A preset performance spacecraft attitude tracking sliding mode control method

Abstract

The application discloses a preset performance spacecraft attitude tracking sliding mode control method and belongs to the technical field of process control. The method is based on a full drive system method and preset performance control. For a spacecraft attitude tracking system with inertia uncertainty, external disturbance and actuator saturation, first, a preset performance function with finite time convergence is used to constrain the spacecraft attitude tracking error, and a conversion function is used to convert the system state to construct a constrained attitude tracking system model. Then, the model is converted into a full drive system model, an adaptive disturbance observer is introduced to estimate the values of inertia uncertainty and external disturbance, and finally, based on the full drive system method, an anti-saturation compensation system is combined to design a preset performance anti-saturation sliding mode controller to control the spacecraft attitude and realize stable tracking of the spacecraft to the target attitude.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of spacecraft control, and relates to spacecraft attitude tracking of a target, in particular to a sliding mode control method for spacecraft attitude tracking with preset performance. BACKGROUND

[0002] In the field of spaceflight, spacecraft attitude tracking control technology is the cornerstone of realizing various spaceflight missions, such as accurate monitoring of ground targets by earth observation satellites, observation and exploration of remote celestial bodies by deep space probes in the universe, and execution of complex tasks such as spacecraft rendezvous and docking and formation flight, which all highly depend on accurate attitude tracking control.

[0003] With the continuous expansion and deepening of spaceflight missions, the performance requirements for spacecraft attitude tracking control are increasingly stringent. On the one hand, there are many uncertain factors in the space system. From the outside, environmental disturbance moments affect the spacecraft at all times, for example, atmospheric resistance will generate a continuous and complex force on the spacecraft, causing its attitude to change; solar radiation pressure, planetary gravitational perturbation and other disturbances cannot be ignored. From the inside, due to the complex structure of the spacecraft, accurate modeling is difficult, and model uncertainties are widespread, such as the parameters of the mass distribution and the moment of inertia of the spacecraft, which are difficult to measure and model absolutely accurately.

[0004] In summary, it is of great significance to develop a spacecraft attitude tracking control method that can fully consider the actuator dynamics, effectively handle various system uncertainties, and is simple in form and easy to implement in engineering. SUMMARY

[0005] In view of the deficiencies of the prior art, the application provides a sliding mode control method for spacecraft attitude tracking with preset performance, establishes a full-drive system model of spacecraft attitude tracking with actuator saturation in combination with a preset performance function, and designs an anti-saturation sliding mode controller in combination with a compensation system, so as to realize stable tracking of the spacecraft to the target attitude and ensure that the system can converge in a limited time while meeting the performance constraints.

[0006] A sliding mode control method for spacecraft attitude tracking with preset performance, and the specific steps are as follows:

[0007] Step 1, using quaternions to describe the attitude motion of a rigid spacecraft, establishing a kinematic model and a dynamic model of the spacecraft attitude tracking system.

[0008] Define the error of the system Performance envelope:

[0009]

[0010]

[0011]

[0012] wherein, denotes the rotation error quaternion of the desired coordinate system to the current spacecraft coordinate system, denotes the initial time value of , are the upper and lower bounds of the performance constraint, respectively. is a preset performance function converging in a finite time , and the constant satisfies , and the constant , denote the initial value and the final value of the preset performance function , respectively.

[0013] The system variable of the spacecraft attitude tracking system model is converted into by using the conversion function , and a constrained system model is established.

[0014] Step 2, the constrained system model is converted into a full drive system model, and a controller is obtained by using the full drive system method under the condition of a given reference signal, so as to control the system input.

[0015] As preferred, an adaptive disturbance observer is designed to estimate the external disturbance.

[0016] As preferred, a sliding mode controller is designed based on the full drive system method to control the system.

[0017] As preferred, an anti-saturation system is designed to compensate for the actuator saturation.

[0018] The present application has the following beneficial effects:

[0019] The system state is constrained by using the preset performance function, the constrained system model is converted into a full drive system model, a disturbance observer is designed to estimate the inertial uncertainty and the external disturbance, and an anti-saturation compensation system and a sliding mode controller are designed for the actuator saturation problem, so that the system can stably track the target attitude under the condition of a given reference signal, and the complexity of the controller design is reduced, and the influence of the input saturation on the system is reduced. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 is the simulation result of the error quaternion changing with time in the embodiment.

[0021] Figure 2 is the simulation result of the angular velocity error changing with time in the embodiment. DETAILED DESCRIPTION

[0022] The application will be further explained in connection with the accompanying drawings, in which:

[0023] Step 1, establishing a constrained spacecraft attitude tracking system model

[0024] Considering a class of rigid spacecraft, define the unit quaternion describing its attitude motion as where is the scalar part of the quaternion, is the vector part of the quaternion, and , T represents transposition.

[0025] The spacecraft currently rotates relative to the inertial space with angular velocity , set the desired coordinate system to rotate relative to the inertial space with angular velocity , the target quaternion is , define the rotation error quaternion from the desired coordinate system to the current spacecraft coordinate system as where represents quaternion multiplication, represents the conjugate quaternion of , and the angular velocity error is , then the spacecraft attitude tracking system kinematics model described by the quaternion is:

[0026]

[0027] where, is the first derivative, and the subscripts x, y, z represent the components in the x-axis, y-axis, and z-axis directions.

[0028] The spacecraft attitude tracking system dynamics model is:

[0029]

[0030] where, . , represents the spacecraft moment of inertia, and diag represents a diagonal matrix. is a time-varying coefficient and satisfies . is the control input, is the external disturbance. represents the inverse of a matrix. , is a 3-dimensional unit matrix.

[0031] ,

[0032] Definition:

[0033] , ,

[0034] Then we have:

[0035]

[0036] where, , are the control input maximum and minimum values, respectively. We have:

[0037]

[0038] denotes the second derivative.

[0039] Define the constraint error:

[0040]

[0041] Define the performance envelope of the constraint error

[0042]

[0043]

[0044]

[0045] where, denotes the rotation error quaternion at the initial time, , are the upper and lower bounds of the performance constraint, respectively. is a pre-specified performance function that converges in finite time , and the constant satisfies , and the constant , denote the initial and final values of the pre-specified performance function , respectively.

[0046] Define as the transformed system variable, and select the transformation function to transform the spacecraft attitude tracking system model into a constrained system model:

[0047]

[0048] Step 2, transform the constrained system model into a full drive system model

[0049] Each state component in the constrained system model is:

[0050] ​

[0051] where, correspond to the three components of the attitude quaternion vector part, respectively.

[0052] Convert the constrained system model to the full actuation system model:

[0053]

[0054] where,

[0055]

[0056]

[0057]

[0058] ,

[0059] ,

[0060] Step 3, adaptive disturbance observer design

[0061] For external disturbance, the following adaptive disturbance observer is designed:

[0062]

[0063] where, is the estimated value of the total disturbance, , is the observer system state, , , is the observer gain.

[0064] Step 4, anti-saturation sliding mode controller design

[0065] The following sliding surface is designed:

[0066]

[0067] Considering the influence of actuator saturation, the compensation system is designed, and the following anti-saturation sliding mode controller u is obtained:

[0068]

[0069]

[0070] where, denotes the 2-norm of the vector, , is the controller parameter, , is the compensation system parameter.

[0071] Step 5, stability analysis of the system

[0072] The Lyapunov function is selected as follows:

[0073]

[0074] When ,

[0075]

[0076] , ,

[0077] When ,

[0078] ,

[0079]

[0080]

[0081] The system converges ultimately and consistently.

[0082] The effectiveness of the method is verified by a numerical simulation experiment as follows:

[0083] The initial value of the error quaternion is , and the initial value of the angular velocity error is rad / s. The target quaternion is , the target angular velocity is rad / s, the inertial uncertainty parameter is , and the external disturbance is .

[0084] In the preset performance function, the finite time , the constant , the initial value and the final value are , respectively. The initial value of the system state of the observer is .

[0085] Through simulation debugging, the observer gain , is obtained. The controller parameters and the compensation system parameters , , . are obtained by the parameterization method.

[0086] The spacecraft is controlled to track the target attitude using the anti-saturation sliding mode controller u, and the results are shown in FIGS. 1 and 2. Figure 1 In the figure, the scalar part of the error quaternion begins to increase after a short decrease and gradually approaches 1, while the vector part of the error quaternion , , continuously decreases and approaches 0, indicating that the spacecraft attitude gradually approaches the target attitude under the action of the controller u. Figure 2 In the figure, the angular velocity error curve first decreases to a negative value, then begins to rise and stabilizes near 0, indicating that the spacecraft angular velocity gradually approaches the target angular velocity under the action of the controller. It can also be seen from the figure that the spacecraft tracks the target attitude in 15 seconds, satisfying the preset convergence time .

Claims

1. A method of sliding mode control for spacecraft attitude tracking with pre-specified performance, characterized by: The specific steps are as follows: Step 1, using quaternions to describe the attitude motion of rigid spacecraft, establishing the kinematics model and dynamics model of the spacecraft attitude tracking system: wherein represents a rotation error quaternion; represents a unit quaternion describing the spacecraft attitude motion, is a scalar part, is a vector part, and T represents a transpose; represents a target quaternion, represents a conjugate quaternion of represents an angular velocity error; represents an angular velocity of the spacecraft relative to the inertial space; represents an angular velocity of the desired coordinate system relative to the inertial space; is a first derivative, and the subscripts x, y, z represent components in the x-axis, y-axis, and z-axis directions; wherein ; , denotes the spacecraft moment of inertia, diag denotes a diagonal matrix; is a time-varying coefficient; is the system input, is an external disturbance; denotes the inverse of a matrix; is a 3-dimensional identity matrix; Defining the performance envelope of system errors : wherein, represents the rotation error quaternion of the desired coordinate system to the current spacecraft coordinate system, represents the initial time value of , are the upper and lower bounds of the performance constraint, respectively; is a pre-specified performance function that converges in finite time , and the constant satisfies , and the constant , represent the initial and final values of the pre-specified performance function , respectively. Using a conversion function The system variables of the spacecraft attitude tracking system model are transformed into A constrained system model is established: Each state component in the constrained system model is: wherein is a first derivative, denotes a second derivative; denotes the vector part of the rotation error quaternion; , respectively, correspond to the three components of the vector part of the attitude quaternion. Step 2, converting the constrained system model into a full-drive system model: 、 、 wherein denotes the spacecraft moment of inertia; is the control input, , are the control input maximum and minimum values, respectively; In the case of a given reference signal, the controller is obtained by using the full-drive system method to control the system input.

2. The sliding mode control method for preset performance spacecraft attitude tracking according to claim 1, characterized in that: In view of the inertial uncertainty and external disturbance of the spacecraft attitude tracking system, the following adaptive disturbance observer is designed to estimate the total disturbance: wherein is an estimate of the total disturbance, , is the observer system state, , , is the observer gain.

3. The preset performance spacecraft attitude tracking sliding mode control method of claim 1, wherein: According to the full-drive system method, combined with the anti-saturation compensation system, the following saturation sliding mode controller u is designed: wherein denotes the 2-norm of a vector, , is a controller parameter, , is a compensation system parameter.

4. The sliding mode control method for preset performance spacecraft attitude tracking according to claim 3, characterized in that: Given the tracking target, the preset performance and the initial value of the system state of the observer, the values of , , , , , are obtained through simulation debugging, and the value of is obtained through a parameterization method.

5. A computer readable storage medium having stored thereon a computer program which, when executed in a computer, causes the computer to perform the method of any one of claims 1-4.

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