Fixed-time fault-tolerant control method for space tethered combination under actuator failure

Abstract

The application relates to a fixed-time fault-tolerant control method for a space tethered combination under actuator failure, a dynamic motion equation of a tethered robot capturing a target and forming a tethered combination with the target is established according to an Euler-Lagrange method; a learning model of internal uncertainty and actuator failure of the tethered combination system is constructed, an observer with a fixed-time convergence characteristic is designed to accurately estimate the lumped uncertainty composed of the internal uncertainty and the failure; in order to ensure that the system state has a fast convergence characteristic under the lumped uncertainty, a fixed-time non-singular terminal sliding mode surface is designed; finally, in combination with the characteristics of the sliding mode control and the observer, a fixed-time fault-tolerant control scheme based on the observer is proposed, the system state can realize fixed-time stable convergence under the internal uncertainty, and high-performance tracking effect can still be maintained when the actuator has failure.

Description

Technical Field

[0001] This invention relates to a high-precision stable control method for space tethered robots, and specifically to a fixed-time fault-tolerant control method for a space tethered assembly under actuator failure. Background Technology

[0002] Space tethered robots have excellent application prospects in space debris capture and active capture and deorbiting of failed spacecraft, and are currently attracting widespread attention from many scholars. Patent CN106502260A studied the attitude control problem of a space tethered satellite after capturing a flexible target and designed an adaptive sliding mode attitude controller. Based on this, patent CN113703468A further studied an integrated pose control method for tethered robots under complex uncertainties. However, none of the above patents considered the problem of actuator failure in the tethered assembly system, which can significantly reduce system performance and even cause subsequent on-orbit control mission failures. Therefore, this project proposes a fixed-time fault-tolerant control method based on an observer to address the problem of rapid and high-precision stabilization of the tethered assembly under conditions of actuator failure and complex uncertainties. This method can not only estimate faults and uncertainties online in real time, but also achieve rapid and precise control of the tethered assembly system. Summary of the Invention

[0003] Technical problems to be solved

[0004] To overcome the shortcomings of existing technologies, this invention proposes a fixed-time fault-tolerant control method for a spatial rope assembly under actuator failure.

[0005] Technical solution

[0006] A fixed-time fault-tolerant control method for a spatial rope assembly under actuator failure, characterized by the following steps:

[0007] Based on the Euler-Lagrange method, the dynamic motion equations of the space tethered robot after capturing a target and forming a tethered assembly with the target are established:

[0008]

[0009] in: Represents the system's generalized coordinate system; The control input force / torque for the system, It is a symmetric positive definite inertial matrix; Represents the Coriolis force matrix. This is the gravitational torque;

[0010] Define the desired trajectory of the combined system as q d (t), the rate of change of tracking error is Tracking error is Rope-tied assembly system error dynamic model:

[0011]

[0012]

[0013] in: Given column vectors, the new set total uncertainty This includes system parameter uncertainties and actuator malfunctions;

[0014] Construct a model of internal uncertainties and actuator failures in the rope-tied assembly system:

[0015]

[0016] in: A diagonal matrix representing the execution control commands generated by n executors. Let be the actuator effectiveness matrix; where 0 ≤ ρ i ≤1 represents the failure level of the i=1,...,n actuator, ρ i =1 indicates that the i-th actuator is working healthily; ρ i =0 indicates that the i-th actuator is turned off or completely disabled; 0 < ρ i <1 indicates that the i-th actuator has lost some of its effectiveness, i.e., the actuator is partially ineffective. The value is a bounded drift fault value;

[0017] A fixed-time non-singular terminal sliding surface was designed:

[0018] s = x² + c₁x₁ + c₂s a

[0019] Where: c1>0, c2>0 are design parameters, and the sliding surface and It is an n×1 column vector;

[0020] Define a new state variable as s = z1, By employing the extended state observer technique, the estimation of lumped uncertainty is achieved, and the definition is... and The output of the extended state observer yields an observer with fixed-time convergence characteristics:

[0021]

[0022] Where: column vector constant λ i ,γ i ,α,ψ iDesign the observer parameters such that γ1=2ε1, λ1 = 2.5, λ2 = 1.1, α is an arbitrarily small positive number, ε1 > 0; parameters ψ1 and ψ2 satisfy ψ1 + ψ2 = 1, and ψ1 is the switching function. T s Indicated as switching time;

[0023] Accurate estimation of lumped uncertainty composed of internal uncertainty and faults using an observer;

[0024] Design a fixed-time fault-tolerant controller for the observer:

[0025]

[0026] Where: k1, k2, k3 > 0 are positive numbers.

[0027] The fixed-time fault-tolerant controller of the observer controls the rope assembly controller, achieving fixed-time stable convergence of the system state under internal uncertainties, and maintaining high-performance tracking even when the actuator has a fault.

[0028] The dynamic equations of motion are transformed into:

[0029]

[0030] in: This is due to internal uncertainty.

[0031] The dynamic equations of motion are transformed into:

[0032]

[0033] in: Given column vectors, Let I represent lumped uncertainty, where I is an n×n identity matrix.

[0034] The n×1 column vector s a The i-th component is:

[0035]

[0036] Among them: 0<μ1<1,μ2>1, ε>0, And sgn(x) 1i ) is a symbolic function, with parameters and Auxiliary vector The component is

[0037] The dynamic equation of the sliding variable of the sliding surface is as follows:

[0038]

[0039] An electronic device, characterized in that it includes a processor and a memory, wherein the processor is configured to implement the data migration method step in the step by executing a computer program stored in the memory.

[0040] A readable storage medium, characterized in that a computer program is stored on the readable storage medium, and when the computer program is executed by a processor, it implements the data migration method step in the above steps.

[0041] Beneficial effects

[0042] This invention proposes a fixed-time fault-tolerant control method for a spatial tethered robot under actuator failure. First, based on the Euler-Lagrange method, the dynamic motion equations of the tethered robot after capturing a target and forming a tethered assembly with the target are established. Second, a mechanical model of the internal uncertainties of the tethered assembly system and the actuator failure is constructed, and an observer with fixed-time convergence characteristics is designed to accurately estimate the lumped uncertainty composed of internal uncertainties and failure. Based on this, to ensure rapid convergence of the system state under lumped uncertainty, a fixed-time non-singular terminal sliding mode surface is designed. Finally, combining the characteristics of sliding mode control and the observer, a fixed-time fault-tolerant control scheme based on the observer is proposed, which can achieve fixed-time stable convergence of the system state under internal uncertainties and maintain high-performance tracking even when the actuator fails.

[0043] This invention relates to a control method for a tethered robot system formed after target capture. Compared with the prior art, this invention has the following advantages:

[0044] 1. This invention can be used to solve the problem of rapid and stable control of rope system assemblies under conditions of actuator malfunction and internal uncertainty;

[0045] 2. The designed state observer can accurately estimate lumped uncertainties, including actuator failures, online in real time, and avoids fault detection and isolation operations;

[0046] 3. The designed fixed-time fault-tolerant controller can realize online real-time processing of sudden faults, ensuring that the rope assembly can achieve rapid and stable control within a fixed time. Attached Figure Description

[0047] Figure 1 This is the observer's estimation curve for the system's lumped uncertainty; the figure shows that the estimation error converges to |e| in 16 seconds. 1i |≤2×10 -4Within the small region (i = 1, 2, 3).

[0048] Figure 2 The figure shows the attitude response curve of the rope assembly; it can be seen from the figure that the attitude angle of the assembly can converge in 16 seconds and converge to |q. i |≤8×10 -3 Within the small region (i = 1, 2, 3).

[0049] Figure 3 The figure shows the angular velocity response curve of the rope assembly; it can be seen from the figure that the angular velocity of the assembly converges to within 16 seconds. Within a small area.

[0050] Figure 4 The control input curve of the rope assembly shows that the unevenness of the control input is within a reasonable range. Detailed Implementation

[0051] The present invention will now be further described in conjunction with the embodiments and accompanying drawings:

[0052] To achieve the above objectives, the technical solution adopted by this invention mainly includes the following steps:

[0053] (1) Establish a dynamic model of the rope assembly and analyze the failure types of the actuator;

[0054] (2) Design a fixed-time state observer with accurate estimation performance;

[0055] (3) Design a fixed-time fault-tolerant controller based on the observer to ensure fast, high-precision and stable control of the rope assembly system under the condition of mechanical failure;

[0056] (4) Perform stability analysis on the closed-loop system.

[0057] Step (1) Establish the following dynamic equations for the spatial rope system assembly based on the Euler-Lagrange method.

[0058]

[0059] in Represents the system's generalized coordinate system; The control input force / torque for the system, It is a symmetric positive definite inertial matrix; Represents the Coriolis force matrix. The torque is the gravitational torque. Since the system control input torque is usually generated by the actuator, considering partial or even complete actuator failure, the control torque model can be expressed as follows:

[0060]

[0061] in A diagonal matrix representing the execution control commands generated by n executors. Let be the actuator effectiveness matrix. Where 0 ≤ ρ i ≤1 represents the fault level of the i-th (i = 1, ..., n) actuator, ρ i =1 indicates that the i-th actuator is working healthily; ρ i =0 indicates that the i-th actuator is turned off or completely disabled; 0 < ρ i <1 indicates that the i-th actuator has lost some of its effectiveness (i.e., the actuator is partially ineffective). This is a bounded drift fault value. This patent considers the possibility of partial failure and drift faults in the actuator.

[0062] Furthermore, considering the internal parameter uncertainties of the rope-tied assembly system, the system matrix can be expressed as M(q) = M0(q) + ΔM(q). And G(q) = G0(q) + ΔG(q). Where ΔM(q), ΔG(q) and ΔG(q) represent the system's parameter uncertainties, therefore, the dynamic model of the combined system under actuator failure and uncertainty can be transformed into:

[0063]

[0064] in This represents internal uncertainty. To facilitate a unified handling of system faults and uncertainties, equation (3) can be rewritten as follows:

[0065]

[0066] in Given column vectors, Let I represent lumped uncertainty, and I be an n×n identity matrix. For ease of discussion, the system state variables will be abbreviated as q and q' in the following text. d M0, C0, and G0, etc.

[0067] Define the desired trajectory of the combined system as q d The tracking error can be expressed as (t), where t is the tracking error. The rate of change of tracking error is expressed as Based on equation (4) and the above definition, the error dynamic model of the rope assembly system can be obtained.

[0068]

[0069] In the above formula Given column vectors, the new set total uncertainty This includes system parameter uncertainties and actuator failures. Before presenting the controller design, the following relevant lemmas and assumptions are given:

[0070] Lemma 1: For any nonlinear system in If there exist constants 0 < π1 < 1, π2 > 1, θ1, θ2 > 0 and a Lyapunov function W(y) such that the following equation holds:

[0071]

[0072] The system state will converge to the equilibrium point y = 0 within a fixed time. The upper bound of the convergence time can be expressed as:

[0073]

[0074] Lemma 2: For an nth-order differentiator error system of the following form

[0075]

[0076] Where the constant L > 0, and α is any small positive number. This represents the estimation error of the differentiator. If the following three conditions are satisfied: (i) positive number... Choice Guarantee (ii) positive number The choice needs to guarantee the polynomial (iii) The eigenvalues ​​are all negative; Where T u To select parameters.

[0077] The system's differential error will occur within a fixed time T. u1 >0 converges to 0, that is

[0078] Assumption 1. System lumped uncertainty Its derivative is bounded and satisfies

[0079]

[0080] Step (2) involves designing a fixed-time observer capable of accurately estimating lumped uncertainties. To achieve fast and high-performance control of the system, a novel non-singular terminal sliding surface is designed as follows:

[0081] s = x² + c₁x₁ + c₂s a (9)

[0082] Where: c1>0, c2>0 are design parameters, and the sliding surface and Let s be an n×1 column vector.a The i-th (i = 1, ..., n) component can be represented as:

[0083]

[0084] In the above formula, 0 < μ1 < 1, μ2 > 1, and ε > 0.

[0085] And sgn(x) 1i ) is a symbolic function;

[0086] parameter

[0087]

[0088] Auxiliary vector The components are:

[0089]

[0090] The dynamic equation for a sliding variable can be expressed as:

[0091]

[0092] Define a new state variable as s = z1, The extended state observer technique is used to estimate lumped uncertainty. Definition and For the output of the extended state observer, the extended state observer for system (11) is constructed as follows.

[0093]

[0094] In the above formula, column vectors constant λ i ,γ i ,α,ψ i (1=1,2) are the observer design parameters, and satisfy γ1=2ε1, λ1 = 2.5, λ2 = 1.1, α is an arbitrarily small positive number, ε1 > 0. Parameters ψ1 and ψ2 satisfy ψ1 + ψ2 = 1, and ψ1 is the switching function. T s This represents the switching time.

[0095] Step (3): Based on the designed sliding surface and the expanded state observer, design a fixed-time fault-tolerant controller of the following form.

[0096]

[0097] Where: k1, k2, k3 > 0 are positive numbers. The main theorem of this invention can be expressed as follows:

[0098] Theorem 1. Considering the rope system assembly model (5) and factors such as parameter uncertainty and actuator failure, if a fixed-time extended state observer (12), a fast non-singular terminal sliding surface (9), and a fault-tolerant controller (13) are used, under the condition of satisfying Assumption 1, the system sliding variable s will converge to the sliding surface s = 0 within a fixed time T1; subsequently, the system states x1 and x2 converge to the equilibrium point along the sliding surface within a fixed time T2.

[0099] Step (4) proves the stability of the closed-loop system.

[0100] First, according to the definition of observer estimation error The dynamic expression for the observation error is:

[0101]

[0102] By Lemma 2 and Assumption 1, we can obtain that when t > T u1 When the system observation error reaches e1(t) = e2(t) = 0, the system lumped uncertainty can be accurately estimated. Furthermore, from (14), it can be seen that during the convergence time T of the observer... u1 Within this range, the system observation error will not escape to infinity. Substituting the controller into the system dynamic equation (11), we can obtain...

[0103]

[0104] Furthermore, construct novel Lyapunov functions. Taking the differential of the Lyapunov function V1 along the system equations, we can obtain...

[0105]

[0106] Because the observer is at time T u1 Since e2 is bounded, V1 is also bounded, therefore the system state will not diverge. When t > T u1 Since the system's lumped uncertainty is fully estimated and precisely compensated by the state observer, we can obtain e2 = 0. Substituting this into equation (16) and combining it with Lemma 1, we can obtain...

[0107]

[0108] in Therefore, it can be concluded that the system's sliding variable s(t) will... It converges inward to s(t) = 0.

[0109] Finally, this invention will prove that after the sliding variables converge to the non-singular terminal sliding surface (9), the system states x1 and x2 will converge to the origin in a fixed time. According to the definition of a sliding surface, when... The system dynamic equations can be expressed as follows:

[0110] x2 = -c1x1 - c2s a (18)

[0111] according to From equation (10), we can see that equation (18) can be rewritten as:

[0112]

[0113] Constructing Lyapunov functions Differentiating it along the dynamic equation (19), we can see that

[0114]

[0115] in

[0116] According to Lemma 1:

[0117] Tethered robots can operate at fixed times The state is achieved at a predetermined time: x1(t) = x2(t) = 0.

[0118] Therefore, the stability of the system has been proven.

[0119] From the appendix Figures 1-4 From the curve, it can be seen that the high-precision stable control method for the space tethered robot of the present invention has the following beneficial effects:

[0120] Figure 1 The graph shows the estimation error curve of the observer. It can be seen from the graph that the estimation error converges to |e| in 16 seconds. 1i |≤2×10 -4 Within the small region (i = 1, 2, 3).

[0121] Figure 2 The figure shows the attitude response curve of the rope assembly. It can be seen from the figure that the assembly's attitude angle converges within 16 seconds and converges to |q|. i |≤8×10 -3 Within the small region (i = 1, 2, 3).

[0122] Figure 3 The graph shows the attitude response curve of the rope assembly. It can be seen from the graph that the angular velocity of the assembly converges to [value missing] within 16 seconds. Within a small area.

[0123] Figure 4 The control input curve of the rope assembly is shown in the figure. It can be seen from the figure that the unevenness of the control input is within a reasonable range.

Claims

1. A fixed-time fault-tolerant control method for a spatial rope assembly under actuator failure, characterized in that... The steps are as follows: Based on the Euler-Lagrange method, the dynamic motion equations of the space tethered robot after capturing a target and forming a tethered assembly with the target are established: in: Represents the system's generalized coordinate system; The control input force / torque for the system, It is a symmetric positive definite inertial matrix; Represents the Coriolis force matrix. This is the gravitational torque; Define the desired trajectory of the combined system as The rate of change of tracking error The tracking error is Dynamic model of rope-tied system error: in: Given column vectors, the new set total uncertainty This includes system parameter uncertainties and actuator malfunctions; Construct a model of internal uncertainties and actuator failures in the rope-tied assembly system: in: Indicates by The execution control commands generated by each executor, a diagonal matrix The actuator effectiveness matrix; where It is the first The degree of failure of each actuator Indicates the first Each actuator is functioning healthily; Indicates the first One actuator is shut down or completely disabled; Indicates the first The actuator losing partial effectiveness means that the actuator is partially ineffective. The value is a bounded drift fault value; A fixed-time non-singular terminal sliding surface was designed: in: , For design parameters, sliding surface and for Column vector; Define the new state variable as By using the extended state observer technique, the estimation of lumped uncertainty is achieved, and the definition is... and The output of the extended state observer yields an observer with fixed-time convergence characteristics: Where: column vector ,constant Design parameters for the observer, and satisfy... , , For any small positive number, ;parameter and satisfy ,and For switching functions , Indicated as switching time; Accurate estimation of lumped uncertainty composed of internal uncertainty and faults using an observer; Design a fixed-time fault-tolerant controller for the observer: in: It is a positive number. ; The fixed-time fault-tolerant controller of the observer controls the rope assembly controller, achieving fixed-time stable convergence of the system state under internal uncertainties, and maintaining high-performance tracking even when the actuator has a fault.

2. The fixed-time fault-tolerant control method for a spatial rope assembly under actuator failure as described in claim 1, characterized in that: The dynamic equations of motion are transformed into: in: This is due to internal uncertainty.

3. The fixed-time fault-tolerant control method for a spatial rope assembly under actuator failure as described in claim 1, characterized in that: The dynamic equations of motion are transformed into: in: Given column vectors, This indicates aggregate uncertainty. for The identity matrix.

4. The fixed-time fault-tolerant control method for a spatial rope assembly under actuator failure as described in claim 1, characterized in that: The column vector The The components are: in: , , and For symbolic functions, parameters and Auxiliary vector The component is ; .

5. The fixed-time fault-tolerant control method for a spatial rope assembly under actuator failure as described in claim 1, characterized in that: The dynamic equation of the sliding variable of the sliding surface is as follows: 。 6. An electronic device, characterized in that, It includes a processor and a memory, wherein the processor is used to execute a computer program stored in the memory to implement the steps of the fixed-time fault-tolerant control method for a space rope assembly under actuator failure as described in any one of claims 1 to 5.

7. A readable storage medium, characterized in that, The readable storage medium stores a computer program that, when executed by a processor, implements the steps of the fixed-time fault-tolerant control method for a space rope assembly under actuator failure as described in any one of claims 1 to 5.

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