of measured data.

[0049] Reference Figure 3 , further, as a preferred embodiment of the present invention, in step S1, a timestamp technology and a signal transmission delay measurement device are used to measure the time-varying time delay τ(t) from the issuance to the execution of the control signal, and establish a time-varying time delay model as τ(t) = a + bsin(ct), where a, b, and c are constants determined by data fitting. Finally, the dynamic model of the industrial robotic arm including the time-varying time delay term is as follows:

[0050] u represents the control input signal applied to the industrial robotic arm.

[0051] Furthermore, as a preferred embodiment of the present invention, step S2 includes the following sub-steps:

[0052] S2.1. Construct the input layer: Based on the fact that the number of neurons in the input layer depends on the dimension of the input information, the input vector The dimension of the joint position vector q is n1, and the dimension of the joint velocity vector is n2. The number of neurons in the input layer is n1 + n2 + 1;

[0053] S2.2. Construct the hidden layer: The number of neurons in the hidden layer is determined by the empirical formula where N i is the number of neurons in the input layer, N o is the number of neurons in the output layer, and a is a constant, generally taken as 5 - 10;

[0054] The hidden layer adopts a time-varying time-delay Sigmoid neuron, and its output is where τ ij (t) is set as a linear time-varying function τ ij (t) = a ij t + b ij , a ij , b ij are determined through experiments or theoretical analysis.

[0055] The connection weight w ij is randomly initialized in the interval [-0.5, 0.5], that is, w ij = rand(-0.5, 0.5); the bias b i is a preset value of 0.01.

[0056] S2.3. Construct the output layer: The number of neurons in the output layer is the same as the dimension of the uncertainty of the dynamic model.

[0057] Furthermore, as a preferred embodiment of the present invention, step S3 includes the following sub-steps:

[0058] S3.1. Determine the desired joint position trajectory q d and the velocity trajectory according to the work task. The desired motion trajectory of the end effector of the robotic arm is obtained through the path planning algorithm, and then the desired trajectories of each joint are obtained through the inverse kinematics solution. The desired position trajectory q d (t) = a0 + a1t + a2t 2 + a3t 3 is represented by a cubic spline curve, and the coefficients a0, a1, a2, a3 are determined through the boundary conditions; S3.2. Real-time calculate the position tracking error e(t) = q d - q(t) and the velocity tracking error

[0059] S3.3. Determine the positive definite proportional and derivative feedback gain matrices \(K\) and \(\hat{K}\) using the pole placement method p and \(\hat{K}\) d , assuming the desired closed-loop poles are \(\lambda_1, \lambda_2, \cdots, \lambda_n\) 2n , solve the characteristic equation \(\det(sI - A + BK - C\hat{K}) = 0\) to determine \(K\) and \(\hat{K}\), where \(n\) is the number of joints, and \(A\), \(B\), and \(C\) are the system state space model matrices; p - \(C\hat{K}\) d ) = 0 to determine \(K\) and \(\hat{K}\) p and \(\hat{K}\) d , where \(n\) is the number of joints, and \(A\), \(B\), and \(C\) are the system state space model matrices;

[0060] S3.4. Substitute the parameters into the control law formula

[0061] where is the estimated value of the uncertain term of the dynamic model by the neural network.

[0062] Furthermore, as a preferred embodiment of the present invention, step S4 includes the following steps:

[0063] S4.1. Construct the Lyapunov function where \(P\) is a positive definite matrix that satisfies the Lyapunov equation \(A^TP + PA=-Q\), where \(A\) is the system matrix and \(Q\) is a positive definite matrix; T \(\tilde{\theta}\) is the neural network parameter estimation error, and \(\theta^*\) is the ideal parameter value; \(\tilde{\theta}\) is the neural network parameter estimation error, and \(\theta^*\) is the ideal parameter value; * is the ideal parameter value;

[0064] S4.2. Take the time derivative of \(V(t)\) Simplify according to the dynamic model and control law of the industrial robot arm, and analyze its sign to ensure the exponential stability of the system, that is where \(\alpha\) is a positive number;

[0065] S4.3. Derive the neural network parameter update algorithm according to the Lyapunov stability theory For the connection weight \(w_{ij}\), the update formula is ij , the update formula is where \(\Gamma\) is the learning rate matrix, and \(\gamma_{ij}\) is the element of \(\Gamma\) corresponding to \(w_{ij}\). ij is the element of \(\Gamma\) corresponding to \(w_{ij}\). ij of \(\Gamma\) corresponding to \(w_{ij}\).

[0066] The following is a further detailed description of the present invention in combination with embodiments:

[0067] An automotive manufacturing plant uses a 6-joint industrial robot arm for component welding. The electromagnetic interference generated by the electrical equipment in the workshop causes time-varying time delay of the control signal, and the load varies between 1 - 5 kg when welding different components, with high requirements for control accuracy and stability.

[0068] As shown Figure 2 in the figure, a 6-axis robotic arm with a load of 6 kg and a repeat positioning accuracy of ±0.05 mm is selected. Absolute encoders are installed at the joints to measure the position (resolution ±0.001°), motor-integrated speed sensors are installed to measure the speed (accuracy ±0.1 r / min), and acceleration sensors are additionally installed to measure the acceleration (measurement range ±10 g, accuracy ±0.01 g). A timestamp device is installed on the line to measure the time delay.

[0069] A large amount of data is collected during the 8-hour operation of the robotic arm. The time delay shows a non-linear change between 0.001 s and 0.01 s. Use lsqcurvefit to fit τ(t) = a0 + a1t + a2t 2 , and by adjusting the initial parameters and optimization options multiple times, we obtain a0 = 0.003 s, a1 = 0.0002 s / s, and a2 = -0.000002 s / s 2 . Use RLS to identify the dynamic model parameters. Normalize the input data and iterate 500 times. For example, the estimated value of M 11 (q) under a specific load is 1.2 kg·m 2 . Figure 4 The results of identifying the dynamic model parameters of the industrial robotic arm using RLS are shown. The abscissa is the number of iterations, and the ordinate is the parameter estimated value. Multiple subplots correspond to parameters such as the inertia matrix. The parameters converge with iteration. For example, M 11 (q) stabilizes at 1.2 kg·m 2 , providing accurate parameters for the control algorithm and ensuring the motion control accuracy of the robotic arm.

[0070] Construct a neural network with an input layer N in = 13, three hidden layers with N h1 = 15, N h2 = 12, and N h3 = 10, and an output layer N out = 8. The connection weights are randomly initialized in [-0.5, 0.5], and the biases are initialized to 0.01. Calculate the input and output of each layer according to the formula. For example, the second passes through the Sigmoid function to obtain the output.

[0071] Plan the trajectory according to the welding process. For example, joint 1 rotates from the initial position to the target position within 1 s, and calculate the position and speed tracking errors in real time. For example, at t = 0.5 s, the position error of joint 1 Verify the controllability of the system, distribute the poles reasonably, such as poles = [-10, -15, …, -65], and calculate the feedback matrix K using the Ackermann formula. Calculate the control law and transmit it to the servo driver. Figure 5The expected trajectory of the robotic arm control and the tracking error graph are shown. The upper sub-graph is the expected joint trajectory. Taking joint 1 as an example, according to the welding process plan, the abscissa is time and the ordinate is the expected position. The lower sub-graph is the position tracking error. For example, there is an error in joint 1 at t = 0.5s. After 1000 actual welds, the average position tracking error of each joint is small, indicating that the control algorithm can enable the robotic arm to better track the expected trajectory and ensure the welding accuracy.

[0072] After 1000 welds, the average position tracking error of each joint is less than ±0.1mm. For example, the root mean square value of the error in joint 3 is 0.08mm. Analyzing the Lyapunov function verifies exponential stability, and the system is stable when the load changes from 1 to 5kg.

[0073] On the other hand, the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the steps of any one of the methods in this embodiment are implemented.

[0074] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of any one of the methods in this embodiment are implemented.

[0075] Although the present invention has been described above with reference to preferred embodiments, it is not intended to limit the present invention. Those with ordinary knowledge in the technical field to which the present invention pertains can make various modifications and refinements without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention shall be determined by the scope defined in the claims.

Claims

1. An industrial robot arm control method based on exponential stability of time-varying delay neural networks, characterized in that, Including the following steps: S1. Collect the position, velocity, and acceleration data of each joint of the industrial robot arm, measure the time-varying time delay of the control signal by combining the timestamp technology, and use the system identification algorithm to construct a dynamic model of the industrial robot arm including the time-varying time delay term. S2. Construct a control neural network for the industrial robot arm with time-varying time delay, including an input layer, a hidden layer, and an output layer; the input layer receives the state of the robot arm and the time delay information output by the dynamic model of the industrial robot arm with the time-varying time delay term, the hidden layer uses neurons with time-varying time delay characteristics, and the output layer outputs an estimated value of the uncertainty of the dynamic model. S3. Train the neural network with time-varying time delay. Based on the Lyapunov stability theory, combined with the desired trajectory generation algorithm, calculate the position and velocity tracking errors, determine the control law parameters using the pole placement method, and design a control law based on exponential stability. S4. Use the Lyapunov function to design a neural network parameter update algorithm to adjust the connection weights and biases of the neural network so that the output of the neural network can accurately track the actual uncertainty, and finally obtain a control model for the industrial robot arm with time-varying time delay. S5. Use the control model of the industrial robot arm with time-varying time delay to implement tracking control of the industrial robot arm.

2. The industrial robot arm control method based on exponential stability of time-varying time-delay neural network according to claim 1, characterized in that, In step S1, the photoelectric encoder measures the joint position q, and the tachogenerator measures the joint speed The accelerometer measures the joint acceleration At the same time, the robotic arm is operated under different working conditions, including no-load, full-load, different speeds, and angular motion combinations, and data is collected in real time.

3. The industrial robot arm control method based on exponential stability of time-varying time-delay neural network according to claim 1, characterized in that, In step S1, system identification is performed using the least squares method. The measured data is y(t), and the model output is The model parameter vector is θ, and the goal is to minimize the error function The parameter values of the inertia matrix M(q), the Coriolis force and centrifugal force matrix G(q) of the gravity vector are adjusted through iterative calculations. For the inertia matrix M(q), its element M ij (q) is continuously optimized in the iteration by the least squares method, where t represents time and N represents the number of measurement data.

4. The industrial robot arm control method based on exponential stability of time-varying time-delay neural network according to claim 1, wherein In step S1, a time-stamp technology and a signal transmission delay measurement device are used to measure the time-varying time delay τ(t) of the control signal from being sent to being executed, and a time-varying time delay model is established as τ(t) = a + bsin(ct), where a, b, and c are constants determined by data fitting. Finally, the dynamic model of the industrial robot arm including the time-varying time delay term is obtained as follows: u represents a control input signal applied to an industrial robotic arm.

5. The industrial robot arm control method based on exponential stability of time-varying time-delay neural network according to claim 1, characterized in that, Step S2 includes the following sub-steps: S2.

1. Construct the input layer: Based on the fact that the number of neurons in the input layer depends on the dimension of the input information, the input vector The dimension of the joint position vector q is n1, the dimension of the joint velocity vector q is n2, and the number of neurons in the input layer is n1 + n2 + 1; S2.

1. Construct the hidden layer: The number of neurons in the hidden layer is determined by the empirical formula where N i is the number of neurons in the input layer, N o is the number of neurons in the output layer, and a is a constant; The hidden layer adopts time-varying time-delay Sigmoid neurons, and its output is where τ ij (t) is set as a linear time-varying function τ ij (t) = a ij t + b ij , a ij , b ij are determined through experiments or theoretical analysis. Connection weight w ij Adopt random initialization in the interval [-0.5, 0.5], that is, w ij = rand(-0.5, 0.5); Bias b i Is a preset value. S2.

2. Construct the output layer: The number of neurons in the output layer is the same as the dimension of the uncertainty of the dynamic model.

6. The industrial robot arm control method based on exponential stability of time-varying time-delay neural network according to claim 1, characterized in that, Step S3 includes the following sub-steps: S3.

1. Determine the expected joint position trajectory q d and the velocity trajectory q d . Obtain the expected motion trajectory of the end effector of the robotic arm through the path planning algorithm, and then obtain the expected trajectory of each joint through inverse kinematics. Represent the expected position trajectory q d (t) = a0 + a1t + a2t 2 + a3t 3 using a cubic spline curve, and determine the coefficients a0, a1, a2, and a3 through the boundary conditions; S3.

2. Calculate the real-time position tracking error e(t) = q d - q(t) and the velocity tracking error S3.

3. Determine the positive definite proportional and derivative feedback gain matrices \(K\) and \(\hat{K}\) using the pole placement method p and \(\hat{K}\) d , assume the desired closed-loop poles are \(\lambda_1, \lambda_2, \cdots, \lambda_n\) 2n , solve the characteristic equation \(\det(sI - A + BK-\hat{C}\hat{K}) = 0\) to determine \(K\) p and \(\hat{K}\) d , where \(n\) is the number of joints, and \(A\), \(B\), \(C\) are the system state-space model matrices p and \(\hat{K}\) d ​ S3.

4. Substitute each parameter into the control rate formula. where is the estimated value of the uncertain term of the dynamic model by the neural network.

7. The industrial robot arm control method based on exponential stability of time-varying time-delay neural network according to claim 1, wherein Step S4 includes the following steps: S4.

1. Construct the Lyapunov function where P is a positive definite matrix satisfying the Lyapunov equation A T P + PA = -Q, where A is the system matrix and Q is a positive definite matrix; is the neural network parameter estimation error, and θ * is the ideal parameter value; S4.

2. Take the time derivative of V(t). According to the simplification of the industrial robot arm dynamics model and the control law, analyze the sign to ensure the exponential stability of the system, that is where α is a positive number; S4.

3. Derive the neural network parameter update algorithm according to Lyapunov stability theory For the connection weight w ij , the update formula is where Γ ij is the element of the learning rate matrix Γ corresponding to w ij .

8. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method according to any one of claims 1 to 7.

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