Observer-based control method and system for nonlinear systems of flexible link robots

Abstract

The present invention proposes an observer-based control method and system for a flexible link robot nonlinear system, which belongs to the field of robot control technology, including: establishing a quasi-unilateral Lipschitz nonlinear system dynamics model of the flexible link robot; creating a state observer based on the state vector of the nonlinear system; constructing an error system and an expanded error system containing foreseeable target signal information; designing a state feedback controller, substituting the state feedback controller into the expanded error system to obtain a closed-loop system; analyzing the stability and H of the closed-loop system. ∞ The performance condition is used to obtain the state feedback controller gain matrix; the state feedback controller gain matrix is ​​regressed to the quasi-unilateral Lipschitz nonlinear system to obtain an observer-based preview controller to track the target signal. The present invention improves the control performance of the closed-loop system by combining the quasi-unilateral Lipschitz condition and utilizing the predictable information of the target signal.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot control, and in particular relates to an observer-based flexible link robot nonlinear system control method and system. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] In complex control fields such as industrial automation and robotics, high-precision output tracking control is a core technology for achieving automation tasks. As robotic applications continue to expand into highly dynamic and highly disturbed environments, controlled objects often exhibit strong nonlinearity, external disturbance uncertainty, and incompletely measurable state vectors. This makes it difficult for traditional control methods to meet the requirements of high-precision tracking control.

[0004] When modeling nonlinear systems of flexible-link robots, the traditional global Lipschitz condition is often used to describe nonlinear terms. However, this method suffers from inherent drawbacks such as strict modeling constraints, insufficient approximation accuracy, and poor dynamic characterization, which inevitably introduce controller conservatism. Furthermore, traditional control methods fail to fully utilize predictable information about the target signal when designing tracking controllers, resulting in closed-loop systems exhibiting significant response lag, large overshoot, and low tracking accuracy. Furthermore, due to limitations in measurement methods and cost, the actual system state information required by the controller is often difficult to obtain directly. Summary of the Invention

[0005] To overcome the deficiencies of the above-mentioned prior art, the present invention proposes an observer-based flexible-link robot nonlinear system control method and system. By introducing a quasi-unilateral Lipschitz condition, the conservative constraint of the traditional Lipschitz condition on the nonlinear term is reduced; at the same time, a predictive compensation mechanism is constructed with the help of the predictive information of the target signal, which significantly improves the output tracking performance of the closed-loop system; in addition, the collaborative design of the observer and the controller is innovatively realized, avoiding the complex calculation process of solving the gain matrix step by step, providing a more advanced and efficient solution for the field of robot tracking control.

[0006] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0007] In a first aspect, a method for controlling a nonlinear system of a flexible link robot based on an observer is disclosed, comprising:

[0008] Establish a quasi-unilateral Lipschitz nonlinear system dynamics model for a flexible linkage robot;

[0009] creating a state observer based on a state vector of the nonlinear system;

[0010] constructing an error system and an expanded error system containing foreseeable target signal information based on the state observer;

[0011] Designing a state feedback controller based on the state vector of the foreseeable target signal information, and substituting the state feedback controller into the amplified error system to obtain a closed-loop system;

[0012] The stability and H of the closed-loop system are analyzed. ∞ The performance condition obtains the state feedback controller gain matrix;

[0013] The state feedback controller gain matrix is ​​regressed to the quasi-unilateral Lipschitz nonlinear system to obtain an observer-based preview controller to track the target signal.

[0014] In a second aspect, an observer-based flexible link robot nonlinear system control system is disclosed, comprising:

[0015] The model building module is configured to: establish a quasi-unilateral Lipschitz nonlinear system dynamics model of the flexible link robot;

[0016] An observer building module is configured to: create a state observer based on a state vector of the nonlinear system;

[0017] an error calculation module, configured to: construct an error system and an expanded error system containing foreseeable target signal information based on the state observer;

[0018] a closed-loop calculation module configured to: design a state feedback controller based on a state vector of the foreseeable target signal information, and substitute the state feedback controller into the expanded error system to obtain a closed-loop system;

[0019] The state analysis module is configured to analyze the stability and H of the closed-loop system. ∞ The performance condition obtains the state feedback controller gain matrix;

[0020] The tracking control module is configured to: regress the state feedback controller gain matrix to the quasi-unilateral Lipschitz nonlinear system to obtain an observer-based preview controller to track the target signal.

[0021] In a third aspect, an electronic device is disclosed, including a memory and a processor, and computer instructions stored in the memory and running on the processor. When the computer instructions are run by the processor, the steps of the above-mentioned observer-based flexible link robot nonlinear system control method are completed.

[0022] In a fourth aspect, a computer-readable storage medium is disclosed for storing computer instructions. When the computer instructions are executed by a processor, the steps of the above-mentioned observer-based flexible link robot nonlinear system control method are completed.

[0023] Compared with the prior art, the present invention has the following beneficial effects:

[0024] The present invention proposes to introduce a quasi-unilateral Lipschitz condition to describe the nonlinear terms of the system. The quasi-unilateral Lipschitz condition contains more useful information about the nonlinear terms, can more accurately reflect the dynamic behavior characteristics of the actual system, reduce the conservative limitations of the traditional Lipschitz condition, and thus expand the scope of application of the technical solution of the present invention.

[0025] The present invention significantly improves the tracking accuracy and response speed of the closed-loop system by constructing a foresight compensation mechanism based on future information of the target signal.

[0026] The one-step linear matrix inequality algorithm proposed in the present invention can simultaneously solve the observer and tracking controller gain matrix parameters, effectively simplifying the calculation process and improving the solution efficiency.

[0027] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0029] Figure 1 This is a flow chart of the observer-based flexible-link robot nonlinear system control method described in Example 1 of the present invention.

[0030] Figure 2 This is a diagram of the output response and target signal trajectory of the nonlinear system described in the first embodiment of the present invention.

[0031] Figure 3 This is a tracking error trajectory diagram of the nonlinear system described in Example 1 of the present invention.

[0032] Figure 4 This is the nonlinear system control output trajectory diagram described in Example 1 of the present invention. DETAILED DESCRIPTION

[0033] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0034] It should be noted that the terms used herein are for describing particular embodiments only and are not intended to limit the exemplary embodiments according to the present invention.

[0035] In the absence of conflict, the embodiments of the present invention and the features thereof may be combined with each other.

[0036] Example 1

[0037] In one or more embodiments, a nonlinear system control method of a flexible link robot based on an observer is disclosed, such as Figure 1 As shown, the following steps are included:

[0038] Step S1, establishing a quasi-unilateral Lipschitz nonlinear system dynamics model of a flexible link robot;

[0039] Specifically, the nonlinear system dynamics model is:

[0040] (1)

[0041] Where, t for t time; is the state estimation vector of the observer, ; is the state vector of the system, and ; is the control input of the system, and ; is the output vector of the system, and ; is an external disturbance and satisfies , For external interference The derivative of is the space of square integrable functions; , , , , , are constant matrices with appropriate dimensions respectively; is a nonlinear term that satisfies the quasi-unilateral Lipschitz condition; n, m, p, q represent the dimensions of the vector space respectively.

[0042] This example makes the following assumptions for subsequent theory:

[0043] Assumption 1. If there exists a matrix and one that depends on The real symmetric matrix So that the inequality:

[0044] (2)

[0045] For any system state If both of them hold true, then it is called a nonlinear vector function. It satisfies the global quasi-unilateral Lipschitz condition, and the matrix is ​​correspondingly called a quasi-unilateral Lipschitz constant matrix.

[0046] Assumption 2. Assume that the target signal Piecewise continuous and differentiable and satisfying ,in is a constant vector, and The derivative of satisfies . Further, from the current moment Target signal is predictable. Here, It is called the look-ahead length of the target signal.

[0047] To facilitate subsequent analysis and proof, the following lemma is given.

[0048] Lemma 1. The matrix logarithm norm has the following properties:

[0049] (3)

[0050] Among them, A and B are matrices, and .

[0051] Lemma 2. Symmetric matrix The necessary and sufficient condition for is that one of the following conditions holds:

[0052] (4)

[0053] (5)

[0054] Lemma 3. For a matrix of appropriate dimension and constant , if the inequality

[0055] (6)

[0056] Then there is an inequality Established.

[0057] Step S2: creating a state observer based on the state vector of the nonlinear system;

[0058] Design a state observer. The state equation of the state observer is:

[0059] (7)

[0060] Where, is the observed state derivative; is the gain matrix of the state observer to be designed; is the output estimate vector of the observer.

[0061] This embodiment takes into account that in practical applications, it is generally impossible to obtain all the states of the system directly through measurement. Therefore, the above-mentioned state observer is designed to estimate the unknown state of the system.

[0062] Derivative the equation of the state observer, and obtain the dynamic equation satisfied by the observed state derivative:

[0063] (8)

[0064] Where, is the derivative of the control input; is the derivative of the observer's output estimate vector.

[0065] This derivation step is to deal with the quasi-unilateral Lipschitz nonlinear term in the original system. By applying Assumption 1 and cleverly combining the differential mean value theorem, the derivative of the nonlinear term obtained after derivation can be effectively solved, facilitating the subsequent design of the predictive controller.

[0066] Step S3: constructing an error system and an expanded error system containing foreseeable target signal information based on the state observer;

[0067] Step S3-1: Define the observation error according to the state observer as:

[0068] (9)

[0069] Where, is the observation error.

[0070] To apply the estimated state The information constructs the expanded error system, and the derivatives on both sides of the above formula are obtained:

[0071] (10)

[0072] The tracking error is defined as:

[0073] (11)

[0074] Where, Output the target signal to be tracked to the system; is the tracking error.

[0075] By taking the derivative of the tracking error, we can obtain the dynamic equation satisfied by the tracking error:

[0076] (12)

[0077] Where, is the tracking error derivative; is the observation error derivative; is the target signal derivative.

[0078] Step S3-2: Combine the dynamic equations satisfied by the observed state derivative and the tracking error to obtain the error system:

[0079] (13)

[0080] Where, for n The identity matrix of order.

[0081] Introducing known future information of the target signal into the error system , define a new state vector, that is, a state vector containing foreseeable information and the new interference vector , where T is the transpose, is the prediction length of the target signal, the error system can be rewritten as:

[0082] (14)

[0083] Where, , , , is the augmented matrix, represents the coefficient matrix of the state vector, and , represents the coefficient matrix of the observation error derivatives, , represents the coefficient matrix of the control input derivatives, , represents the coefficient matrix of the interference vector, ; is an augmented nonlinear vector function, and .

[0084] According to hypothesis 2, the target signal From the current moment Start, the future Step-wide information This embodiment makes full use of this information and uses some clever mathematical operations to transform the system, thereby facilitating the subsequent controller design to introduce a predictive feedforward compensation mechanism for the target signal.

[0085] Step S3-3, constructing an expanded error system based on the error system, the observation error, and the performance signal;

[0086] First, the observation error is derived, and the state equation of the nonlinear system (i.e., Formula 1) and the state equation of the state observer are combined to obtain the observation error dynamic equation:

[0087] (15)

[0088] Taking the second derivative of the above observation error dynamic equation, we can get the observation error derivative The dynamic equations satisfied are:

[0089] (16)

[0090] Where, is an augmented matrix, and .

[0091] In order to evaluate the tracking performance of the system, a linear quadratic performance index function is introduced :

[0092] (17)

[0093] Where, , and is a weight matrix of a given appropriate dimension;

[0094] Define performance signals as:

[0095] (18)

[0096] Where, is the weight matrix of the augmented state, ; is the weight matrix of the observation error derivative, ; is the weight matrix controlling the input derivatives, and .

[0097] The performance indicator function can be further expressed as the square of the 2-norm of the performance signal, that is:

[0098] (19)

[0099] Combining the error system, the dynamic equations satisfied by the observed error derivatives, and the performance signal, we obtain the expanded error system:

[0100] (20)

[0101] In the theory of predictive control, the above system is usually called the expanded error system. At this point, the predictive control problem of system (1) is transformed into the H of the expanded error system (20) under the performance signal. ∞ Control issues.

[0102] Step S4: introducing the state vector of the foreseeable information of the target signal to design a state feedback controller, and substituting the state feedback controller into the expanded error system to obtain a closed-loop system;

[0103] The state feedback controller is designed based on the state vector of the foreseeable information of the target signal:

[0104] (twenty one)

[0105] Where, is the feedback controller gain matrix to be determined, is the state vector that introduces the predictable information of the target signal.

[0106] Among them, during the controller design process, the following two conditions need to be met:

[0107] (1) When the augmented external interference is zero When , the closed-loop system of the expanded error system is asymptotically stable;

[0108] (2) Under zero initial conditions, for a given constant and any non-zero , the closed-loop system of the expanded error system satisfies H ∞ Performance indicators, namely:

[0109] (twenty two)

[0110] Where, To increase external interference. Indicates H ∞ Performance index (attenuation level). Formula (22) means: If The smaller it is, the better the impact of external interference on system performance is suppressed and the stronger the system robustness is.

[0111] Substituting the state feedback controller into the expanded error system, the closed-loop system is obtained as follows:

[0112] (twenty three)

[0113] At this point, the research problem is transformed into the stability of the closed-loop system and H ∞ Performance analysis issues.

[0114] Step S5: Analyze the stability of the closed-loop system and H ∞ Performance conditions are given, and the calculation method of the state feedback controller gain matrix is ​​given.

[0115] Specifically, the stability analysis process of the closed-loop system includes:

[0116] For convenience of representation, the following matrix is ​​defined:

[0117] (twenty four)

[0118] Theorem 1. Assume that Assumptions 1-2 hold. For a given scalar , , if there exists a matrix , and matrix , , , making

[0119] (25)

[0120] in, , , then the closed-loop system (Formula 23) of the expanded error system (Formula 20) is asymptotically stable and satisfies H ∞ Performance index criterion (Formula 22). Further, the observer gain matrix and the controller gain matrix Can be respectively and Calculated.

[0121] Proof: Using theorem 1 and , construct the following Lyapunov function:

[0122] (26)

[0123] To make the closed-loop system (23) asymptotically stable and have H ∞ Interference suppression performance only requires the following inequality to hold:

[0124] (27)

[0125] By taking the derivative of the left side of equation (27), we can obtain:

[0126] (28)

[0127] From Assumption 1, Lemma 1, the properties of the matrix norm and the mean inequality, we can see that

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134] (29)

[0135] Similarly, we can get:

[0136] (30)

[0137] (31)

[0138] Combining equations (29) - (31), equation (28) can be further expressed as:

[0139]

[0140] (32)

[0141] By definition

[0142]

[0143]

[0144] The left side of formula (27) can be expressed as:

[0145] (33)

[0146] in, .

[0147] At this point, the problem becomes finding inequalities Sufficient conditions for the establishment of . Applying Lemma 2, we can see that Equivalent to

[0148] (34)

[0149] Make the same transformation on the left side matrix of Equation (34): multiply the left side by the reversible matrix , multiplying right by its transpose, we can get

[0150] (35)

[0151] Using formula (24), formula (35) , , can be rewritten as

[0152] (36)

[0153] (37)

[0154] (38)

[0155] Therefore, from the above equations (36) - (38), equation (35) can be rewritten as

[0156] (39)

[0157] Among them, T1, T2, T3, T4, and T5 are all constant matrices, and their definitions can refer to formula (24).

[0158] In order to deal with the nonlinear coupling terms in inequality (39), the variable substitution and auxiliary matrix method are used. Let ,but In order to facilitate the calculation of the observer gain matrix, a non-singular matrix is ​​introduced , and define ,but

[0159] (40)

[0160] (41)

[0161] The left matrix of inequality (39) is From equations (40) and (41), the left matrix of equation (39) can be rewritten as

[0162] (42)

[0163] in, .

[0164] According to Lemma 3, Established, as long as the following conditions are met:

[0165] (43)

[0166] in, .

[0167] Inequality (43) is the inequality condition (25) in Theorem 1. Therefore, if condition (43) is satisfied, then condition (25) is established, and thus . Theorem 1 is proved.

[0168] It should be understood that in order to more clearly illustrate the structure of the controller, the controller gain matrix Breaks down to:

[0169] (44)

[0170] Where, is the observer-based state feedback gain matrix, ; is the gain matrix of the tracking error integral term and the look-ahead feedforward compensation term, .

[0171] Step S6: Return the state feedback controller to the quasi-unilateral Lipschitz nonlinear system and give the observer-based H ∞ The specific form of the foresight controller is:

[0172] (45)

[0173] Thereby, the tracking control of the target signal by the nonlinear system is realized.

[0174] According to the right side of the above formula, the controller proposed by the present invention consists of the following three parts: is the state feedback term based on the observer, the second part is the integral term of the output tracking error, which is used to eliminate the static error of the system. It is a feedforward compensation term that predicts the future information of the target signal and is used to improve the tracking performance of the system.

[0175] Furthermore, based on a flexible link robot system, a simulation experiment is conducted to compare the method proposed in this embodiment with the control scheme of the prior art to verify the effectiveness and superiority of the control method proposed in this embodiment.

[0176] The flexible link robot system is:

[0177]

[0178] Select a matrix with the following structure

[0179]

[0180] The constant . It has been verified that the nonlinear term Satisfy the quasi-unilateral Lipschitz condition (2) in Assumption 1. Select the parameter , , , , Based on Theorem 1, the LMI toolbox in MATLAB is used to calculate the gain matrix of the preview controller and the observer gain matrix as follows:

[0181]

[0182] .

[0183] In order to perform numerical simulation, the foreseeable target signal is assumed to be

[0184]

[0185] The initial state of the system is taken as , the initial state of the observer is taken as .

[0186] like Figure 2-Figure 4 As shown in Figure 2, the system’s output response, tracking error, and control input response curves are shown respectively. Figure 2 As shown, the system output under both control schemes can track the target signal without static error. Notably, the preview compensation controller designed in this invention achieves advanced perception of the target signal through a feedforward compensation mechanism, enabling the system to proactively respond to changes in the reference input. This control strategy significantly improves the system's dynamic response characteristics, achieving rapid regulation and optimized response time.

[0187] Example 2

[0188] In one or more embodiments, an observer-based flexible link robot nonlinear system control system is disclosed, comprising:

[0189] The model building module is configured to: establish a quasi-unilateral Lipschitz nonlinear system dynamics model of the flexible link robot;

[0190] An observer building module is configured to: create a state observer based on a state vector of the nonlinear system;

[0191] an error calculation module, configured to: construct an error system and an expanded error system containing foreseeable target signal information based on the state observer;

[0192] a closed-loop calculation module configured to: design a state feedback controller based on a state vector of the foreseeable target signal information, and substitute the state feedback controller into the expanded error system to obtain a closed-loop system;

[0193] The state analysis module is configured to analyze the stability and H of the closed-loop system. ∞ The performance condition obtains the state feedback controller gain matrix;

[0194] The tracking control module is configured to: regress the state feedback controller gain matrix to the quasi-unilateral Lipschitz nonlinear system to obtain an observer-based preview controller to track the target signal.

[0195] Example 3

[0196] This embodiment provides an electronic device, including a memory and a processor, and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the steps of the above-mentioned observer-based flexible link robot nonlinear system control method are completed.

[0197] Example 4

[0198] This embodiment provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps of the above-mentioned observer-based flexible-link robot nonlinear system control method are completed.

[0199] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0200] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0201] These computer program instructions can also be loaded onto a computer or other programmable data processing device, and a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide the functions for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0202] The description of each embodiment in the above embodiments has different emphases. For parts not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0203] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A nonlinear system control method for a flexible link robot based on an observer, characterized in that: include: Establish a quasi-unilateral Lipschitz nonlinear system dynamics model for a flexible linkage robot; creating a state observer based on a state vector of the nonlinear system; constructing an error system and an expanded error system containing foreseeable target signal information based on the state observer; Designing a state feedback controller based on the state vector of the foreseeable target signal information, and substituting the state feedback controller into the amplified error system to obtain a closed-loop system; The stability and H of the closed-loop system are analyzed. ∞ The performance condition obtains the state feedback controller gain matrix; Regressing the state feedback controller gain matrix to the quasi-unilateral Lipschitz nonlinear system to obtain an observer-based preview controller to track the target signal; The state equation of the state observer is: Where, is the observed state derivative; is the control input of the system; is the output vector of the system; is the gain matrix of the state observer to be designed; is the output estimation vector of the observer; 、 、 、 is a constant matrix; is the state estimation vector of the observer; is a nonlinear term that satisfies the quasi-unilateral Lipschitz condition; Derivative the state equation of the state observer to obtain a dynamic equation of the observed state derivative; An error system and an expanded error system containing foreseeable target signal information are constructed based on the state observer, including: an observation error is the difference between a state vector of the nonlinear system and a state estimation vector of the observer; a tracking error is the difference between an output vector of the nonlinear system and a target signal to be tracked by the system, and a dynamic equation satisfied by the tracking error is obtained by differentiating the tracking error; and an error system is obtained based on the dynamic equation satisfied by the observation state derivative and the tracking error; defining a state vector and an interference vector containing predictable information, and substituting the state vector and the interference vector containing predictable information into the error system to obtain a predictable error system; An augmented error system is constructed based on the foreseeable error system, the observed error and the performance signal.

2. The observer-based flexible link robot nonlinear system control method according to claim 1, characterized in that: The structural enlargement error system includes: The observation error is differentiated and combined with the state equation of the nonlinear system and the state equation of the state observer to obtain the observation error dynamic equation, and the observation error dynamic equation is quadratically differentiated to obtain a dynamic equation satisfied by the observation error derivative; The performance signal is ; Where, is the weight matrix of the augmented state, ; is the weight matrix of the observation error derivative, ; is the weight matrix controlling the input derivatives, and ; is the derivative of the control input; , and is the weight matrix; is the observation error derivative; is the state vector containing foreseeable information; For performance signals; The predictable error system, the dynamic equation satisfied by the observed error derivative, and the performance signal are combined to obtain the expanded error system.

3. The observer-based flexible link robot nonlinear system control method according to claim 1, characterized in that: The state feedback controller is designed to meet the following requirements: When the augmented external disturbance is zero, the closed-loop system of the augmented error system is asymptotically stable; Under zero initial conditions, for a given constant and any non-zero , the closed-loop system of the expanded error system satisfies H ∞ Performance indicators: Where, For performance signals; To increase external interference; is the space of square integrable functions.

4. The observer-based flexible link robot nonlinear system control method according to claim 1, characterized in that: The closed-loop system is: Where, is the derivative of the augmented state; is the state vector of the system; , , , is an augmented matrix, and , , , , for n The unit matrix of order; is the augmented matrix; To increase external interference; is an augmented nonlinear vector function, and ; is the observation error derivative; For performance signals; is the feedback controller gain matrix to be determined; is the weight matrix of the augmented state; is the weight matrix of the observation error derivative; is the weight matrix controlling the input derivatives.

5. The observer-based flexible link robot nonlinear system control method according to claim 1, characterized in that: The state feedback controller gain matrix is ​​regressed to the quasi-unilateral Lipschitz nonlinear system to obtain an observer-based preview controller. The specific form of the preview controller is: Where, t For the moment t ; is the observer-based state feedback gain matrix; is the gain matrix of the tracking error integral term and the look-ahead feedforward compensation term; is the state estimation vector of the observer; is the tracking error; Output the target signal to be tracked to the system; is the look-ahead length of the target signal.

6. A nonlinear system control system for a flexible link robot based on an observer, characterized in that: include: The model building module is configured to: establish a quasi-unilateral Lipschitz nonlinear system dynamics model of the flexible link robot; An observer building module is configured to: create a state observer based on a state vector of the nonlinear system; an error calculation module, configured to: construct an error system and an expanded error system containing foreseeable target signal information based on the state observer; a closed-loop calculation module configured to: design a state feedback controller based on a state vector of the foreseeable target signal information, and substitute the state feedback controller into the expanded error system to obtain a closed-loop system; The state analysis module is configured to analyze the stability and H of the closed-loop system. ∞ The performance condition obtains the state feedback controller gain matrix; A tracking control module is configured to: regress the state feedback controller gain matrix to the quasi-unilateral Lipschitz nonlinear system to obtain an observer-based preview controller to track the target signal; The state equation of the state observer is: Where, is the observed state derivative; is the control input of the system; is the output vector of the system; is the gain matrix of the state observer to be designed; is the output estimation vector of the observer; 、 、 、 is a constant matrix; is the state estimation vector of the observer; is a nonlinear term that satisfies the quasi-unilateral Lipschitz condition; Derivative the state equation of the state observer to obtain a dynamic equation of the observed state derivative; An error system and an expanded error system containing foreseeable target signal information are constructed based on the state observer, including: an observation error is the difference between a state vector of the nonlinear system and a state estimation vector of the observer; a tracking error is the difference between an output vector of the nonlinear system and a target signal to be tracked by the system, and a dynamic equation satisfied by the tracking error is obtained by differentiating the tracking error; and an error system is obtained based on the dynamic equation satisfied by the observation state derivative and the tracking error; defining a state vector and an interference vector containing predictable information, and substituting the state vector and the interference vector containing predictable information into the error system to obtain a predictable error system; An augmented error system is constructed based on the foreseeable error system, the observed error and the performance signal.

7. An electronic device, characterized in that: The invention comprises a memory and a processor, and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the observer-based flexible link robot nonlinear system control method according to any one of claims 1 to 5 is completed.

8. A computer-readable storage medium, characterized in that Used to store computer instructions, which, when executed by a processor, complete the observer-based flexible link robot nonlinear system control method according to any one of claims 1 to 5.

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