A modal observer-based preset time attitude tracking control method and system for rigid-flexible coupling spacecraft

Abstract

This invention proposes a pre-set time attitude tracking control method and system for rigid-flexible coupled spacecraft based on a modal observer. The control method includes the following steps: attitude dynamics modeling of the rigid-flexible coupled spacecraft; real-time estimation of the modal coordinates η and modal velocities χ using a modal observer to solve the problem that modal coordinates η and modal velocities χ cannot be measured by sensors; and controller design based on the assumption of bounded perturbation torque. This invention can ensure that the actual attitude of the rigid-flexible coupled spacecraft converges to the vicinity of the desired attitude with sufficient accuracy within a pre-set time T after receiving the attitude tracking mission command, and the value of T can be flexibly adjusted according to specific mission requirements; it avoids the singularity problem of the controller, ensuring the reliability of the controller in practical applications; it ensures the continuity of the control torque, avoids chattering, and reduces the burden on the actuators in practical applications.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft attitude control, specifically relating to a rigid-flexible coupled spacecraft attitude tracking control method and system based on a modal observer at a preset time. Background Technology

[0002] Modern spacecraft, in addition to a central rigid body, typically include flexible attachments such as solar panels and communication antennas. The physical quantities characterizing the deformation information of these flexible attachments (modal coordinates) are difficult to measure using sensors, and these modal coordinates determine the coupling torque of the flexible attachments with respect to the central rigid body. When the size of the flexible attachments is relatively small, the coupling torque they generate with respect to the central rigid body is also relatively small, and can be treated as a disturbance during attitude control.

[0003] However, when the size of the flexible attachment is relatively large, in order to ensure sufficient control accuracy, a modal observer is usually designed to estimate the modal coordinates in real time, and a compensation term is constructed in the control law based on the estimated value.

[0004] For rigid-flexible coupled spacecraft attitude tracking control methods, existing technologies can be categorized into four types based on the speed at which the spacecraft's attitude approaches the desired value: asymptotic control, finite-time control, fixed-time control, and preset-time control. Asymptotic control requires an infinite convergence time, thus limiting its application in engineering tasks with specific convergence speed requirements. Finite-time control guarantees convergence within a finite upper bound, but this upper bound is usually directly related to the system's initial conditions. Fixed-time control is a special case of finite-time control, where the upper bound of convergence time is independent of the initial conditions; however, this upper bound is typically a complex functional expression of the control parameters, making it difficult to determine the values ​​of each parameter from the required convergence time. Preset-time control can be considered a special case of fixed-time control. It guarantees that under any initial conditions, the controlled variable converges to the desired value or a sufficiently small neighborhood of the desired value within a certain upper bound, and this upper bound is explicitly present in the controller parameters, allowing technicians to easily adjust it according to task requirements.

[0005] Terminal sliding mode is an effective method for achieving preset-time control. This method typically requires mathematical lemmas regarding convergence at the preset time as an aid. However, terminal sliding modes constructed based on these lemmas often contain terms with exponents less than 1, and their derivatives are used in the control law, leading to singularity issues in the control law. Furthermore, to suppress disturbances, controllers designed based on sliding mode methods usually include a robust term, which is often discontinuous, resulting in chattering problems in the controller. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention proposes a pre-set time attitude tracking control method for rigid-flexible coupled spacecraft based on a modal observer, based on the terminal sliding mode control method, comprising the following steps:

[0007] Step 1. Stiff-flexible coupled spacecraft attitude dynamics modeling;

[0008] Step 2. Use a modal observer to estimate the values ​​of modal coordinates η and modal velocities χ in real time, solving the problem that modal coordinates η and modal velocities χ cannot be measured by sensors;

[0009] Step 3. Design the controller based on the assumption that the disturbance torque is bounded.

[0010] Further, step 1 includes the following steps:

[0011] 1.1 The attitude of the rigid-flexible coupled spacecraft is represented by modified Rodriguez parameters (MRPs), and the attitude kinematics and dynamics model of the rigid-flexible coupled spacecraft is established;

[0012] 1.2 with q d (t) represents the desired attitude, ω d (t) represents the corresponding expected angular velocity, and the attitude tracking error and angular velocity tracking error are calculated.

[0013] 1.3 Defining Modal Velocity Establish the kinematic and dynamic equations of error;

[0014] The attitude kinematics and dynamics model of the rigid-flexible coupled spacecraft described in step 1.1 is as follows:

[0015]

[0016] Where q represents the spacecraft attitude in MRPs, ω is the angular velocity of the spacecraft relative to the inertial coordinate system, J is the total moment of inertia of the spacecraft relative to its center of mass, τ is the control torque, and d is the disturbance torque; η is the modal coordinates representing the deformation of the flexible appendage, δ is the rigid-flexible coupling matrix between the central rigid body and the flexible appendage, and C = diag{2ξ1Λ1,...,2ξ m Λ m} is the damping matrix. It is the stiffness matrix, m is the order of the modal coordinates of the intercepted flexible attachment, Λ j and ξ j (j=1,...,m) represent the j-th natural frequency of the flexible attachment and its corresponding damping ratio, respectively.

[0017] The attitude tracking error and angular velocity tracking error mentioned in step 1.2 are respectively:

[0018]

[0019] ω e =ω-C qe ω d (5)

[0020] in This represents the corresponding attitude tracking error q. e The rotation matrix.

[0021] The error kinematics and dynamic equations mentioned in step 1.3 are as follows:

[0022]

[0023] in:

[0024]

[0025] H = -ω × δ T χ+δ T (Cχ+Kη-Cδω).

[0026] Furthermore, step 2 includes the following steps:

[0027] 2.1 Constructing Variables Where γ1, γ2, and γ3 are all m-dimensional column vectors, and the variable γ is made to satisfy a given adaptive law;

[0028] 2.2 Based on the variable γ, construct estimates for the modal coordinates η and modal velocities χ.

[0029] Furthermore, the adaptive law described in step 2.1 is as follows:

[0030]

[0031] in:

[0032]

[0033] B = [KCI] m (11)

[0034]

[0035] Furthermore, the estimated values ​​of the modal coordinates η and modal velocities χ mentioned in step 2.2 are:

[0036]

[0037] They asymptotically converge to η and χ, respectively.

[0038] Furthermore, step 3 includes the following steps:

[0039] 3.1 Treat the estimation error of the modal observer as part of the total disturbance and perform a mathematical transformation on the error dynamics equation;

[0040] 3.2 Construct the terminal sliding surface;

[0041] 3.3 Design a preset time controller based on the terminal sliding surface constructed in step 3.2.

[0042] Furthermore, the mathematical transformation of the error dynamics equation described in step 3.1 is as follows:

[0043] Assuming the disturbance torque d is bounded, let Then the error dynamics equation (7) can be written as:

[0044]

[0045] Where d t =d+(δ) T C-ω × δ T )e χ +δ T Ke η In the controller design process, it can be treated as a total disturbance, and d can be assumed. t The 2norm has an unknown upper bound D.

[0046] Furthermore, the terminal sliding surface mentioned in step 3.2 specifically refers to:

[0047]

[0048] Where 0 < μ < 1, T p1 >0, k1>0,

[0049]

[0050] Where ε > 0, β1 = -2με -1-2μ β2=(1+2μ)ε -2μ .

[0051] Furthermore, the preset time controller mentioned in step 3.3 specifically refers to:

[0052]

[0053] in It satisfies the following adaptive law:

[0054]

[0055] Where c and g are both constants greater than 0.

[0056] Under the action of the controller (18), the attitude tracking error of the rigid-flexible coupled spacecraft system can be controlled within a preset time T = T p1 +T p2 It converges to a sufficiently small neighborhood near the origin.

[0057] The present invention also relates to a system for a pre-set time attitude tracking control method for a rigid-flexible coupled spacecraft based on a modal observer, the system comprising a computer module containing the pre-set time attitude tracking control method for a rigid-flexible coupled spacecraft based on a modal observer.

[0058] Invention effects:

[0059] 1. This invention can ensure that the actual attitude of the rigid-flexible coupled spacecraft converges to the vicinity of the desired attitude with sufficient high accuracy within a preset time after receiving the attitude tracking mission command. The preset time can be flexibly adjusted according to specific mission requirements.

[0060] 2. This invention uses piecewise functions to replace terms with exponents less than 1 in traditional terminal sliding mode, thus avoiding the singularity problem of the controller and ensuring the reliability of the controller in practical applications.

[0061] 3. This invention uses a hyperbolic tangent function instead of the sign function in the robust term of the traditional sliding mode controller, which ensures the continuity of the control torque, avoids chattering, and reduces the burden on the actuator in practical applications. Attached Figure Description

[0062] Figure 1 A block diagram of a time attitude tracking and control system for a rigid-flexible coupled spacecraft;

[0063] Figure 2 The example shows the attitude tracking error response curve;

[0064] Figure 3 Here is the angular velocity tracking error response curve for an example.

[0065] Figure 4 The control torque curve is shown in the example.

[0066] Figure 5 The modal coordinate response curve is shown in the example. Detailed Implementation

[0067] The following description, in conjunction with the accompanying drawings, illustrates this embodiment.

[0068] Figure 1 The diagram shown is a block diagram of a pre-set time attitude tracking control system for a rigid-flexible coupled spacecraft. Figure 1As can be seen, the system includes a modal observer and a preset time controller. The modal observer's function is to estimate the values ​​of modal coordinates η and modal velocities χ in real time. The modal observer relies on the angular velocity information of the rigid-flexible coupled spacecraft fed back by onboard sensors to function. The preset time controller is constructed based on the desired attitude and the actual attitude and angular velocity of the rigid-flexible coupled spacecraft fed back by onboard sensors. Simultaneously, the preset time controller also includes a compensation term constructed based on the estimates from the modal observer to offset the interference caused by the vibration of the flexible appendages on attitude control. By calculating the control torque applied to the rigid-flexible coupled spacecraft according to the algorithm in this invention, preset time attitude tracking control can be achieved under external disturbances and parameter uncertainties.

[0069] The rigid-flexible coupling spacecraft preset time attitude tracking control method based on modal observer proposed in this invention includes the following steps:

[0070] S1. Stiff-flexible coupled spacecraft attitude dynamics modeling;

[0071] 1.1 The attitude of the rigid-flexible coupled spacecraft is represented by modified Rodriguez parameters (MRPs), and the attitude kinematics and dynamics model of the rigid-flexible coupled spacecraft is established;

[0072] The attitude kinematics and dynamics model of the rigid-flexible coupled spacecraft is as follows:

[0073]

[0074] Where q represents the spacecraft attitude in MRPs, ω is the angular velocity of the spacecraft relative to the inertial coordinate system, J is the total moment of inertia of the spacecraft relative to its center of mass, τ is the control torque, and d is the disturbance torque; η is the modal coordinates representing the deformation of the flexible appendage, δ is the rigid-flexible coupling matrix between the central rigid body and the flexible appendage, and C = diag{2ξ1Λ1,...,2ξ m Λ m} is the damping matrix. It is the stiffness matrix, m is the order of the modal coordinates of the intercepted flexible attachment, Λ j and ξ j (j=1,...,m) represent the j-th natural frequency of the flexible attachment and its corresponding damping ratio, respectively.

[0075] 1.2 with q d (t) represents the desired attitude, ω d (t) represents the corresponding expected angular velocity, and the attitude tracking error and angular velocity tracking error are calculated.

[0076] The attitude tracking error and angular velocity tracking error are respectively:

[0077]

[0078] ω e =ω-C qe ω d (twenty four)

[0079] in This represents the corresponding attitude tracking error q. e The rotation matrix.

[0080] 1.3 Defining Modal Velocity Establish the kinematic and dynamic equations of error;

[0081] The error kinematics and dynamics equations are as follows:

[0082]

[0083] in:

[0084]

[0085] H = -ω × δ T χ+δ T (Cχ+Kη-Cδω).

[0086] S2. Use a modal observer to estimate the values ​​of modal coordinates η and modal velocities χ in real time, solving the problem that modal coordinates η and modal velocities χ cannot be measured by sensors;

[0087] 2.1 Constructing Variables Where γ1, γ2, and γ3 are all m-dimensional column vectors, and the variable γ is made to satisfy a given adaptive law;

[0088] 2.2 Based on the variable γ, construct estimates for the modal coordinates η and modal velocities χ.

[0089] Furthermore, the adaptive law described in step 2.1 is as follows:

[0090]

[0091] in:

[0092]

[0093] B = [KCI] m (30)

[0094]

[0095] Furthermore, the estimated values ​​of the modal coordinates η and modal velocities χ mentioned in step 2.2 are:

[0096]

[0097] They asymptotically converge to η and χ, respectively.

[0098] S3. Design the controller based on the assumption that the disturbance torque is bounded;

[0099] 3.1 Treat the estimation error of the modal observer as part of the total disturbance and perform a mathematical transformation on the error dynamics equation;

[0100] The mathematical transformation of the error dynamics equation is as follows:

[0101] Assuming the disturbance torque d is bounded, let Then the error dynamics equation (7) can be written as:

[0102]

[0103] Where d t =d+(δ) T C-ω × δ T )e χ +δ T Ke η In the controller design process, it can be treated as a total disturbance, and d can be assumed. t The 2norm has an unknown upper bound D.

[0104] 3.2 Construct the terminal sliding surface;

[0105] The terminal sliding surface is specifically:

[0106]

[0107] Where 0 < μ < 1, T p1 >0, k1>0,

[0108]

[0109] Where ε > 0, β1 = -2με -1-2μ β2=(1+2μ)ε -2μ .

[0110] 3.3 Design a preset time controller based on the terminal sliding surface constructed in step 3.2;

[0111] The preset time controller is specifically:

[0112]

[0113] in It satisfies the following adaptive law:

[0114]

[0115] Where c and g are both constants greater than 0.

[0116] Under the action of the controller (18), the attitude tracking error of the rigid-flexible coupled spacecraft system can be controlled within a preset time T = T p1 +T p2 It converges to a sufficiently small neighborhood near the origin.

[0117] This invention has been verified through numerical simulation. The numerical simulation problem, simulation design process, and simulation results are described below:

[0118] In this embodiment, the parameter J in the error kinematics and dynamic equations described in step 1.3 mb The value is:

[0119]

[0120] The order of the modal coordinates of the flexible attachment captured in the simulation is m=4, and the value of the rigid-flexible coupling matrix between the central rigid body and the flexible attachment is:

[0121]

[0122] The first four natural frequencies are Λ1 = 0.7681 rad / s, Λ2 = 1.1038 rad / s, Λ3 = 1.8733 rad / s, and Λ4 = 2.5496 rad / s, respectively, with corresponding damping ratios of ξ1 = 0.005607, ξ2 = 0.008620, ξ3 = 0.01283, and ξ4 = 0.02516. The desired attitude is taken as q. d (t)=0.1[cos(0.05t) sin(0.05t) -cos(0.05t)] T The disturbance torque is set as d = 0.3[sin(t / 4) cos(t / 3) -sin(t / 5)] T Nm. Controller parameters are selected as follows: T p1 =T p2 =100s, c=0.04, g=0.002, a=0.002, k1=k2=0.01, μ=0.48, ε=0.04. The initial attitude of the rigid-flexible coupled spacecraft is set as q(0)=[12-0.5] T The initial value of the angular velocity of the rigid-flexible coupled spacecraft is set as ω(0) = [0 0 0] T rad / s. The initial value of variable γ is taken as a 12-dimensional column vector with all components equal to zero. The initial value is set to 0.1.

[0123] Under the conditions set above, the numerical simulation results are as follows: Figure 2 — Figure 5 As shown. Figure 2 , Figure 3 The figures show the response curves for attitude tracking error and angular velocity tracking error, respectively. It can be seen that the attitude tracking error of the rigid-flexible coupled spacecraft occurs within a preset time (T = T...). p1 +T p2 It converged to the vicinity of the origin within 200s. Figure 4 The figure shows the control torque required for this process. It can be seen that the control torque is continuous, thus avoiding chattering. Figure 5 The figure shows the response curves of the four components of the modal coordinate η, which represent the deformation of the flexible attachment, during this process.

[0124] The above description is only a preferred embodiment of the present invention and is not intended to limit the implementation of the present invention. Those skilled in the art can easily make corresponding modifications or alterations based on the main concept and spirit of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of protection claimed in the claims.

Claims

1. A method for pre-set time attitude tracking control of a rigid-flexible coupled spacecraft based on a modal observer, comprising the following steps: Step 1. Stiff-flexible coupled spacecraft attitude dynamics modeling; Step 2. Use the modal observer to measure the modal coordinates. and modal velocity Real-time estimation of the values ​​is performed to resolve modal coordinate issues. and modal velocity Problems that cannot be measured by sensors; Step 3. Design the controller based on the assumption that the disturbance torque is bounded; Step 1 includes the following steps: 1.1 The attitude of the rigid-flexible coupled spacecraft is represented by modified Rodriguez parameters (MRPs), and the attitude kinematics and dynamics model of the rigid-flexible coupled spacecraft is established. 1.2 with Indicates the desired posture, This represents the corresponding expected angular velocity; the attitude tracking error and angular velocity tracking error are then calculated. 1.3 Defining Modal Velocity Establish the kinematic and dynamic equations of error; The attitude kinematics and dynamics model of the rigid-flexible coupled spacecraft described in step 1.1 is as follows: in, The spacecraft attitude is represented by MRPs. Let be the angular velocity of the spacecraft relative to the inertial coordinate system. The total moment of inertia of the spacecraft relative to its center of mass. To control the torque, For disturbance torque; The modal coordinates represent the deformation of the flexible attachment. The rigid-flexible coupling matrix between the central rigid body and the flexible attachments. It is the damping matrix. is the stiffness matrix, and m is the order of the modal coordinates of the intercepted flexible attachment. and These are the j-th natural frequency of the flexible attachment and its corresponding damping ratio, respectively. The attitude tracking error and angular velocity tracking error mentioned in step 1.2 are respectively: in Indicates the corresponding attitude tracking error rotation matrix; The error kinematics and dynamic equations mentioned in step 1.3 are as follows: in: ， ， ； Step 3 includes the following steps: 3.1 Treat the estimation error of the modal observer as part of the total disturbance and perform a mathematical transformation on the error dynamics equation; 3.2 Construct the terminal sliding surface; 3.3 Design a preset time controller based on the terminal sliding surface constructed in step 3.2; The terminal sliding surface mentioned in step 3.2 is specifically as follows: in , , , in , , .

2. The method for pre-set time attitude tracking control of a rigid-flexible coupled spacecraft based on a modal observer according to claim 1, characterized in that, Step 2 includes the following steps: 2.1 Constructing Variables ,in , , Both are m-dimensional column vectors, let the variables... It satisfies the given adaptive law; 2.2 Variable-based Construct modal coordinates and modal velocity The estimated value.

3. The rigid-flexible coupling spacecraft preset time attitude tracking control method based on a modal observer according to claim 2, characterized in that, The adaptive law described in step 2.1 is as follows: in: 。 4. The method for preset time attitude tracking control of a rigid-flexible coupled spacecraft based on a modal observer according to claim 2, characterized in that, The modal coordinates mentioned in step 2.2 and modal velocity The estimated value is: , They converge asymptotically to , .

5. The method for pre-set time attitude tracking control of a rigid-flexible coupled spacecraft based on a modal observer according to claim 1, characterized in that, The mathematical transformation of the error dynamics equation described in step 3.1 is as follows: Assuming disturbance torque It is bounded, making , , Then the error dynamics equation (7) can be written as: in In the controller design process, it is treated as a total disturbance, assuming The 2norm has an unknown upper bound D.

6. The method for pre-set time attitude tracking control of a rigid-flexible coupled spacecraft based on a modal observer according to claim 1, characterized in that, The preset time controller mentioned in step 3.3 is specifically as follows: in It satisfies the following adaptive law: in and All are constants greater than 0.

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