A sliding mode control method for spacecraft attitude tracking based on all-wheel drive system

Abstract

The present invention discloses a sliding mode control method for spacecraft attitude tracking based on an all-drive system method, and belongs to the field of spacecraft control technology. Based on the all-drive system method, the method establishes a second-order all-drive system model of the system for a spacecraft attitude tracking system with external disturbances and actuator saturation. An anti-saturation auxiliary system is designed to reduce the influence of actuator saturation. At the same time, an interference observer based on a fixed-time multivariable superhelical system is designed to estimate external disturbances. Based on the all-drive system method, a linear steady-state closed-loop system is obtained through a state feedback controller, and a sliding mode controller based on the all-drive system method is designed, so that the system can stably track the target attitude under the influence of external disturbances, thereby realizing effective control of the spacecraft attitude tracking system.

Description

Technical Field

[0001] The present invention belongs to the field of spacecraft control technology, and relates to a spacecraft attitude tracking control system, and in particular to a spacecraft attitude tracking sliding mode control method based on an all-wheel drive system method. Background Art

[0002] Spacecraft attitude tracking control is an important part of spacecraft navigation and autonomous control. It has been widely used in earth observation satellites, deep space exploration, spacecraft rendezvous and docking, spacecraft formation flying and many other fields. The goal of spacecraft attitude tracking control is to design a control law that can drive the attitude and angular velocity of the spacecraft in real time and track the target state trajectory that changes with time, so that the spacecraft can accurately point to the target and maintain its attitude stably. This is a nonlinear dynamic problem characterized by the uncertainty of internal parameters and the existence of external interference.

[0003] As space missions become increasingly complex, higher requirements are placed on the convergence speed, control accuracy, and anti-disturbance capability of spacecraft attitude tracking control systems. Existing control methods rely on state-space methods, and the design of their controllers is relatively complex. A high-order all-wheel drive system is a descriptive form of the control system model. Once the all-wheel drive system model is established, the control law can be easily designed to eliminate nonlinear terms and achieve closed-loop control of the system. Existing spacecraft attitude tracking control based on the all-wheel drive system method rarely considers the influence of actuator saturation, and generally has a long convergence time. Therefore, it is necessary to continue to study spacecraft attitude tracking control based on the all-wheel drive system method. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention proposes a sliding mode control method for spacecraft attitude tracking based on an all-wheel drive system method. Firstly, a second-order all-wheel drive system model of the spacecraft is established, and the influence of actuator saturation and external disturbance is considered. An anti-saturation auxiliary system and a disturbance observer based on a fixed-time multivariable superhelical system are introduced, and a corresponding sliding mode controller is constructed to achieve stable tracking of the spacecraft to the target attitude.

[0005] A spacecraft attitude tracking sliding mode control method based on an all-drive system method, the specific steps are as follows:

[0006] Step 1: Establish a second-order all-wheel drive system model for spacecraft attitude tracking

[0007] Consider a rigid spacecraft, and define the unit quaternion describing its attitude motion as ,in is the scalar part of the quaternion, is the vector part of the quaternion, and The spacecraft's current angular velocity relative to inertial space is Rotation, assuming that the desired coordinate system is moving at an angular velocity relative to the inertial space Rotation, the rotation quaternion is , define the rotation quaternion from the desired coordinate system to the current spacecraft coordinate system as the error quaternion , the angular velocity error is , then the kinematic model of the spacecraft attitude tracking system described by quaternion is:

[0008]

[0009] in, , Respectively , The first derivative of .

[0010] The dynamic model of the spacecraft attitude tracking system is:

[0011]

[0012] in, is the vector part of the error quaternion, is the spacecraft moment of inertia, express The inverse matrix of , u is the system control input, is the external disturbance to the system, , Respectively , The first derivative of represents an antisymmetric matrix, , is the rotation matrix from the target body coordinate system to the body coordinate system:

[0013]

[0014] Consider the effect of actuator saturation according to the all-wheel drive system approach , we get the following spacecraft attitude tracking second-order all-wheel drive system model:

[0015]

[0016]

[0017] in, Indicates the system saturation control input and the current system control input The difference, represents the actuator saturation function, is the maximum output of the actuator, is the minimum output of the actuator.

[0018] is the known nonlinear term of the second-order all-wheel drive system, where:

[0019] ,

[0020] ,

[0021] ,

[0022] ,

[0023] ,

[0024] ,

[0025] .

[0026] ,

[0027] ,

[0028] ,

[0029] .

[0030] is the unknown disturbance of the system, is the input matrix. express The second derivative of express The first derivative of .

[0031] Step 2: Anti-saturation system design

[0032] Considering the actuator saturation problem of the spacecraft, the following anti-saturation auxiliary system is designed:

[0033]

[0034] Where C1 and C2 are constant diagonal matrices whose diagonal elements are all positive. and To compensate the state variables of the system, , They are , The first derivative of; According to the compensated state variables, define new tracking errors e1, e2, and modify the system model as follows:

[0035]

[0036] in, , are the first derivatives of e1 and e2 respectively, , They are , The second derivative of . is the 3D identity matrix.

[0037] Step 3: Design of disturbance observer based on fixed-time multivariable superhelical system

[0038] Considering the influence of external disturbances, the following disturbance observer based on fixed-time multivariable superhelical system is designed:

[0039]

[0040] in, , yes The estimated value of , , , p is a constant and , is the estimated value of the disturbance observer system state, i.e., the total disturbance, is an upper bound on the derivative of the total disturbance. , They are , The first derivative of .

[0041] Step 4: Sliding mode controller design based on full drive system approach

[0042] Design the following sliding surface:

[0043]

[0044] Among them, A0 and A1 are the parameters of the parametric design method. Based on the sliding surface, the following sliding mode controller is obtained:

[0045]

[0046] in, express The inverse matrix of , . is a positive real number, , are all positive odd numbers, and , It is a column vector whose elements are positive real numbers. Under the condition of satisfying the stability of the system, the values ​​of parameters β, k, g, η, C1, and C2 are designed to obtain the sliding mode controller.

[0047] The present invention has the following beneficial effects:

[0048] Aiming at the spacecraft attitude tracking control system with actuator saturation and external disturbance, a second-order all-drive system model was established based on the all-drive system method, and an anti-saturation auxiliary system was designed to avoid actuator saturation. A disturbance observer and a sliding mode controller based on the all-drive system method were designed, so that the system can stably track the target attitude under the influence of external disturbances. Given a reference signal, the complexity of the controller design is reduced, and the influence of disturbances on the system is reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Schematic diagram of the error quaternion changing with time in the embodiment;

[0050] Figure 2 FIG. 4 is a schematic diagram of the angular velocity error changing with time in an embodiment. DETAILED DESCRIPTION

[0051] The present invention will be further explained below with reference to the accompanying drawings;

[0052] A spacecraft attitude tracking sliding mode control method based on an all-drive system method, the specific steps are as follows:

[0053] Step 1: Establish a second-order all-wheel drive system model for spacecraft attitude tracking

[0054] Consider a rigid spacecraft, and define the unit quaternion describing its attitude motion as ,in is the scalar part of the quaternion, is the vector part of the quaternion, and The spacecraft's current angular velocity relative to inertial space is Rotation, assuming that the desired coordinate system is moving at an angular velocity relative to the inertial space Rotation, the rotation quaternion is , define the rotation quaternion from the desired coordinate system to the current spacecraft coordinate system as the error quaternion , the angular velocity error is , then the kinematic model of the spacecraft attitude tracking system described by quaternion is:

[0055]

[0056] in, , Respectively , The first derivative of .

[0057] The dynamic model of the spacecraft attitude tracking system is:

[0058]

[0059] in, is the vector part of the error quaternion, is the spacecraft moment of inertia, express The inverse matrix of , u is the system control input, is the external disturbance to the system, , Respectively , The first derivative of represents an antisymmetric matrix, , is the rotation matrix from the target body coordinate system to the body coordinate system:

[0060] .

[0061] Consider the effect of actuator saturation according to the all-wheel drive system approach , we get the following spacecraft attitude tracking second-order all-wheel drive system model:

[0062]

[0063]

[0064] in, Indicates the system saturation control input and the current system control input The difference, represents the actuator saturation function, is the maximum output of the actuator, is the minimum output of the actuator.

[0065] is the known nonlinear term of the second-order all-wheel drive system, where:

[0066] ,

[0067] ,

[0068] ,

[0069] ,

[0070] ,

[0071] ,

[0072] .

[0073] ,

[0074] ,

[0075] ,

[0076] .

[0077] is the unknown disturbance of the system, is the input matrix. express The second derivative of express The first derivative of .

[0078] Step 2: Anti-saturation system design

[0079] Considering the actuator saturation problem of the spacecraft, the following anti-saturation auxiliary system is designed:

[0080]

[0081] Where C1 and C2 are constant diagonal matrices with positive diagonal elements. λ1 and λ2 are the state variables of the compensation system. , They are , The first derivative of; define new tracking errors e1, e2, and modify the system model as follows:

[0082]

[0083] in, , are the first derivatives of e1 and e2 respectively, , They are , The second derivative of E n is the 3D identity matrix.

[0084] Step 3: Design of disturbance observer based on fixed-time multivariable superhelical system

[0085] Considering the influence of external disturbances, the following disturbance observer based on fixed-time multivariable superhelical system is designed:

[0086]

[0087] in, , yes The estimated value of , , , p is a constant and , is an estimate of the total disturbance, obtained by solving the differential equation. is an upper bound on the derivative of the total disturbance. , They are , The first derivative of .

[0088] Step 4: Sliding mode controller design based on full drive system approach

[0089] Design the following sliding surface:

[0090]

[0091] Among them, A0 and A1 are the parameters of the parametric design method. Based on the sliding surface, the following sliding mode controller is obtained:

[0092]

[0093] in, express The inverse matrix of , . is a positive real number, , are all positive odd numbers, and , It is a column vector whose elements are positive real numbers. Under the condition of satisfying the stability of the system, the values ​​of parameters β, k, g, η, C1, and C2 are designed to obtain the sliding mode controller.

[0094] Step 5: System stability analysis

[0095] ①The following analyzes the stability of the system from a theoretical perspective.

[0096] Depend on Available ,so , and because , are all positive odd numbers, so .

[0097] Select the Lyapunov function as , and take its derivative:

[0098]

[0099] in, , They are , The first derivative of ,so ,when , ,Right now , the closed-loop system is stable. t represents time.

[0100] when When , the system convergence time becomes shorter, the upper limit of the control input amplitude becomes larger, When , the system convergence time becomes longer and the upper limit of the control input amplitude becomes smaller. According to this change rule, the values ​​of parameters β, k, g, η, C1, and C2 can be selected according to requirements.

[0101] ②The following analyzes the stability of the system from the perspective of simulation experiments.

[0102] Get the initial value of the error quaternion , initial value of angular velocity error . Target quaternion , target angular velocity The unit of angular velocity is rad / s.

[0103] Perturbation , the unit is .

[0104] Observer parameters , .

[0105] Controller Parameters .

[0106] Compensation system parameters .

[0107] The simulation results are as follows Figure 1 , Figure 2 As shown, in Figure 1 In the quaternion, the scalar part After a brief decrease, it begins to increase and gradually approaches 1. At the same time, the vector part of the quaternion It decreases and approaches 0, indicating that the spacecraft attitude is gradually approaching the target attitude under the action of the controller. Figure 2 The angular velocity error curve drops to a negative value, then starts to rise and finally stabilizes near 0. It can be seen that the spacecraft can track the target attitude within 15 seconds, and the convergence time is very short.

Claims

1. A spacecraft attitude tracking sliding mode control method based on an all-drive system method, characterized in that: Step 1: Establish the kinematic and dynamic models of the attitude tracking system described by the spacecraft quaternion, and consider the influence of actuator saturation according to the full drive system method. , establish a second-order all-wheel drive system model for spacecraft attitude tracking; is the input matrix; Indicates the system saturation control input and the current system control input The difference between Step 2: Consider the actuator saturation problem of the spacecraft and design an anti-saturation auxiliary system: ； in, The vector part of the error quaternion from the desired coordinate system to the current spacecraft coordinate system; and C2 is a constant diagonal matrix with positive diagonal elements; and To compensate the state variables of the system, , They are , The first derivative of; define tracking errors e1, e2: ； in, is the known nonlinear term of the second-order all-wheel drive system, is the unknown disturbance of the system, is the 3D identity matrix; , are the first derivatives of e1 and e2 respectively, , They are , The second derivative of Step 3: Considering the influence of external disturbances, design a disturbance observer based on a fixed-time multivariable superhelical system: ； in, , yes The estimated value of , , , p is a constant and , is an estimate of the total disturbance, is an upper bound on the derivative of the total disturbance; , They are , The first derivative of Step 4: Design the controller based on the all-wheel drive system approach ,in , ; A0 and A1 are the parameters of the parametric design method, and v is the external input signal or other controller; express The inverse matrix of .

2. A spacecraft attitude tracking sliding mode control method based on an all-wheel drive system method as claimed in claim 1, characterized in that: The kinematic model of the spacecraft attitude tracking system described by quaternion is defined as: ； in, , represents the angular velocity error; represents the current angular velocity of the spacecraft relative to the inertial space, represents the angular velocity of the desired coordinate system relative to the inertial space; , represents the error quaternion from the desired coordinate system to the current spacecraft coordinate system; is the vector part of the error quaternion, is the vector part of the error quaternion; , Respectively , The first derivative of The dynamic model of the spacecraft attitude tracking system is: ； in, , Respectively , The first derivative of is the spacecraft moment of inertia, express The inverse matrix of , u is the controller output, is the external disturbance to the system, represents an antisymmetric matrix, , is the rotation matrix from the target body coordinate system to the body coordinate system: ； Consider the effect of actuator saturation , establish the following spacecraft attitude tracking second-order all-wheel drive system model: ； ； in, represents the actuator saturation function, is the maximum output of the actuator, is the minimum output of the actuator; is the known nonlinear term of the second-order all-wheel drive system, is the unknown disturbance of the system, is the input matrix; ; express The second derivative of express The first derivative of .

3. A spacecraft attitude tracking sliding mode control method based on an all-wheel drive system method as claimed in claim 2, characterized in that: Known nonlinear terms of the second-order all-wheel drive system ,in: ， 、 、 、 、 ； ， 、 、 。 4. A spacecraft attitude tracking sliding mode control method based on an all-wheel drive system method as claimed in claim 1, characterized in that: Use the sliding film controller as the signal v in the controller u to design the sliding surface ; Based on the sliding surface, the following sliding controller is obtained: ； in, is a positive real number, , are all positive odd numbers, and , It is a column vector whose elements are positive real numbers. Under the condition of satisfying the stability of the system, the values ​​of parameters β, k, g, η, C1, and C2 are designed to obtain the controller gain.

5. A spacecraft attitude tracking sliding mode control method based on an all-wheel drive system method as claimed in claim 3, characterized in that: when When , the system convergence time becomes shorter, the upper limit of the control input amplitude becomes larger, , the system convergence time becomes longer and the upper limit of the control input amplitude becomes smaller.

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