CN110667890B - Nonlinear attitude stabilization method for spacecraft - Google Patents

Abstract

The invention provides a nonlinear attitude stabilization method of a spacecraft, which comprises the following steps: step 1, establishing a spacecraft attitude model; and 2, establishing a nonlinear attitude stabilization controller.

Description

Nonlinear attitude stabilization method for spacecraft

Technical Field

The invention relates to an aircraft control technology, in particular to a nonlinear attitude stabilization method for a space aircraft.

Background

The accurate attitude motion description of the spacecraft is expressed as a group of multi-input multi-output cross-coupled nonlinear equations by a least element representation method of three Euler angles. For the attitude control problem of the spacecraft represented by the Euler angle description method, the prior art adopts a backstepping control method to design a nonlinear attitude control law, however, the robustness of the attitude control under the condition of slow external disturbance change is not considered, the steady-state precision problem of the attitude stability control under the condition of slow external disturbance change is not considered, and the steady-state precision of the attitude stability control under the condition of simultaneous existence of the slow external disturbance change and unknown inertial parameters of the spacecraft is not considered.

Disclosure of Invention

The invention aims to provide a nonlinear attitude stabilization method for a spacecraft.

The invention provides a nonlinear attitude stabilization method of a spacecraft, which comprises the following steps:

step 1, establishing a spacecraft attitude model;

and 2, establishing a nonlinear attitude stabilization controller.

Further, the spacecraft attitude model in the step 1 is an attitude dynamics model described by Euler angles

Wherein,

denotes pitch angle, psi yaw angle, gamma inclination angle, and ω ═ ω [ ω ]_x ω_y ω_z]^TIs the angular velocity vector in the body coordinate system.

Further, the nonlinear attitude stabilization controller in step 2 is:

wherein,

z₂＝x₂-α₁

z₃＝x₃-α₂

x₃＝[ω_x ω_y ω_z]^T

α₁、α₂is a virtual control quantity, c₃And c₄Is a constant, Γ is a positive definite diagonal matrix, L is a linear operator

In the backstepping systematic control technology, the slowly-changing external disturbance of the spacecraft is subjected to self-adaptive estimation, so that the slowly-changing external disturbance has robustness when the spacecraft is subjected to attitude stabilization control, and because the integral of the attitude Euler angle is introduced in the design, the steady-state precision of the attitude stabilization control under the condition that the external disturbance changes slowly can be improved compared with the conventional control algorithm.

The invention is further described below with reference to the accompanying drawings.

Drawings

Fig. 1 is a schematic view of euler angle stabilization, in which a) is a schematic view of pitch angle stabilization, b) is a schematic view of yaw angle stabilization, and c) is a schematic view of roll angle stabilization.

FIG. 2 is a schematic view of angular velocity, wherein a) is angular velocity ω_xSchematic, b) is angular velocity ω_ySchematic, c) is angular velocity ω_zSchematic representation.

FIG. 3 is a schematic diagram of the control force rejection, wherein a) is the control torque T_xSchematic view, b) is the control torque T_yAnd c) is the control torque T_zSchematic illustration.

FIG. 4 is a schematic flow chart of the method of the present invention.

Detailed Description

With reference to fig. 4, a method for stabilizing nonlinear attitude of a spacecraft includes the following steps:

step 1, establishing a spacecraft attitude model;

and 2, establishing a nonlinear attitude stabilization controller.

The specific process of the step 1 is as follows:

step 1.1, establishing a posture dynamics model

Considering the external disturbance torque, a rigid-body spacecraft attitude dynamics model is described by

Wherein J is diag [ J ═ d_x J_y J_z]Representing a nominal moment of inertia matrix in a body coordinate system, ω ═ ω [ ω ]_x ω_yω_z]^TIs the angular velocity vector in the body coordinate system, u ═ T_x T_y T_z]^TIs a control torque, which can be generated by a reaction control propeller, and f (t) is an external disturbance torque vector, assuming that f (t) changes slowly in the present embodiment, and the operation symbol ω × acts on ω ═ ω _xω_y ω_z]^TForming an antisymmetric array:

step 1.2, establishing an attitude kinematics model described by an Euler angle

The attitude motion of the spacecraft adopts a mathematical model described by an Euler angle

Pitch angle is indicated, yaw angle is indicated by ψ, and bank angle is indicated by γ. By using

Attitude kinematics equation for obtaining Euler angle description by sequence conversion

The advantage of these equations described in euler angles is that they are well defined physically and are a minimal elemental representation of the attitude of the spacecraft. However, the poses of the three Euler angles represent a problem of singularity, and the equations and equations show that the singularities are at

Thus, in practice, a particular order of rotation may be preferred. In many engineering attitude control problems, this attitude description can be adopted because of the working pitch angle

Not close to ± 90 °. Formally, these equations are for ω_x、ω_yAnd ω_zAre all linear but are non-linear with respect to euler angles.

The specific process of the step 2 is as follows:

defining a vector

x₃＝[ω_x ω_y ω_z]^T，x₁＝∫x₂dt∈R³。

The overall attitude stabilization system is expressed as

In the formula

Definition of

z₁＝x₁，z₂＝x₂-α₁，z₃＝x₃-α₂

In the formula, alpha₁And alpha₂Is a virtual control quantity, can obtain

Order to

α₁＝-c₁x₁

In the formula, c₁Is a normal number, can obtain

Order to

In the formula, c₂Is a normal number and can be obtained

The design is popularized to a self-adaptive condition, and the moment of inertia of the space vehicle is estimated by designing a self-adaptive law, wherein the moment of inertia is J_x、J_yAnd J_z. To separate these moments of inertia, a linear operator L is defined: r³→R³×R³It acts on a vector b ═ b₁ b₂ b₃]^TTo obtain

Let θ become [ J ]_x J_y J_z]^TJb ═ L (b) can be obtained) Theta. Then there are

In the formula,

order to

Is an estimated value of F, with an estimated error of F

Assuming that the external disturbance torque F (t) changes slowly, take

By using

Representing an estimated value of the moment of inertia theta, defining an estimation error of the moment of inertia as

A Lyapunov function defining the system is

Derived from the above equation along the system

Designing adaptive nonlinear attitude stabilization controller

In the formula, c₃And c₄Is a positive constant, and Γ is a positive definite diagonal matrix.

Thereby can obtain

It can be known that the controller of design can guarantee the stability of attitude system.

As can be seen from fig. 1, the adaptive nonlinear attitude stabilization controller provides a better transient process in the case where the moment of inertia of the aircraft is unknown, as seen in fig. 1a), 1b) and 1c), with a smaller steady overshoot in euler angle, and after the transient process the attitude of the aircraft stabilizes to 0.

Fig. 1 shows that the adaptive nonlinear attitude stabilization controller can not only mitigate the influence of external disturbances, but also achieve better stability performance under the condition that the moment of inertia of the aircraft is unknown. The angular velocity and the control moment under the action of the self-adaptive nonlinear attitude stabilization controller are respectively drawn in fig. 2 and fig. 3, and it can be seen from the drawings that after the transient process, the change of the Euler angle of the aircraft attitude is very small, the angular velocity approaches to 0, the control moment is small, and it shows that a large moment does not need to be output.

Examples

By using the self-adaptive nonlinear attitude stabilization controller designed by the system in the technical scheme, the spacecraft can be automatically controlled under the condition that the rotational inertia of the spacecraft is unknown. This section will illustrate the detailed implementation and verify the effectiveness of the proposed control algorithm by numerical simulation analysis. Suppose the moment of inertia of the aircraft is J_x＝0.3kgm²，J_y＝J_z＝2kgm². The initial attitude angle of the aircraft is

ψ (0) — 40 °, γ (0) — 10 °, and the initial angular velocity ω_x(0)＝0°/s，ω_y(0)＝0°/s，ω_z(0) 0 °/s. The saturation limit of the actuator is 5 Nm. Suppose flightThe machine performs a gestural maneuver from one static state to another with a terminal attitude angle of 0. Since it is assumed in the design of this patent that F (t) changes slowly, it can be assumed that

F(t)＝[0.15sin(0.1t) 0.2sin(0.1t) 0.1sin(0.1t)]^T Nm (10)

The parameter in the adaptive nonlinear attitude stabilization controller is taken as c₁＝0.1，c₂＝11，c₃C is chosen as 11₄＝30，

An initial estimate of the moment of inertia of the aircraft is set to

The control gain in the adaptation law is taken to be Γ ═ diag [ 809080]。

In order to improve the transient process, the euler angle instruction is planned in the simulation, and the transient process is designed into a ramp signal (see fig. 1).

Claims (1)

1. A nonlinear attitude stabilization method for a spacecraft is characterized by comprising the following steps:

step 1, establishing a spacecraft attitude model, specifically as follows:

Step 1.1, establishing a posture dynamics model

Considering the external disturbance torque, the attitude dynamics model of a rigid-body spacecraft is described by

Wherein J is diag [ J ]_x J_y J_z]Representing a nominal moment of inertia matrix in a body coordinate system, ω ═ ω [ ω ]_x ω_y ω_z]^TIs the angular velocity vector in the body coordinate system, u ═ T_x T_y T_z]^TIs the control moment, F (t) is the external disturbance moment vector, assuming that F (t) changes slowly, the operation symbol ω is activeAt ω ═ ω_x ω_y ω_z]^TForming an antisymmetric array:

step 1.2, establishing an attitude kinematics model described by an Euler angle

The attitude motion of the spacecraft adopts a mathematical model described by an Euler angle

Denotes pitch angle, ψ denotes yaw angle, and γ denotes tilt angle; adopts psi →

Pose kinematics equation for Euler angle description by rotation order of → gamma (2 → 3 → 1)

Step 2, establishing a nonlinear attitude stabilization controller, which comprises the following specific steps:

defining a vector

Vector x₃＝[ω_x ω_y ω_z]^TVector x₁＝∫x₂dt∈R³；

The overall attitude stabilization system is expressed as

In the formula

Definition of

z₁＝x₁，z₂＝x₂-α₁，z₃＝x₃-α₂

In the formula, alpha₁And alpha₂Is a virtual control quantity, is obtained

Order to

α₁＝-c₁x₁

In the formula, c₁Is a normal number, and is obtained

Order to

In the formula, c₂Is a normal number, and is obtained

The design is popularized to a self-adaptive condition, and the rotary inertia of the space vehicle is estimated by designing a self-adaptive law Moment of inertia of J_x、J_yAnd J_z；

To separate these moments of inertia, a linear operator L is defined: r³→R³×R³It acts on a vector b ═ b₁ b₂b₃]^TTo obtain

Let theta equal to [ J_x J_y J_z]^TTo yield Jb ═ l (b) θ; then there are

In the formula,

order to

Is an estimated value of F, an estimated error of F

Assuming that the external disturbance torque F (t) changes slowly, take

By using

Representing an estimated value of the moment of inertia theta, defining an estimated error of the moment of inertia

Designing adaptive nonlinear attitude stabilization controller

In the formula, c₃And c₄Is a positive constant and Γ is a positive definite diagonal matrix.

Images