Rigid-flexible coupled spacecraft preset time attitude tracking control method and system based on modal observer

Abstract

The invention provides a rigid-flexible coupled spacecraft preset time attitude tracking control method and system based on a modal observer. The control method comprises the following steps: rigid-flexible coupled spacecraft attitude dynamics modeling; the modal observer is used for estimating the values of the modal coordinate eta and the modal speed chi in real time, and the problem that the modal coordinate eta and the modal speed chi cannot be measured through a sensor is solved; and designing the controller based on the assumption that the disturbance torque is bounded. According to the method, it can be ensured that the actual attitude is converged to be near the expected attitude with sufficiently high precision within the preset time T after the rigid-flexible coupled spacecraft receives the attitude tracking task instruction, and the value of T can be flexibly adjusted according to specific task requirements; the singularity problem of the controller is avoided, and the reliability of the controller in practical application is ensured; the continuity of the control torque is guaranteed, the chattering phenomenon is avoided, and the burden of an executing mechanism in practical application is reduced.

Description

Technical Field

[0001] The present invention belongs to the field of spacecraft attitude control, and in particular relates to a method and system for tracking and controlling a rigid-flexible coupling spacecraft preset time attitude based on a modal observer. Background Art

[0002] In addition to the central rigid body, modern spacecraft usually also include some flexible accessories, such as solar panels, communication antennas, etc. The physical quantity (modal coordinates) that characterizes the deformation information of the flexible accessories is difficult to measure through sensors, and the modal coordinates determine the coupling torque of the flexible accessories to the central rigid body. When the size of the flexible attachment is relatively small, the coupling torque it generates to the central rigid body will also be relatively small, and it 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 the attitude tracking control method of rigid-flexible coupling spacecraft, according to the speed at which the attitude of the spacecraft tends to the expected value, the existing technologies can be divided into four categories: asymptotic control, finite time control, fixed time control and preset time control. The convergence time required for asymptotic control is infinite, so its application is limited in engineering tasks that have clear requirements for convergence speed. Finite time control can ensure that the convergence process is completed within a finite time upper bound, but this convergence time upper bound is usually directly related to the initial conditions of the system. Fixed time control is a special case of finite time control, and its convergence time upper bound is independent of the initial conditions, but the convergence time upper bound is usually a more complex function expression of each control parameter. How to determine the value of each control parameter from the required convergence time is a more difficult problem. Preset time control can be considered as a special case of fixed time control. It can ensure that under any initial conditions, the controlled variable can converge to the expected value or a sufficiently small neighborhood near the expected value within a certain time upper bound, and this time upper bound is explicitly present in the controller parameters, and technicians can easily adjust it according to task requirements.

[0005] Terminal sliding mode is an effective method to achieve preset time control. This method usually requires mathematical lemmas about the convergence of preset time as an aid, and the terminal sliding mode constructed based on these mathematical lemmas usually contains terms with exponents less than 1, and its derivatives are used in the control law, which will lead to singularity problems in the control law. At the same time, in order to suppress disturbances, the controller designed based on the sliding mode method usually includes a robust term, which is often discontinuous, which will lead to the controller's chattering problem. Summary of the invention

[0006] In order to solve the problems existing in the prior art, the present invention proposes a preset time attitude tracking control method of a rigid-flexible coupling spacecraft based on a modal observer based on a terminal sliding mode control method, comprising the following steps:

[0007] Step 1. Modeling of attitude dynamics of rigid-flexible coupling spacecraft;

[0008] Step 2. Use the modal observer to estimate the values ​​of the modal coordinate η and the modal velocity χ in real time to solve the problem that the modal coordinate η and the modal velocity χ cannot be measured by the sensor;

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

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

[0011] 1.1 Use modified Rodriguez parameters (MRPs) to represent the attitude of the rigid-flexible coupling spacecraft, and establish the attitude kinematics and dynamics model of the rigid-flexible coupling spacecraft;

[0012] 1.2 With q d (t) represents the desired posture, ω d (t) represents the expected angular velocity corresponding to it, and the attitude tracking error and angular velocity tracking error are calculated;

[0013] 1.3 Definition of modal velocity Establish error kinematics and dynamics equations;

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

[0015]

[0016] where q is the spacecraft attitude expressed 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 coordinate representing the deformation of the flexible attachment, δ is the rigid-flexible coupling matrix between the central rigid body and the flexible attachment, and C = diag{2ξ1Λ1,...,2ξ m Λ m} is the damping matrix, is the stiffness matrix, m is the order of the intercepted flexible attachment modal coordinates, Λ j and j (j=1,...,m) are the jth order natural frequency of the flexible attachment and the corresponding damping ratio.

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

[0018]

[0019] ω e =ω-C qe ω d (5)

[0020] in Indicates the corresponding posture tracking error q e The rotation matrix of .

[0021] The error kinematics and dynamics equations described in step 1.3 are:

[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 Construction variables Among them, γ1, γ2, and γ3 are all m-dimensional column vectors, and the variable γ is set to satisfy the given adaptive law;

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

[0029] Furthermore, the adaptive rule 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 coordinate η and modal velocity χ in step 2.2 are:

[0036]

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

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

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

[0040] 3.2 construct 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 in step 3.1 is specifically:

[0043] Assuming that 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 ) χ +δ T Ke η , it can be treated as a total disturbance in the controller design process, and it can be assumed that d t The bi-norm of has an unknown upper bound D.

[0046] Furthermore, the terminal sliding surface in step 3.2 is specifically:

[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 in step 3.3 is specifically:

[0052]

[0053] in The following adaptive rules are met:

[0054]

[0055] Wherein 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 coupling spacecraft system can be set within a preset time T = T p1 +T p2 It converges to a small enough neighborhood near the origin.

[0057] The present invention also relates to a system for a rigid-flexible coupling spacecraft preset time attitude tracking control method based on a modal observer, and the system includes a computer module containing the rigid-flexible coupling spacecraft preset time attitude tracking control method based on a modal observer.

[0058] Effect of the invention:

[0059] 1. The present invention can ensure that the actual attitude of the rigid-flexible coupling spacecraft converges to the vicinity of the expected attitude with sufficiently high accuracy within a preset time after receiving the attitude tracking mission instruction. The preset time can be flexibly adjusted according to specific mission requirements.

[0060] 2. The present invention adopts piecewise functions to replace the items with exponents less than 1 in the traditional terminal sliding mode, thereby avoiding the singularity problem of the controller and ensuring the reliability of the controller in practical applications.

[0061] 3. The present invention adopts a hyperbolic tangent function to replace the sign function in the robust term of the traditional sliding mode controller, thereby ensuring the continuity of the control torque, avoiding the chattering phenomenon, and reducing the burden of the actuator in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 Preset the time attitude tracking control system block diagram for the rigid-flexible coupling spacecraft;

[0063] Figure 2 is the attitude tracking error response curve of the embodiment;

[0064] Figure 3 Angular velocity tracking error response curve of the embodiment;

[0065] Figure 4 Control torque curve for the embodiment;

[0066] Figure 5 1 is the modal coordinate response curve of the embodiment. DETAILED DESCRIPTION

[0067] The present embodiment is described below with reference to the accompanying drawings.

[0068] Figure 1 The figure shows the block diagram of the preset time attitude tracking control system of the rigid-flexible coupling spacecraft. Figure 1It can be seen that the system includes a modal observer and a preset time controller. The function of the modal observer is to estimate the values ​​of the modal coordinates η and the modal velocity χ in real time. The modal observer uses the angular velocity information of the rigid-flexible coupling spacecraft fed back by the onboard sensor to play its role. The preset time controller is constructed based on the desired attitude and the actual attitude and angular velocity of the rigid-flexible coupling spacecraft fed back by the onboard sensor. At the same time, the preset time controller also includes a compensation term constructed based on the estimated value of the modal observer to offset the interference of the flexible attachment vibration on the attitude control. According to the algorithm in the present invention, the control torque is calculated to act on the rigid-flexible coupling spacecraft, and the preset time attitude tracking control can be achieved under the interference of external disturbances and parameter uncertainties.

[0069] The present invention proposes a method for tracking and controlling a rigid-flexible coupling spacecraft with preset time attitude based on a modal observer, comprising the following steps:

[0070] S1. Modeling of attitude dynamics of rigid-flexible coupling spacecraft;

[0071] 1.1 Use modified Rodriguez parameters (MRPs) to represent the attitude of the rigid-flexible coupling spacecraft, and establish the attitude kinematics and dynamics model of the rigid-flexible coupling spacecraft;

[0072] The attitude kinematics and dynamics models of the rigid-flexible coupling spacecraft are:

[0073]

[0074] where q is the spacecraft attitude expressed 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 coordinate representing the deformation of the flexible attachment, δ is the rigid-flexible coupling matrix between the central rigid body and the flexible attachment, and C = diag{2ξ1Λ1,...,2ξ m Λ m} is the damping matrix, is the stiffness matrix, m is the order of the intercepted flexible attachment modal coordinates, Λ j and j (j=1,...,m) are the jth order natural frequency of the flexible attachment and the corresponding damping ratio.

[0075] 1.2 With q d (t) represents the desired posture, ω d (t) represents the expected angular velocity corresponding to it, 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 Indicates the corresponding posture tracking error q e The rotation matrix of .

[0080] 1.3 Definition of modal velocity Establish error kinematics and dynamics equations;

[0081] The error kinematics and dynamics equations are:

[0082]

[0083] in:

[0084]

[0085] H=-ω × δ T χ+δ T (Cχ+Kη-Cδω).

[0086] S2. Use the modal observer to estimate the values ​​of the modal coordinate η and the modal velocity χ in real time to solve the problem that the modal coordinate η and the modal velocity χ cannot be measured by the sensor;

[0087] 2.1 Construction variables Among them, γ1, γ2, and γ3 are all m-dimensional column vectors, and the variable γ is set to satisfy the given adaptive law;

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

[0089] Furthermore, the adaptive rule 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 coordinate η and modal velocity χ in step 2.2 are:

[0096]

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

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

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

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

[0101] Assuming that 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 ) χ +δ T Ke η , it can be treated as a total disturbance in the controller design process, and it can be assumed that d t The bi-norm of has an unknown upper bound D.

[0104] 3.2 construct 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 Satisfy the following adaptive rules:

[0114]

[0115] Wherein 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 coupling spacecraft system can be set within a preset time T = T p1 +T p2 It converges to a small enough neighborhood near the origin.

[0117] The present invention is verified by numerical simulation. The numerical simulation problem, simulation design process and simulation results are described as follows:

[0118] In this embodiment, the parameter J in the error kinematics and dynamics equations described in step 1.3 is mb The values ​​are:

[0119]

[0120] The order of the modal coordinates of the flexible attachment intercepted 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, Λ4 = 2.5496 rad / s, and the corresponding damping ratios are: ξ1 = 0.005607, ξ2 = 0.008620, ξ3 = 0.01283, ξ4 = 0.02516. The desired attitude is q d (t)=0.1[cos(0.05t) sin(0.05t) -cos(0.05t)] T The disturbance torque is set to d = 0.3 [sin (t / 4) cos (t / 3) - sin (t / 5)] T Nm. The 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 value of the attitude of the rigid-flexible coupling spacecraft is set to q(0)=[12-0.5] T , the initial value of the angular velocity of the rigid-flexible coupling spacecraft is set to ω(0) = [0 0 0] T rad / s. The initial value of the variable γ is taken as a 12-dimensional column vector with all components zero. The initial value of is taken as 0.1.

[0123] Under the above conditions, the numerical simulation results are as follows: Figure 2 — Figure 5 shown. Figure 2 , Figure 3 The following are the response curves of attitude tracking error and angular velocity tracking error, respectively. It can be seen that the attitude tracking error of the rigid-flexible coupling spacecraft is within the preset time (T = T p1 +T p2 =200s) and converged to the origin. Figure 4 The figure shows the control torque required in this process. It can be seen that the control torque is continuous, avoiding the vibration phenomenon. Figure 5 Shown are the response curves of the four components of the modal coordinate η representing the deformation of the flexible attachment during this process.

[0124] The above contents are only preferred embodiments of the present invention and are not intended to limit the implementation scheme of the present invention. A person skilled in the art can easily make corresponding changes or modifications based on the main concept and spirit of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope required by the claims.

Claims

1. A method for tracking and controlling a rigid-flexible coupling spacecraft with preset time attitude based on a modal observer, comprising the following steps: Step 1. Modeling of attitude dynamics of rigid-flexible coupling spacecraft; Step 2. Use the modal observer to estimate the values ​​of the modal coordinate η and the modal velocity χ in real time to solve the problem that the modal coordinate η and the modal velocity χ cannot be measured by the sensor; Step 3. Design the controller based on the assumption that the disturbance torque is bounded.

2. The method for tracking and controlling a rigid-flexible coupling spacecraft with preset time attitude based on a modal observer according to claim 1, characterized in that: Step 1 includes the following steps: 1.1 Use modified Rodriguez parameters (MRPs) to represent the attitude of the rigid-flexible coupling spacecraft, and establish the attitude kinematics and dynamics model of the rigid-flexible coupling spacecraft; 1.2 With q d (t) represents the desired posture, ω d (t) represents the expected angular velocity corresponding to it, and the attitude tracking error and angular velocity tracking error are calculated; 1.3 Definition of modal velocity Establish error kinematics and dynamics equations; The attitude kinematics and dynamics model of the rigid-flexible coupling spacecraft described in step 1.1 is: where q is the spacecraft attitude expressed 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 coordinate representing the deformation of the flexible attachment, δ is the rigid-flexible coupling matrix between the central rigid body and the flexible attachment, and C = diag{2ξ1Λ1,...,2ξ m Λ m } is the damping matrix, is the stiffness matrix, m is the order of the intercepted flexible attachment modal coordinates, Λ j and j (j=1,...,m) are the jth order natural frequency of the flexible attachment and the corresponding damping ratio. The attitude tracking error and angular velocity tracking error in step 1.2 are: oh e =ω-C qe oh d (5) in Indicates the corresponding posture tracking error q e The rotation matrix of . The error kinematics and dynamics equations described in step 1.3 are: in: H=-ω × d T x+d T (Cx+Kn-Csω).

3. The method for tracking and controlling a rigid-flexible coupling spacecraft with preset time attitude based on a modal observer according to claim 1, characterized in that: Step 2 includes the following steps: 2.1 Construction variables Among them, γ1, γ2, and γ3 are all m-dimensional column vectors, and the variable γ is set to satisfy the given adaptive law; 2.2 Based on the variable γ, construct estimates of the modal coordinates η and modal velocity χ.

4. The method for tracking and controlling a rigid-flexible coupling spacecraft with preset time attitude based on a modal observer according to claim 3, characterized in that: The adaptive rules described in step 2.1 are as follows: in: B=[K C I m ] (11) 5. The method for tracking and controlling a rigid-flexible coupling spacecraft with preset time attitude based on a modal observer according to claim 3, characterized in that: The estimated values ​​of the modal coordinates η and modal velocities χ described in step 2.2 are: They converge asymptotically to η and χ respectively.

6. The method for tracking and controlling a rigid-flexible coupling spacecraft with preset time attitude based on a modal observer according to claim 1, characterized in that: Step 3 includes the following steps: 3.1 Consider the estimated error of the modal observer as part of the total disturbance and perform mathematical transformation on the error dynamics equation; 3.2 construct terminal sliding surface; 3.3 Design a preset time controller based on the terminal sliding surface constructed in step 3.

2.

7. The method for tracking and controlling a rigid-flexible coupling spacecraft with preset time attitude based on a modal observer according to claim 6, characterized in that: The mathematical transformation of the error dynamics equation in step 3.1 is specifically: Assuming that the disturbance torque d is bounded, let Then the error dynamics equation (7) can be written as: where d t =d+(δ T C-ω × δ T ) χ +δ T Ke η , it can be treated as a total disturbance in the controller design process, and it can be assumed that d t The bi-norm of has an unknown upper bound D.

8. The method for tracking and controlling a rigid-flexible coupling spacecraft with preset time attitude based on a modal observer according to claim 6, characterized in that: The terminal sliding surface in step 3.2 is specifically: Where 0<μ<1, T p1 >0,k1>0, Where ε>0,β1=-2with -1-2μ ,β2=(1+2μ)ε -2μ 。 9. The method for tracking and controlling a rigid-flexible coupling spacecraft with preset time attitude based on a modal observer according to claim 6, characterized in that: The preset time controller in step 3.3 is specifically: in The following adaptive rules are met: Wherein c and g are both constants greater than 0.

10. A system for implementing the method for tracking and controlling a rigid-flexible coupling spacecraft preset time attitude based on a modal observer as claimed in any one of claims 1 to 9, characterized in that: The system includes a computer module containing a rigid-flexible coupling spacecraft preset time attitude tracking control method based on a modal observer.

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