Anti-saturation tracking control method for industrial manipulator based on extended state observer

Abstract

The present invention discloses an anti-saturation tracking control method for an industrial manipulator based on an extended state observer, belonging to the field of automated trajectory control for industrial manipulators. The method comprises the following steps: based on the dynamic model of the industrial manipulator, a hyperbolic tangent function is used to model the output saturation characteristics of the actuator to obtain a dynamic model that has undergone anti-saturation processing; based on the dynamic model that has undergone anti-saturation processing, an extended state observer is designed with semi-globally consistent final stability characteristics, and an unknown function estimate is output based on the extended state observer; based on the unknown function estimate, a recursive anti-saturation control signal is designed using a dynamic surface control architecture to achieve precise tracking control of the industrial manipulator. The design of the extended state observer in the present invention not only enables real-time estimation of unknown dynamics in the controlled system, but also eliminates the computational overhead associated with training neural network weights, resulting in faster execution and deployment efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of automated operation trajectory control of industrial robots, and in particular relates to an anti-saturation tracking control method for industrial robots based on an extended state observer. Background Art

[0002] The field of automated trajectory control for industrial manipulators has long faced the challenge of degraded control accuracy due to the coupling of actuator output saturation and unmodeled dynamics (also known as unknown functions). With increasing demands for dynamic tracking performance in manipulators in scenarios such as high-precision manufacturing and flexible assembly, the limitations of traditional anti-saturation control strategies and disturbance compensation techniques have become increasingly prominent. For suppressing control output saturation, existing solutions often employ fixed limits or static compensation mechanisms, which struggle to adapt to the asymmetric dynamic constraints of the joint torques in multi-degree-of-freedom industrial manipulators and can easily lead to overshoot oscillations or response lags. While online approximation methods based on neural networks can improve adaptability when the controlled system encounters unmodeled dynamics or external disturbances, the weights of the hidden layer nodes must be continuously iteratively updated, resulting in an exponential increase in computational complexity and making it difficult to meet the real-time requirements of industrial sites for millisecond-level control cycle responses. To address these issues, the present invention proposes an anti-saturation tracking control method for industrial manipulators based on an extended state observer. Summary of the Invention

[0003] In order to solve the above technical problems, the present invention proposes an anti-saturation tracking control method for an industrial robot based on an extended state observer to solve the problems existing in the above prior art.

[0004] To achieve the above objectives, the present invention provides an anti-saturation tracking control method for an industrial manipulator based on an extended state observer, comprising:

[0005] Based on the dynamic model of the industrial robot, the hyperbolic tangent function is used to model the output saturation characteristics of the actuator, and a dynamic model with anti-saturation treatment is obtained.

[0006] Based on the anti-saturation processed dynamic model, an extended state observer with semi-global consistent final stability characteristics is designed, and an estimated value of the unknown function is output based on the extended state observer; wherein the extended state observer includes an extended state observer corresponding to the first unknown function and an extended state observer corresponding to the second unknown function;

[0007] Based on the estimated value of the unknown function, a recursive anti-saturation control signal is designed using a dynamic surface control architecture to achieve precise tracking control of the industrial robot.

[0008] Optionally, a process of modeling the output saturation characteristic of the actuator using a hyperbolic tangent function to obtain a dynamic model that has undergone anti-saturation processing includes:

[0009] Based on the dynamic model of the industrial robot, the maximum and minimum output torques of the actuator are obtained;

[0010] obtaining an output torque range based on the maximum output torque and the minimum output torque;

[0011] A saturation characteristic model is performed on the output torque range using a hyperbolic tangent function to obtain a continuously differentiable anti-saturation compensation function;

[0012] The original kinetic model is transformed based on the anti-saturation compensation function to obtain a kinetic model that has undergone anti-saturation processing.

[0013] Optionally, the expression of the kinetic model after anti-saturation treatment is:

[0014] ;

[0015] Where, represents the mass of the connecting rod, Indicates the connecting rod length, represents the joint stiffness, represents the motor's moment of inertia, represents the angular displacement of the connecting rod, is the angular velocity of the connecting rod, represents the angular displacement of the drive motor, represents the angular velocity of the drive motor, represents the first unknown function, represents the second unknown function, is the output signal of the industrial robot, It represents the approximation error after the output saturation model is approximated by the bitangent tangent function. To obtain the final anti-saturation command torque control signal, is represented as a saturation-limited parameter, for The derivative of for The derivative of for The derivative of for The derivative of .

[0016] Optionally, the process of designing an extended state observer with semi-global consistent final stability characteristics based on the anti-saturation processed dynamic model includes:

[0017] extracting unknown functions of the system based on the anti-saturation treated kinetic model;

[0018] For the observer being designed, define the observation error;

[0019] Constructing a Lyapunov function inequality constraint relationship related to the observation error;

[0020] Based on the Lyapunov function inequality constraint relationship, an extended state observer based on an unknown function and having a semi-global consistent final stability characteristic is constructed.

[0021] Optionally, the expression of the extended state observer designed based on the first unknown function is:

[0022] ;

[0023] Where, For The designed observer model, for The estimated value of is a design parameter greater than zero, for The estimated value of for The derivative of for The derivative of .

[0024] Optionally, the expression of the extended state observer designed based on the second unknown function is:

[0025] ;

[0026] Where, For The designed observer model, is the actual output torque, t is the time, F is the subscript of the actual output torque, for The estimated value of for The estimated value of for The derivative of for The derivative of .

[0027] Optionally, the process of designing a recursive anti-saturation control signal using a dynamic surface control architecture includes:

[0028] Based on the deviation between the system output and the reference trajectory, the initial tracking error is obtained;

[0029] Based on the initial tracking error, a cascade filter is used to perform derivative approximation processing on virtual control signals at each level to obtain a filtered reference signal;

[0030] Based on the filtered reference signal and the unknown function estimate, the compensation control amount of each subsystem is obtained;

[0031] Based on the compensation control variable, a final anti-saturation command torque control signal is obtained.

[0032] Optionally, a process of using a cascade filter to process virtual control signals at various levels and compensate subsystems at various levels to obtain a final anti-saturation command torque control signal includes:

[0033] designing a first virtual control signal based on an initial tracking error of the first-order subsystem, and processing the first virtual control signal through a first filter to obtain a derivative of a first reference signal;

[0034] Based on the tracking error of the second-order subsystem and the derivative of the first reference signal, combined with the estimated value of the extended state observer corresponding to the first unknown function, a second virtual control signal is designed, and the second virtual control signal is processed through a second filter to obtain a derivative of the second reference signal;

[0035] designing a third virtual control signal based on the tracking error of the third-order subsystem and the derivative of the second reference signal, and processing the third virtual control signal through a third filter to obtain a derivative of the third reference signal;

[0036] Based on the tracking error of the terminal subsystem and the derivative of the third reference signal, combined with the estimated value of the extended state observer of the second unknown function, a final anti-windup command torque control signal is designed.

[0037] Optionally, the design of the first virtual control signal includes:

[0038] Based on the tracking error of the first-order subsystem, the basic control component is designed using the proportional control term;

[0039] The square term of tracking error is introduced as a stable compensation component;

[0040] The base control component and the stabilization compensation component are combined to form a first virtual control signal.

[0041] Optionally, the final anti-saturation command torque control signal is obtained as:

[0042] ;

[0043] Where, represents the fourth positive design parameter, is the tracking error corresponding to the fourth-order subsystem, The final anti-saturation command torque control signal is obtained, I is the command torque subscript, is the derivative of the third reference signal.

[0044] Compared with the prior art, the present invention has the following advantages and technical effects:

[0045] The present invention proposes a dynamic surface control architecture that combines the anti-saturation mechanism of the hyperbolic tangent function with the extended state observer model. The saturation problem of the actuator is effectively suppressed by constructing an anti-saturation compensation mechanism based on the hyperbolic tangent function. Its continuous differentiable performance can effectively avoid the chattering phenomenon of the control signal at the saturation boundary.

[0046] Compared with the processing scheme of using neural networks to estimate unknown functions, the present invention uses an extended state observer to estimate unknown functions in the dynamic system of an industrial robot in real time, which can significantly reduce the parameter training cost and computational complexity of traditional neural network controllers, thereby meeting the technical index requirements of high dynamic response of industrial robots. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0048] Figure 1 This is a flow chart of an anti-saturation tracking control method for an industrial manipulator based on an extended state observer according to an embodiment of the present invention;

[0049] Figure 2 A comparison diagram of tracking characteristics of the control algorithm according to an embodiment of the present invention;

[0050] Figure 3 This is a graph showing the tracking error variation of the tracking control algorithm according to an embodiment of the present invention;

[0051] Figure 4 This is a diagram showing changes in actual output torque and command torque of the tracking control algorithm according to an embodiment of the present invention. DETAILED DESCRIPTION

[0052] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0053] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0054] like Figure 1 As shown, this embodiment provides an anti-saturation tracking control method for an industrial robot based on an extended state observer. This method is a composite dynamic surface control architecture that integrates a hyperbolic tangent function dynamic anti-saturation model with a nonlinear extended state observer. By constructing a hyperbolic tangent function compensator with asymmetric saturation characteristics, the limitations of the traditional symmetric saturation model are overcome to meet the anti-saturation output control requirements of the joint torque of the industrial robot arm. The continuous differentiability of the hyperbolic tangent function effectively avoids the chattering phenomenon of the control signal at the saturation boundary. The innovatively designed nonlinear extended state observer can estimate the unknown function in real time, thereby significantly reducing the parameter training cost of the traditional neural network controller and improving the response speed.

[0055] The present invention first constructs an anti-saturation model based on the bitangent tangent function to address the output saturation problem of the actuators of a class of industrial robots. Then, an extended state observer (ESO) is designed and used to estimate the unknown functions in the industrial robot control system. Finally, based on the dynamic surface framework, virtual control signals are designed for the low-order subdynamic system and actual output anti-saturation command torque control signals are designed for the terminal subsystem. Specifically, the present invention includes the following steps: based on the dynamic model of the industrial robot, the output saturation characteristics of the actuator are modeled using the hyperbolic tangent function to obtain an anti-saturation dynamic model; based on the anti-saturation dynamic model, an extended state observer is designed, and the estimated value of the unknown function is output based on the extended state observer; the extended state observer includes an extended state observer corresponding to the first unknown function and an extended state observer corresponding to the second unknown function; based on the estimated value of the unknown function, a recursive anti-saturation control signal is designed using the dynamic surface control framework to achieve precise tracking control of the industrial robot.

[0056] Step 1: Utilize an anti-saturation mechanism based on the bitangent tangent function to address the anti-saturation problem of the industrial robot and obtain a dynamic model for controller design. This method, based on the bitangent tangent function, addresses the anti-saturation problem of the industrial robot and obtains a dynamic model for controller design. The method first constructs a fourth-order dynamic equation for asymmetric output saturation related to the motor angle, the connecting rod output angle, and its angular velocity. Then, a hyperbolic tangent function is used to smooth the asymmetric output saturation problem, thereby remodeling the actual output torque. Finally, this hyperbolic tangent saturation function model is substituted into the original dynamic model and relevant variables are replaced to construct a dynamic model for controller design.

[0057] Step 2: Construct an observer model with semiglobally consistent ultimate stability for the unknown functions in the industrial robot control system. The specific method is to first treat the unknown function in a subsystem as an extended state; then define an appropriate observer error variable; and finally, use Lyapunov's stability theorem as a guide to design the relevant data items in the extended state observer model. The unknown functions include the first unknown function and the second unknown function.

[0058] Step 3: Design a dynamic surface anti-output saturation control signal with recursive characteristics. The specific method is to first construct the tracking error of each subsystem using the reference trajectory signal or the filter output signal; then, design virtual control signals and corresponding filter models for the first three subsystems. The second-order subsystem also needs to introduce an observer signal to process the unknown function; finally, the command torque anti-saturation control signal is designed using the third filter and the real-time estimation signal of the second extended state observer.

[0059] An anti-saturation mechanism based on the bitangent tangent function is used to deal with the anti-saturation problem of an industrial robot and obtain a dynamic model for controller design. The specific method is as follows: based on the dynamic model of the industrial robot, the maximum and minimum output torques of the actuator are obtained; based on the maximum and minimum output torques, the output torque range is obtained; the saturation characteristics of the output torque range are modeled using the hyperbolic tangent function to obtain a continuously differentiable anti-saturation compensation function; based on the anti-saturation compensation function, the original dynamic model is transformed to obtain a dynamic model that has been processed for anti-saturation.

[0060] (1) The dynamic model of a common industrial robot can be described as follows:

[0061]

[0062] in, , , , , They represent the mass of the connecting rod, the length of the connecting rod, the stiffness of the joint, the moment of inertia of the motor and the damping characteristic parameters respectively; , , denote the angular displacement, angular velocity and angular acceleration of the connecting rod respectively; , , Represent the angular displacement, angular velocity and angular acceleration of the drive motor respectively; Indicates the actual output torque of the motor, where the motor rotor outputs positive torque when rotating counterclockwise and outputs negative torque when rotating clockwise. t is time, and F is the subscript of the actual output torque; g=9.8m / s 2 represents the gravitational acceleration constant.

[0063] Industrial robots use stepper motors or servo motors installed at their joints to drive corresponding connecting rods to perform gripping, spraying, or welding operations. However, due to power factor limitations, excessive command torque The actual output torque obtained when input into the motor drive control system is often There is a saturation phenomenon, and the relationship between the two can be modeled as follows:

[0064]

[0065] in, , Respectively represent the maximum and minimum output torques that the drive motor can output. Next, after using the hyperbolic tangent smooth differentiable function to deal with the torque output saturation problem described in Equation (2), its actual output torque can be re-expressed as follows:

[0066]

[0067] in, It represents the approximation error after the output saturation model is approximated by the double tangent function. is a bounded function, so the approximation error The absolute value of satisfies the following inequality relationship:

[0068]

[0069] in, Represents a real number greater than zero. When the conditions are met, the mean value theorem can be used to Expressed as follows:

[0070]

[0071] in, represents a positive real number. From formula (3), we can solve The first derivative of :

[0072]

[0073] The saturation limited parameter can be explained by formula (6) The value range belongs to In order to facilitate the analysis and design of control signals, the dynamic model shown in Equation (1) is usually converted into a standard differential equation form that can be solved by MATLAB and the relevant variables are replaced, that is, , , and Therefore, the dynamic model of the industrial robot for controller design can be expressed as follows:

[0074]

[0075] in, ; Can be regarded as the output signal of an industrial robot , that is, the angular displacement of a joint; However, factors such as the uncertainty of the load mass and mechanical friction often make it difficult to accurately express the first unknown function , the second unknown function , so they are better not to appear in the designed control signal. To this end, the present invention will use the extended state observer technology to estimate and model the above two unknown functions.

[0076] An observer model with semi-globally consistent and ultimately stable characteristics is constructed for the unknown functions existing in the control system of an industrial robot arm. The specific method is as follows: based on a dynamic model that has undergone anti-saturation processing, the unknown functions of the system are extracted; for the designed observer, the observation error is defined; a Lyapunov function inequality constraint relationship related to the observation error is constructed; and based on the Lyapunov function inequality constraint relationship, an extended state observer with semi-globally consistent and ultimately stable characteristics based on the unknown function is constructed.

[0077] (1) For the observer to be designed, define the following observation error: , observation error :

[0078]

[0079] in, and Represents state variables and the first unknown function (This is also considered an expansion state) The estimated value related to . According to the Lyapunov stability theorem, the Lyapunov function related to the observation error must satisfy the following inequality:

[0080]

[0081] in, and All represent a positive constant, Represents a variable or vector related to the observation error. Usually, it is necessary to find a Lyapunov function with positive definite characteristics for each observer model. , and it also has the following three properties:

[0082]

[0083] in, Represents the first positive real number.

[0084]

[0085] in, Represents the second positive real number.

[0086]

[0087] in, , They represent the third positive real number and the fourth positive real number respectively.

[0088] (2) According to the inequality constraint relationship related to the observation error function given by formula (9), after repeated adaptation and derivation attempts, the first unknown function can be obtained Designed observer model :

[0089]

[0090] in, Represents the first unknown function estimated value.

[0091] (3) The present invention mainly adopts the following derivation and adaptation design route to obtain the extended state observer design model described by formula (13), in which the key steps are given as follows.

[0092] 1. Order , then the observation error vector The derivative of the relevant Lyapunov function can be expressed as:

[0093]

[0094] 2. According to the designed extended state observer mathematical model (13) and the dynamic equation of the second-order subsystem The expression for , can be used to calculate the derivative of the observation error:

[0095]

[0096] in, It should be noted that different extended state observer mathematical models will significantly affect the expression of the derivative of the observation error, thereby further affecting its convergence characteristics. Therefore, it is necessary to reasonably design the relevant expressions in the extended state observer model based on the subsequent analysis and derivation framework, so as to facilitate the derivation of the derivative of the observation error to meet the stability standard form described by Equation (9). Substituting Equation (15) into Equation (14) yields the following result:

[0097]

[0098] 3. According to the relevant properties of Lyapunov function, equation (16) Simplify and organize. First, according to the first property (10) and the related properties of the absolute value inequality, formula (16) can be simplified into the following form:

[0099]

[0100] in, is a positive real number, which represents the first unknown function Then, according to the second property (11), formula (17) can be organized into:

[0101]

[0102] After transposing and square rooting the left half of the third property (12), we can get , so formula (18) can be transformed into:

[0103]

[0104] make and It can be found that formula (19) satisfies the Lyapunov stability criterion formula (9). So we can deduce the first unknown function The designed extended state observer model is semi-globally consistent and ultimately bounded and stable.

[0105] (4) Similarly, combined with the dynamic equation of the fourth-order subsystem The expression for the second unknown function Design the following extended state observer model :

[0106]

[0107] A dynamic surface anti-output saturation control signal with recursive characteristics is designed. The specific method is as follows: based on the deviation between the system output and the reference trajectory, the initial tracking error is obtained; based on the initial tracking error, a cascade filter is used to perform derivative approximation processing on the virtual control signals at each level to obtain a filtered reference signal; based on the filtered reference signal and the estimated value of the unknown function, the compensation control quantity of each subsystem is obtained; based on the compensation control quantity, the final anti-saturation command torque control signal is obtained.

[0108] Furthermore, a cascade filter is used to process virtual control signals at each level and compensate subsystems at each level to obtain a final anti-saturation command torque control signal, including: designing a first virtual control signal based on the initial tracking error of the first-order subsystem, and processing the first virtual control signal through the first filter to obtain the derivative of the first reference signal; designing a second virtual control signal based on the tracking error of the second-order subsystem and the derivative of the first reference signal, combined with an estimated value of an extended state observer corresponding to the first unknown function, and processing the second virtual control signal through the second filter to obtain the derivative of the second reference signal; designing a third virtual control signal based on the tracking error of the third-order subsystem and the derivative of the second reference signal, and processing the third virtual control signal through the third filter to obtain the derivative of the third reference signal; designing a final anti-saturation command torque control signal based on the tracking error of the terminal subsystem and the derivative of the third reference signal, combined with an estimated value of the extended state observer corresponding to the second unknown function.

[0109] (1) By observing the first-order subsystem, we can find that its corresponding state variable is the output signal that the user is concerned about. Whether it is spraying or welding, the user expects the robot to complete the relevant mechanical action along the given reference trajectory. Therefore, the output signal of the first-order subsystem can be and reference trajectory The difference between them is defined as the tracking error:

[0110]

[0111] The first virtual control signal The purpose is to make the tracking error As small as possible and able to converge quickly, so, Should be Furthermore, the present invention converts the first virtual control signal Designed as follows:

[0112]

[0113] in, represents the first positive design parameter. However, when designing the second virtual control signal In the process, it is necessary to use In order to avoid the derivative information of To perform complex derivative operations, a first-order filter, namely the first filter, can be introduced to approximately obtain its derivative information. The present invention designs the first filter as follows:

[0114]

[0115] in, represents the design parameters of the first filter, which can determine the convergence speed of the filter; and Respectively represent the signals output by the first filter, where is the first reference signal, The derivative of the first reference signal, which is used to approximate ; Similarly, Can be used instead of The purpose of designing the virtual control signal and filter into Equation (22) and Equation (23) is to derive the following equations related to the first-order subsystem tracking error and filtering error: Related Lyapunov function inequalities:

[0116]

[0117] in, Indicates the upper bound of the absolute value of the filtering error.

[0118] (2) According to the design idea of ​​the recursive controller framework, the second virtual control signal The role is to fast track , then the following tracking error can be defined:

[0119]

[0120] Since the second-order dynamic system contains some first unknown functions that cannot be accurately modeled , then, design It is necessary to introduce an extended state observer model to estimate the changing trends of these unknown functions in real time. Designed for

[0121]

[0122] in, represents the second positive design parameter. It can be found that Contains the derivative of the first reference signal ,and and There are also complex functional relationships. Derivative calculation involves the derivation of composite functions, and such a long derivation chain makes the controller design very cumbersome. Because, in order to avoid complex derivation operations and provide reference trajectory information for subsequent virtual control signals, a second filter needs to be introduced:

[0123]

[0124] in, represents the design parameters of the second filter, represents the signal output by the second filter, i.e., the second reference signal, represents the derivative of the second reference signal. Thus, the second-order subsystem tracking error and filtering error can be derived Related Lyapunov function inequalities:

[0125]

[0126] in, Indicates the upper bound of the absolute value of the filtering error.

[0127] (3) With the second reference signal To track the target, define the tracking error of the third-order subsystem:

[0128]

[0129] It should be noted that in designing the third virtual control signal to control the trend of the state trajectory of the third-order subsystem When considering the tracking error, we should not only introduce the tracking error but also consider the residual term of the second-order subsystem corresponding to the Lyapunov inequality in Equation (28): , it will seriously affect the stability of the system. Try to offset the process Therefore, the present invention will Designed for

[0130]

[0131] in, represents the third positive design parameter. Next, design the third filter:

[0132]

[0133] in, represents the design parameters of the third filter; represents the signal output by the third filter, i.e., the third reference signal, represents the derivative of the third reference signal, which provides the reference trajectory for the last-order subsystem. Based on the designed virtual control signal and filter, the Lyapunov function inequality corresponding to the third-order subsystem can be derived:

[0134]

[0135] in, represents the filtering error, Indicates the upper bound of the absolute value of the filtering error.

[0136] (4) Design a command torque control signal with anti-saturation characteristics for the fourth-order subsystem:

[0137]

[0138] in, represents the tracking error corresponding to the subsystem, represents the fourth positive design parameter. Since the fourth-order subsystem is the last-order subsystem, no additional filter design is required. Then, there is only the Lyapunov function related to the tracking error of this subsystem:

[0139]

[0140] Next, we construct the total Lyapunov function for the entire control system. , then its derivative can be expressed as follows:

[0141]

[0142] Substituting the Lyapunov function corresponding to each subsystem into equation (35) we can obtain the following conclusions:

[0143]

[0144] Since the designed extended state observer has semi-global uniform convergence characteristics, its observation error , observation error It will tend to an infinitesimal normal number in the neighborhood near the origin within a certain period of time. When appropriate filter parameters are selected, the following inequality must be guaranteed to hold:

[0145]

[0146] So there are positive real numbers and , The Lyapunov function inequality of the entire control system Satisfies Lyapunov's stability criterion formula (9). Therefore, the control system designed by the present invention is able to ensure stable convergence, and the data flow and interaction relationship between it are as follows: Figure 1 shown.

[0147] As a specific implementation of this embodiment, the following steps are included:

[0148] (1) Build a simulation environment, which includes constructing a dynamic model of the industrial robot and giving its inherent attribute parameters, and setting the reference trajectory that the industrial robot needs to track. And further calculator derivative information ;

[0149] (2) Based on the tracking error information, design the first virtual control signal corresponding to the first subsystem and its corresponding filter model, where the first reference signal It can be regarded as the reference trajectory of the second-order subsystem;

[0150] (3) Design the second virtual control signal corresponding to the second subsystem And its filter model, in addition, the corresponding extended state observer is designed for the first unknown function , where the second reference signal It can be regarded as the reference trajectory of the third-order subsystem;

[0151] (4) Design the third virtual control signal corresponding to the third subsystem and its filter model, where the third reference signal It can be regarded as the reference trajectory of the fourth-order subsystem;

[0152] (5) Design command torque control signal and its corresponding extended state observer ;

[0153] (6) Data analysis of controller simulation results.

[0154] Furthermore, the key attribute parameters of the actual industrial robot can be obtained from the technical parameter manual or through actual measurement. For example, the inherent parameters of a flexible two-degree-of-freedom industrial robot mainly include the following: connecting rod length: L=1m; joint stiffness: ; Connecting rod mass: m=0.25kg; Motor rotor inertia: ; Natural damping: 0.6; Friction coefficient: 0.01. After the above inherent parameters are determined, the dynamic model of the industrial robot for controller design can be expressed as follows:

[0155]

[0156] in:

[0157]

[0158] It should be noted that and It only appears in the simulation dynamics model of industrial robots, where it is used to simulate position dynamics or disturbances. and The deterministic expressions of cannot be used as components of the controller because they are unknown or difficult to model. In addition, the actual output torque of the drive motor installed in the industrial robot The range is A reference trajectory for testing the tracking accuracy of an industrial manipulator terminal is designed as The initial values ​​of each state variable and filter are set to , , , , .

[0159] Design the first virtual control signal:

[0160]

[0161] in, , the first positive design parameter is set to 15. In order to obtain The derivative information of needs to be input into the following first-order filter:

[0162]

[0163] in, is set to 0.002, Can represent The approximate value of It means The approximate derivative of .

[0164] Constructing tracking error for the second-order subsystem And its virtual control signal:

[0165]

[0166] Among them, the second positive design parameter ; Represents an unknown function The estimated value of is mainly estimated in real time by the following extended state observer:

[0167]

[0168] Among them, the convergence speed attenuation parameter is set to 0.001. Input to the second filter:

[0169]

[0170] Among them, the design parameters of the second filter are is set to 0.002.

[0171] Tracking error based on the third-order subsystem Design virtual control signals:

[0172]

[0173] Among them, the third positive design parameter Next, we design the third filter:

[0174]

[0175] The design parameters of the third filter are Set to 0.002.

[0176] 5. Design a command torque control signal with anti-saturation characteristics for the fourth-order subsystem:

[0177]

[0178] in, Represents the tracking error corresponding to the subsystem, the fourth positive design parameter , Set to 0.98. The following extended state observer model is used To perform real-time estimation:

[0179]

[0180] The anti-saturation control algorithm of the present invention was simulated and tested in a dynamic model of an industrial robot. The simulation test results are shown in Figure 2. Figure 2、 Figure 3 、 Figure 4 shown. Figure 2 Demonstrating the end-of-line output of an industrial robot (dashed line) tracking reference trajectory The simulation results (solid line) show that the control algorithm has strong real-time performance. When the controller receives the tracking instruction, it tracks the specified nonlinear reference trajectory after 0.5 seconds. Figure 3 The tracking error of the anti-windup control algorithm is further described in In 0.5 seconds, it has changed regularly between -0.008195 and 0.009982, with a total amplitude of 0.0182rad, as shown by the black solid line. The magnitude of the tracking error has been reduced to within the order of magnitude range. Figure 4 The black dotted line and solid line represent the actual output torque respectively. and command output torque The change with time t; It can be found that within the time range of 0.1 to 0.2 seconds, the drive motor cannot fully execute the large value command torque instruction under the strict limitation of output power, and can only always maintain it within the range of -2Nm, which causes the controller to saturate. However, the present invention has already made proper treatment of the controller saturation problem at the beginning of the design, so it can also obtain satisfactory tracking performance and small tracking error, such as Figure 2 and Figure 3 shown.

[0181] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. An anti-saturation tracking control method for an industrial robot based on an extended state observer, characterized in that: The following steps are involved: Based on the dynamic model of the industrial robot, the hyperbolic tangent function is used to model the output saturation characteristics of the actuator, and a dynamic model with anti-saturation treatment is obtained. The process of obtaining a dynamic model that has undergone anti-saturation processing includes: obtaining a maximum output torque and a minimum output torque of an actuator based on a dynamic model of an industrial manipulator; obtaining an output torque range based on the maximum output torque and the minimum output torque; using a hyperbolic tangent function to perform saturation characteristic modeling on the output torque range to obtain a continuously differentiable anti-saturation compensation function; and transforming the original dynamic model based on the anti-saturation compensation function to obtain a dynamic model that has undergone anti-saturation processing. The expression of the kinetic model after anti-saturation treatment is: ； Where, represents the mass of the connecting rod, Indicates the connecting rod length, represents the joint stiffness, represents the motor's moment of inertia, represents the angular displacement of the connecting rod, is the angular velocity of the connecting rod, represents the angular displacement of the drive motor, represents the angular velocity of the drive motor, represents the first unknown function, represents the second unknown function, is the output signal of the industrial robot, It represents the approximation error after the output saturation model is approximated by the bitangent tangent function. To obtain the final anti-saturation command torque control signal, is represented as a saturation-limited parameter, for The derivative of for The derivative of for The derivative of for The derivative of Based on the anti-saturation processed dynamic model, an extended state observer with semi-global consistent final stability characteristics is designed, and an estimated value of the unknown function is output based on the extended state observer; wherein the extended state observer includes an extended state observer corresponding to the first unknown function and an extended state observer corresponding to the second unknown function; Based on the estimated value of the unknown function, a recursive anti-saturation control signal is designed using a dynamic surface control architecture to achieve precise tracking control of the industrial robot.

2. The anti-saturation tracking control method for an industrial robot based on an extended state observer according to claim 1 is characterized in that: Based on the anti-saturation treated dynamic model, the process of designing an extended state observer with semi-globally consistent final stability characteristics includes: extracting unknown functions of the system based on the anti-saturation treated kinetic model; For the observer being designed, define the observation error; Constructing a Lyapunov function inequality constraint relationship related to the observation error; Based on the Lyapunov function inequality constraint relationship, an extended state observer based on an unknown function and having a semi-global consistent final stability characteristic is constructed.

3. The anti-saturation tracking control method for an industrial robot based on an extended state observer according to claim 2 is characterized in that: The expression of the extended state observer designed based on the first unknown function is: ； Where, For The designed observer model, for The estimated value of is a design parameter greater than zero, for The estimated value of for The derivative of for The derivative of .

4. The anti-saturation tracking control method for an industrial robot based on an extended state observer according to claim 2, characterized in that: The expression of the extended state observer designed based on the second unknown function is: ； Where, For The designed observer model, is the actual output torque, t is the time, F is the subscript of the actual output torque, for The estimated value of for The estimated value of for The derivative of for The derivative of .

5. The anti-saturation tracking control method for an industrial robot based on an extended state observer according to claim 4 is characterized in that: The process of designing a recursive anti-saturation control signal using a dynamic surface control architecture includes: Based on the deviation between the system output and the reference trajectory, the initial tracking error is obtained; Based on the initial tracking error, a cascade filter is used to perform derivative approximation processing on virtual control signals at each level to obtain a filtered reference signal; Based on the filtered reference signal and the unknown function estimate, the compensation control amount of each subsystem is obtained; Based on the compensation control variable, a final anti-saturation command torque control signal is obtained.

6. The anti-saturation tracking control method for an industrial robot based on an extended state observer according to claim 5, characterized in that: The process of using cascade filters to process virtual control signals at all levels and compensate subsystems at all levels to obtain the final anti-saturation command torque control signal includes: designing a first virtual control signal based on an initial tracking error of the first-order subsystem, and processing the first virtual control signal through a first filter to obtain a derivative of a first reference signal; Based on the tracking error of the second-order subsystem and the derivative of the first reference signal, combined with the estimated value of the extended state observer corresponding to the first unknown function, a second virtual control signal is designed, and the second virtual control signal is processed through a second filter to obtain a derivative of the second reference signal; designing a third virtual control signal based on the tracking error of the third-order subsystem and the derivative of the second reference signal, and processing the third virtual control signal through a third filter to obtain a derivative of the third reference signal; Based on the tracking error of the terminal subsystem and the derivative of the third reference signal, combined with the estimated value of the extended state observer of the second unknown function, a final anti-windup command torque control signal is designed.

7. The anti-saturation tracking control method for an industrial robot based on an extended state observer according to claim 6, characterized in that: The design of the first virtual control signal includes: Based on the tracking error of the first-order subsystem, the basic control component is designed using the proportional control term; The square term of tracking error is introduced as a stable compensation component; The base control component and the stabilization compensation component are combined to form a first virtual control signal.

8. The anti-saturation tracking control method for an industrial robot based on an extended state observer according to claim 5, characterized in that: The final anti-saturation command torque control signal obtained is: ； Where, represents the fourth positive design parameter, is the tracking error corresponding to the fourth-order subsystem, The final anti-saturation command torque control signal is obtained, I is the command torque subscript, is the derivative of the third reference signal.

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