Industrial manipulator anti-saturation tracking control method based on extended state observer

Abstract

The invention discloses an industrial manipulator anti-saturation tracking control method based on an extended state observer, and belongs to the field of industrial manipulator automatic moving trajectory control, and the method comprises the following steps: based on a dynamic model of an industrial manipulator, carrying out modeling processing on the output saturation characteristic of an execution mechanism by adopting a hyperbolic tangent function, and obtaining an output saturation characteristic of the execution mechanism; obtaining a kinetic model subjected to anti-saturation processing; designing an extended state observer with a semi-global consistent final stability characteristic on the basis of the dynamic model subjected to anti-saturation processing, and outputting an unknown function estimation value on the basis of the extended state observer; and based on an unknown function estimation value, a recursive anti-saturation control signal is designed by adopting a dynamic surface control architecture, and accurate tracking control of the industrial manipulator is realized. The design of the extended state observer not only can estimate the unknown dynamic state in the controlled system in real time, but also saves the calculation overhead caused by training the weight of the neural network, so that the execution and deployment efficiency is relatively high.

Description

Technical Field

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

[0002] In the field of industrial manipulator automatic operation trajectory control, there has long been a problem of degraded control accuracy under the combined action of actuator output saturation and unmodeled dynamics (also known as unknown functions) interference. With the increasing requirements for the dynamic tracking performance of manipulators in scenarios such as high-precision manufacturing and flexible assembly, the limitations of traditional anti-saturation control strategies and disturbance compensation technologies have become increasingly prominent: in terms of suppressing control output saturation, existing solutions mostly adopt fixed limit or static compensation mechanisms, which are difficult to adapt to the asymmetric characteristics of the dynamic torque constraints of multi-degree-of-freedom industrial manipulator joints and are prone to overshoot oscillation or response lag problems. Especially when the controlled system encounters unmodeled dynamics or external disturbances, although the online approximation method based on neural networks can improve adaptability, the weights of its hidden layer nodes need to be continuously iteratively updated, resulting in an exponential increase in computational complexity and making it difficult to meet the real-time requirements of millisecond-level response for the control cycle in industrial fields. To address the above problems, the present invention proposes an anti-saturation tracking control method for industrial manipulators based on an extended state observer. Summary of the Invention

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

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

[0005] Based on the dynamic model of the industrial manipulator, the output saturation characteristics of the actuator are modeled using the hyperbolic tangent function to obtain a dynamic model after anti-saturation processing;

[0006] Based on the dynamic model after anti-saturation processing, an extended state observer with semi-global uniformly ultimately bounded 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 framework to achieve precise tracking control of the industrial manipulator.

[0008] Optionally, the process of using the hyperbolic tangent function to model the output saturation characteristic of the actuator and obtaining the anti-saturation processed dynamic model includes:

[0009] Based on the dynamic model of the industrial manipulator, obtain the maximum output torque and the minimum output torque of the actuator;

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

[0011] Use the hyperbolic tangent function to model the saturation characteristic of the output torque range to obtain a continuously differentiable anti-saturation compensation function;

[0012] Based on the anti-saturation compensation function, perform transformation processing on the original dynamic model to obtain the anti-saturation processed dynamic model.

[0013] Optionally, the expression of the anti-saturation processed dynamic model is:[[ID=??]] [[ID=??]]

[0014] [[ID=??]] ;[[ID=??]] [[ID=??]]

[0015] In the formula,[[ID=??]] represents the link mass,[[ID=??]] represents the link length,[[ID=??]] represents the joint stiffness,[[ID=??]] represents the moment of inertia of the motor,[[ID=??]] represents the angular displacement of the link,[[ID=??]] represents the angular velocity of the link,[[ID=??]] represents the angular displacement of the drive motor,[[ID=??]] represents the angular velocity of the drive motor,[[ID=??]] represents the first unknown function,[[ID=??]] represents the second unknown function,[[ID=??]] is the output signal of the industrial manipulator,[[ID=??]] represents the approximation error generated after approximately modeling the output saturation model using the double tangent function,[[ID=??]] is the finally obtained anti-saturation command torque control signal,[[ID=??]] represents the saturation limit parameter,[[ID=??]] is[[ID=??]] the derivative of[[ID=??]] is[[ID=??]] the derivative of[[ID=??]] is[[ID=??]] the derivative of[[ID=??]] is[[ID=??]] the derivative of.

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

[0017] It should be noted that there seem to be some missing or incorrect tags in the provided text, which may affect the accuracy of the overall understanding and translation. The above translation is based on the best understanding of the existing content.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 cascaded filter is used to perform derivative approximation processing on virtual control signals at all levels to obtain a filtered reference signal;

[0030] Based on the filtered reference signal and the estimated value of the unknown function, compensation control quantities for subsystems at all levels are obtained;

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

[0032] Optionally, the process of using a cascaded filter to process virtual control signals at all levels and compensating subsystems at all levels to obtain a final anti-saturation commanded torque control signal includes:

[0033] Based on the initial tracking error of the first-order subsystem, a first virtual control signal is designed, and the derivative of the first reference signal is obtained by processing the first virtual control signal through a first filter;

[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 derivative of the second reference signal is obtained by processing the second virtual control signal through a second filter;

[0035] Based on the tracking error of the third-order subsystem and the derivative of the second reference signal, a third virtual control signal is designed, and the derivative of the third reference signal is obtained by processing the third virtual control signal through a third filter;

[0036] Based on the tracking error of the end 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-saturation commanded 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, a basic control component is designed using a proportional control term;

[0039] A squared term of the tracking error is introduced as a stability compensation component;

[0040] The basic control component and the stability compensation component are combined to form the first virtual control signal.

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

[0042] ;

[0043] where represents the fourth positive design parameter, is the tracking error corresponding to the fourth-order subsystem, is the obtained final anti-windup command torque control signal, where I is the subscript of the command torque, 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 a hyperbolic tangent function anti-windup mechanism with an extended state observer model. Among them, an anti-windup compensation mechanism based on the hyperbolic tangent function is constructed to effectively suppress the saturation problem of the actuator, and its continuously differentiable property can effectively avoid the chattering phenomenon of the control signal at the saturation boundary.

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

[0047] The drawings constituting a part of this application are used to provide a further understanding of this application. The schematic embodiments and descriptions thereof of this application are used to explain this application and do not constitute an improper limitation of this application. In the drawings:

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

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

[0050] Figure 3 is the change chart of the tracking error of the tracking control algorithm according to an embodiment of the present invention;

[0051] Figure 4 is the change chart of the actual output torque and command torque of the tracking control algorithm according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0052] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The following will refer to the drawings and combine the embodiments to detail this application.

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

[0054] As shown Figure 1 in the figure, in this embodiment, a saturation-resistant tracking control method for an industrial manipulator based on an extended state observer is provided. This method is a composite dynamic surface control architecture that integrates a hyperbolic tangent function dynamic anti-saturation model and a non-linear extended state observer. By constructing a hyperbolic tangent function compensator with asymmetric saturation characteristics, the limitations of the traditional symmetric saturation model are broken through, and the anti-saturation output control requirements of the industrial manipulator joint torque are met. The continuous differentiability of the hyperbolic tangent function effectively avoids the chattering phenomenon of the control signal at the saturation boundary; the innovatively designed non-linear 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 a double-tangent hyperbolic function for the output saturation problem of the actuator of a class of industrial manipulators; then, designs an extended state observer and uses it to estimate the unknown functions existing in the industrial manipulator control system; finally, based on the dynamic surface framework, virtual control signals are designed for the low-order sub-dynamic system and actual output anti-saturation command torque control signals are designed for the end subsystem. Specifically, it includes the following steps: Based on the dynamic model of the industrial manipulator, the hyperbolic tangent function is used to model the output saturation characteristics of the actuator to obtain a dynamic model after anti-saturation processing; based on the dynamic model after anti-saturation processing, an extended state observer is designed, and an estimated value of the unknown function is output based on the extended state observer; among them, 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 architecture to achieve precise tracking control of the industrial manipulator.

[0056] Step 1: Use an anti-saturation mechanism based on a double-tangent hyperbolic function to handle the anti-saturation problem of the industrial manipulator and obtain a dynamic model for controller design. An anti-saturation mechanism based on a double-tangent hyperbolic function is used to handle the anti-saturation problem of the industrial manipulator and obtain a dynamic model for controller design. The specific method is to first construct an asymmetric output saturation fourth-order dynamic equation related to the motor rotation angle, the link output rotation angle, and their angular velocities; then, use the hyperbolic tangent function to smooth the asymmetric output saturation problem to achieve the effect of reconstructing the actual output torque; finally, substitute this hyperbolic tangent saturation function model into the original dynamic model and perform relevant variable substitution, thereby constructing a dynamic model for controller design.

[0057] Step 2: Construct an observer model with semi-globally uniformly ultimately stable characteristics for the unknown functions existing in the industrial manipulator control system. The specific method is as follows: First, regard the unknown function in a certain subsystem as an extended state; then define appropriate observer error variables; finally, design the relevant data items in the extended state observer model guided by the Lyapunov stability theorem. 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 as follows: First, it is necessary to construct the tracking error of each subsystem by using the reference trajectory signal or the output signal of the filter; then, design virtual control signals and corresponding filter models for the first three-order subsystems respectively, and an observer signal also needs to be introduced in the second-order subsystem to handle the unknown function; finally, design the command torque anti-saturation control signal by using the real-time estimation signals of the third filter and the second extended state observer.

[0059] Use an anti-saturation mechanism based on the double tangent function to handle the anti-saturation problem of the industrial manipulator and obtain the dynamic model for controller design. The specific method is as follows: Based on the dynamic model of the industrial manipulator, obtain the maximum and minimum output torques of the actuator; obtain the output torque range based on the maximum and minimum output torques; use the hyperbolic tangent function to model the saturation characteristics of the output torque range to obtain a continuously differentiable anti-saturation compensation function; perform transformation processing on the original dynamic model based on the anti-saturation compensation function to obtain the dynamic model after anti-saturation processing.

[0060] (1) The dynamic model of a common industrial manipulator can be described in the following form:

[0061]

[0062] Where, , , , , represent the link mass, link length, joint stiffness, moment of inertia of the motor, and damping characteristic parameters respectively; , , represent the angular displacement, angular velocity, and angular acceleration of the link respectively; , , represent the angular displacement, angular velocity, and angular acceleration of the drive motor respectively; represents the actual output torque of the motor. When the motor rotor rotates counterclockwise, a positive torque is output, and when it rotates clockwise, a negative torque is output. t is the time, and F is the subscript of the actual output torque; g = 9.8m / s 2 represents the gravitational acceleration constant.

[0063] Industrial manipulators drive the corresponding connecting rods through stepping motors or servo motors installed at the joints to achieve grasping, spraying, or welding operations. However, due to power factor limitations, when an excessive command torque is input into the drive control system of the motor, the actual output torque obtained finally often exhibits a saturation phenomenon. The relationship between the two can be modeled in the following form:

[0064]

[0065] where , represent the maximum and minimum output torques that the drive motor can output respectively. Next, after processing the torque output saturation problem described by Equation (2) using the hyperbolic tangent smooth differentiable function, its actual output torque can be re-expressed in the following form:

[0066]

[0067] where represents the approximation error generated after approximately modeling the output saturation model using the double tangent function. Since the double tangent function is a bounded function, the absolute value of the approximation error satisfies the following inequality relationship:

[0068] \

[0069] where represents a real number greater than zero. When the condition holds, using the mean value theorem, can be expressed in the following form:

[0070]

[0071] where represents a certain positive real number. From Equation (3), the first derivative of with respect to can be solved:

[0072]

[0073] It can be shown from Equation (6) that the value range of the saturation-limited parameter belongs to . To facilitate the analysis and design of control signals, the kinetic model shown in Equation (1) is usually converted into a standard differential equation form that can be solved by MATLAB and relevant variable substitutions are made, that is, let , , and . Then the kinetic model of the industrial manipulator for controller design can be expressed in the following form:

[0074]

[0075] Among them, ; can be regarded as the output signal of the industrial manipulator , that is, the angular displacement of a certain 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 preferably not to appear in the designed control signal. For this reason, the present invention will use the extended state observer technology to estimate and model the above two unknown functions.

[0076] Construct an observer model with semi-globally uniformly ultimately stable characteristics for the unknown functions existing in the industrial manipulator control system. The specific method is as follows: Based on the kinetic model after anti-saturation processing, extract the unknown functions of the system; for the observer to be designed, define the observation error; construct the Lyapunov function inequality constraint relationship related to the observation error; based on the Lyapunov function inequality constraint relationship, construct an extended state observer with semi-globally uniformly ultimately stable characteristics based on the unknown functions.

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

[0078]

[0079] Among them, and respectively represent the estimated values related to the state variable and the first unknown function (which is also regarded as the extended state). According to the Lyapunov stability theorem, it is necessary to make the Lyapunov function related to the observation error satisfy the following inequality:

[0080]

[0081] Among them, and Both represent a certain positive constant. represents a variable or vector related to the observation error. Usually, a Lyapunov function with positive definite characteristics needs to be found for each observer model. , and it also has the following three properties:

[0082]

[0083] Among them, represents the first positive real number.

[0084]

[0085] Among them, represents the second positive real number.

[0086]

[0087] Among them, , 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 Equation (9), through repeated adaptation and derivation attempts, an observer model designed for the first unknown function can be obtained:

[0089]

[0090] Among them, represents the estimated value of the first unknown function .

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

[0092] 1. Let , then the derivative of the Lyapunov function related to the observation error vector can be expressed as:

[0093]

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

[0095]

[0096] Among them, , it should be noted that different mathematical models of the extended state observer will significantly affect the expression of the derivative of the observation error, thereby further affecting its convergence characteristics. Therefore, relevant expressions in the extended state observer model should be reasonably designed according to the subsequent analysis and derivation framework, so as to facilitate the derivation that the derivative of the observation error satisfies the stability standard form described by Equation (9). Substituting Equation (15) into Equation (14) can obtain the following results:

[0097]

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

[0099]

[0100] is a positive real number, which represents the upper bound value of the first unknown function . Then, according to the second property Equation (11), Equation (17) can be organized into: After transposing and taking the square root of the left half of the third property Equation (12), we can get

[0101]

[0102] , so Equation (18) can be transformed into: Let

[0103]

[0104] and and be set, and it can be found that Equation (19) satisfies the Lyapunov stability criterion Equation (9). Thus, it can be deduced that the extended state observer model designed for the first unknown function is semi-globally uniformly ultimately bounded stable.

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

[0106]

[0107] Design a dynamic surface anti-saturation control signal with recursive characteristics, and the specific method is as follows: Based on the deviation between the system output and the reference trajectory, obtain the initial tracking error; Based on the initial tracking error, use a cascaded filter to perform derivative approximation processing on each level of virtual control signal to obtain the filtered reference signal; Based on the filtered reference signal and the estimated value of the unknown function, obtain the compensation control amount of each subsystem; Based on the compensation control amount, obtain the final anti-saturation command torque control signal.

[0108] Furthermore, the process of using a cascaded filter to process each level of virtual control signal and compensate each subsystem to obtain the final anti-saturation command torque control signal includes: Based on the initial tracking error of the first-order subsystem, design the first virtual control signal, and process the first virtual control signal through the first filter to obtain the derivative of the 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, design the second virtual control signal, and process the second virtual control signal through the second filter to obtain the derivative of the second reference signal; Based on the tracking error of the third-order subsystem and the derivative of the second reference signal, design the third virtual control signal, and process the third virtual control signal through the third filter to obtain the derivative of the third reference signal; Based on the tracking error of the end subsystem and the derivative of the third reference signal, combined with the estimated value of the extended state observer corresponding to the second unknown function, design the final anti-saturation command torque control signal.

[0109] (1) Observing the first-order subsystem, it can be found that the corresponding state variable is the output signal that the user cares about. Whether it is spraying or welding operations, the user expects the manipulator to complete relevant mechanical actions along the given reference trajectory. Therefore, the difference between the output signal of the first-order subsystem and the reference trajectory can be defined as the tracking error:

[0110]

[0111] The role of the first virtual control signal is to make the tracking error as small as possible and converge quickly. Therefore, should be used as an important part of . Furthermore, the present invention designs the first virtual control signal in the following form:

[0112]

[0113] where, represents the first positive design parameter. However, in the process of designing the second virtual control signal , it is necessary to utilize 's derivative information. To avoid complex differentiation operations on , a first-order filter, namely the first filter, can be introduced to approximately obtain its derivative information. The present invention designs the first filter in the following form:

[0114]

[0115] wherein, represents the design parameter of the first filter, which can determine the convergence speed of the filter; and respectively represent the signals output by the first filter. Among them, is the first reference signal, the derivative of the first reference signal, which is used to approximate ; similarly, can be used to replace 's derivative information. The purpose of designing the virtual control signal and the filter into equations (22) and (23) respectively is to be able to derive the following Lyapunov function inequality related to the tracking error and filtering error[[ID=A]] :

[0116]

[0117] wherein, represents the upper bound of the absolute value of the filtering error.

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

[0119]

[0120] Since there are some first unknown functions that cannot be accurately modeled in the second-order dynamic system, then, when designing , an extended state observer model needs to be introduced to estimate the changing trend of these unknown functions in real time. The present invention designs as

[0121]

[0122] wherein, represents the second positive design parameter. It can be found including the derivative of the first reference signal , and there is also a complex functional relationship with . Then, taking the derivative of involves the problem of derivative of composite functions, and such a long derivative chain will make the controller design very cumbersome. Therefore, in order to avoid complex derivative operations and provide reference trajectory information for subsequent virtual control signals, a second filter needs to be introduced:

[0123]

[0124] wherein, represents the design parameter of the second filter, represents the signal output by the second filter, that is, the second reference signal, represents the derivative of the second reference signal. Thus, the Lyapunov function inequality related to the tracking error and filtering error of the second-order subsystem can be deduced:

[0125]

[0126] wherein, represents the upper bound of the absolute value of the filtering error.

[0127] (3) Taking the second reference signal as the tracking target, the tracking error of the third-order subsystem is defined as:

[0128]

[0129] It should be noted that when designing the third virtual control signal for controlling the change trend of the state trajectory of the third-order subsystem, not only the tracking error should be introduced, but also the residual term in formula (28) of the Lyapunov inequality corresponding to the second-order subsystem should be considered, which will seriously affect the stability of the system. Therefore, an attempt can be made to cancel during the design of . Thus, the present invention designs

[0130]

[0131] wherein, represents the third positive design parameter. Next, a third filter is designed:

[0132]

[0133] wherein, Denote the design parameters of the third filter; Denote the signal output by the third filter, i.e., the third reference signal, Denote the derivative of the third reference signal, which provides a 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] where, Denote the filtering error, Denote 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] where, Denote the tracking error corresponding to this subsystem, Denote the fourth positive design parameter. Since the fourth - order subsystem is the last - order subsystem, there is no need to design an additional filter. Then, there is only a Lyapunov function related to the tracking error of this subsystem:

[0139]

[0140] Next, construct the total Lyapunov function for the entire control system , then its derivative can be expressed in the following form:

[0141]

[0142] Substitute the Lyapunov function corresponding to each subsystem into Equation (35) to obtain the following conclusion:

[0143]

[0144] Since the designed extended state observer has the semi - global uniform convergence property, then its observation error , the observation error will tend to an infinitesimal positive constant within a neighborhood near the origin within a certain time . When appropriate filter parameters are selected, it is certain to ensure that the following inequality holds:

[0145]

[0146] There exist positive real numbers and , such that the Lyapunov function inequality of the entire control system satisfies the Lyapunov stability criterion formula (9). Therefore, the control system designed by the present invention can ensure stable convergence, and the data flow and interaction relationship among its internal components are as Figure 1 shown.

[0147] As a specific implementation manner of this embodiment, it includes the following steps:

[0148] (1) Build a simulation environment, which includes constructing the dynamic model of the industrial manipulator and giving its own inherent property parameters, setting the reference trajectory that the industrial manipulator needs to track and further calculating its derivative information ;

[0149] (2) According to 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 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, design a corresponding extended state observer for the first unknown function existing therein , where the second reference signal 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 can be regarded as the reference trajectory of the fourth-order subsystem;

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

[0153] (6) Analyze the data of the controller simulation results.

[0154] Furthermore, obtain its own key property parameters from the technical parameter manual of the actual industrial manipulator or through actual measurement. For example, the inherent parameters of a flexible two-degree-of-freedom industrial manipulator mainly include the following contents: Link length: L = 1m; Joint stiffness: ; Link mass: m = 0.25 kg; Motor rotor inertia: ; Natural damping: 0.6; Friction coefficient: 0.01. After determining the above inherent parameters, the dynamic model of the industrial manipulator for controller design can be expressed in the following form:

[0155]

[0156] Where:

[0157]

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

[0159] Design the first virtual control signal:

[0160]

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

[0162]

[0163] Where, is set to 0.002, can represent the approximate value of , then represents the approximate derivative of .

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

[0165] ​​​​​​​​​​​

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

[0167]

[0168] Among them, the convergence speed decay parameter is set to 0.001. Continue to input into the second filter:

[0169]

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

[0171] Based on the tracking error of the third-order subsystem design the virtual control signal:

[0172]

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

[0174]

[0175] Among them, the design parameter of the third filter is set to 0.002.

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

[0177]

[0178] Among them, represents the tracking error corresponding to this subsystem, and the fourth positive design parameter , is set to 0.98. Adopt the following extended state observer model for real-time estimation:

[0179]

[0180] The anti-saturation control algorithm of the present invention has been simulated and tested in the dynamic model of a class of industrial manipulators, and its simulation test results are as Figure 2, Figure 3 , Figure 4 as shown Figure 2 shows the simulation experiment results of the output at the end of an industrial manipulator (dashed line) tracking the reference trajectory (solid line). It can be found that the real-time performance of the control algorithm is relatively strong. When the controller receives the tracking instruction, it has tracked the specified non-linear reference trajectory after 0.5 seconds. Figure 3 The tracking error of the anti-saturation control algorithm is further described in which has regularly changed between -0.008195 and 0.009982 at 0.5 seconds, and the total change amplitude is 0.0182 rad, as shown by the black solid line. The order of magnitude of the tracking error has been reduced to the order of magnitude range. Figure 4 The black dashed line and solid line in respectively represent the real output torque and the commanded output torque Figure 2 and Figure 3 as shown

[0181] The above is only a preferred specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. An anti-saturation tracking control method for industrial manipulators based on an extended state observer, characterized in that It includes the following steps: Based on the dynamic model of the industrial manipulator, the hyperbolic tangent function is used to model the output saturation characteristic of the actuator, and the dynamic model after anti-saturation processing is obtained; Based on the dynamic model after anti-saturation processing, an extended state observer with semi-globally uniformly ultimately stable characteristics is designed, and the 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 manipulator.

2. The anti-saturation tracking control method for an industrial manipulator based on an extended state observer according to claim 1, characterized in that The process of using the hyperbolic tangent function to model the output saturation characteristic of the actuator and obtaining the dynamic model after anti-saturation processing includes: Based on the dynamic model of the industrial manipulator, the maximum output torque and minimum output torque of the actuator are obtained; The output torque range is obtained based on the maximum output torque and the minimum output torque; The hyperbolic tangent function is used to model the saturation characteristic of the output torque range to obtain a continuously differentiable anti-saturation compensation function; Based on the anti-saturation compensation function, the original dynamic model is transformed to obtain the dynamic model after anti-saturation processing.

3. The anti-saturation tracking control method for an industrial manipulator based on an extended state observer according to claim 2, characterized in that, The expression of the dynamic model after anti-saturation processing is: ； In the formula, represents the mass of the connecting rod, represents the length of the connecting rod, represents the joint stiffness, represents the moment of inertia of the motor, represents the angular displacement of the connecting rod, represents the angular velocity of the connecting rod, represents the angular displacement of the driving motor, represents the angular velocity of the driving motor, represents the first unknown function, represents the second unknown function, is the output signal of the industrial manipulator, represents the approximation error generated after approximately modeling the output saturation model using the double tangent function, is the final anti-saturation command torque control signal obtained, represents the saturation limit parameter, is the derivative of is the derivative of is the derivative of is the derivative of.

4. The anti-saturation tracking control method for an industrial manipulator based on an extended state observer according to claim 3, wherein The process of designing an extended state observer with semi-globally uniformly ultimately stable characteristics based on the dynamic model after anti-saturation processing includes: Based on the dynamic model after anti-saturation processing, the unknown function of the system is extracted; For the observer to be designed, the observation error is defined; Construct the Lyapunov function inequality constraint relationship related to the observation error; Based on the Lyapunov function inequality constraint relationship, an extended state observer with semi-globally uniformly ultimately stable characteristics based on the unknown function is constructed.

5. The anti-saturation tracking control method for an industrial manipulator based on an extended state observer according to claim 4, wherein The expression of the extended state observer designed based on the first unknown function is: ； In the formula, is the observer model designed for , is the estimated value of , is a design parameter greater than zero, is the estimated value of , is the derivative of , is the derivative of .

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

7. The anti-saturation tracking control method for an industrial manipulator based on an extended state observer according to claim 6, 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 approximately process the derivatives of the virtual control signals at all levels to obtain the filtered reference signal; Based on the filtered reference signal and the estimated value of the unknown function, the compensation control amounts of all levels of subsystems are obtained; Based on the compensation control amounts, the final anti-saturation command torque control signal is obtained.

8. The anti-saturation tracking control method for an industrial manipulator based on an extended state observer according to claim 7, wherein The process of using a cascade filter to process the virtual control signals at all levels and compensate all levels of subsystems to obtain the final anti-saturation command torque control signal includes: Based on the initial tracking error of the first-order subsystem, a first virtual control signal is designed, and the derivative of the first reference signal is obtained by processing the first virtual control signal through a first filter; 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, design the second virtual control signal, and process the second virtual control signal through a second filter to obtain the derivative of the second reference signal; Based on the tracking error of the third-order subsystem and the derivative of the second reference signal, design the third virtual control signal, and process the third virtual control signal through a third filter to obtain the derivative of the third reference signal; Based on the tracking error of the end subsystem and the derivative of the third reference signal, combined with the estimated value of the extended state observer of the second unknown function, design the final anti-saturation command torque control signal.

9. The anti-saturation tracking control method for an industrial manipulator based on an extended state observer according to claim 8, characterized in that, The design of the first virtual control signal includes: Based on the tracking error of the first-order subsystem, design the basic control component using a proportional control term; Introduce the square term of the tracking error as the stability compensation component; Combine the basic control component and the stability compensation component to form the first virtual control signal.

10. The anti-saturation tracking control method for an industrial manipulator based on an extended state observer according to claim 7, characterized in that The obtained final anti-saturation command torque control signal is: ； In the formula, represents the fourth positive design parameter, is the tracking error corresponding to the fourth-order subsystem, is the obtained final anti-windup command torque control signal, where I is the subscript of the command torque, is the derivative of the third reference signal.

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