CN109507892A - The adaptive sliding mode pose stabilization control method of flexible spacecraft - Google Patents

Abstract

The present invention provides a kind of adaptive sliding mode pose stabilization control methods of flexible spacecraft, found kinematical equation and kinetics equation of the flexible spacecraft based on quaternary number, spacecraft has flexible appendage, and rotary inertia contains perturbing term.The beneficial effects of the present invention are: providing a kind of adaptive sliding mode pose stabilization control method of flexible spacecraft, Space Vehicle System can be made with good stability using the adaptive sliding mode pose stabilization control method, when Space Vehicle System inertia parameter varies widely, the posture of spacecraft can tend towards stability quickly；Space Vehicle System can be made to possess the ability for preferably flexible mode being inhibited to vibrate using the adaptive sliding mode pose stabilization control method, the vibration of flexible appendage can effectively be inhibited.

Description

Self-adaptive sliding mode attitude stability control method of flexible spacecraft

Technical Field

The invention relates to a spacecraft, in particular to a self-adaptive sliding mode attitude stability control method of a flexible spacecraft.

Background

In the traditional attitude control algorithm, perturbation is not considered in the moment of inertia of the flexible spacecraft, and the traditional sliding mode control algorithm can cause large buffeting.

Disclosure of Invention

In order to solve the problems in the prior art, the invention provides a self-adaptive sliding mode attitude stability control method for a flexible spacecraft.

The invention provides a self-adaptive sliding mode attitude stability control method of a flexible spacecraft, which comprises the following steps of firstly establishing a system model of the flexible spacecraft based on quaternion as follows:

wherein omega is the attitude angular velocity of the flexible spacecraft,q₀,q_va scalar part and a vector part which are attitude quaternions respectively;

delta is a coupling matrix between the flexible portion of the flexible spacecraft and the rigid body main body; c and K are damping matrix \ \ and rigidity matrix,

ω_niwhere i is 1,2, …, N is the natural frequency, ζ_iI is 1, …, and N is damping coefficient; j. the design is a square_mbIs the moment of inertia of the rigid body part and has J_mb＝J-δ^Tδ, wherein J ═ J₀+△J，J₀The method is characterized in that the method is a rotational inertia nominal value, △ J is a rotational inertia uncertain coefficient, the flexible spacecraft is provided with a flexible attachment, and the rotational inertia contains perturbation terms, and the following sliding mode switching function is designed:

s＝w+Gq_v

wherein G is a symmetrical positive definite matrix of 3 × 3;

the upper bound of uncertainty is estimated by the following adaptive law:

wherein,are respectively c₀,c₁And has an estimated value of

Wherein l₀,l₁Are all positive numbers;

the adaptive sliding mode attitude stability control law of design state feedback is as follows:

wherein W, D, G are positive definite diagonal matrixes,

l₀,l₁is a positive number.

As a further improvement of the present invention, the switching function F(s) included in the adaptive sliding mode attitude stabilization control law of state feedback is replaced by F1(s) as follows:

F₁(s)＝{f(s₁),f(s₂),f(s₃)}^T

finally, the following adaptive sliding mode attitude stability control law is obtained:

wherein W, D, G are positive definite diagonal matrix, l₀,l₁Is a positive number, f(s)_i) I ═ 1,2,3, defined as follows:

the invention has the beneficial effects that: by adopting the scheme, the self-adaptive sliding mode attitude stability control method for the flexible spacecraft is provided, the spacecraft system can have good stability by adopting the self-adaptive sliding mode attitude stability control method, and when the inertia parameters of the spacecraft system are changed greatly, the attitude of the spacecraft can tend to be stable quickly; by adopting the self-adaptive sliding mode attitude stability control method, the spacecraft system can have better capability of inhibiting flexible mode vibration, and the vibration of the flexible accessory can be effectively inhibited.

Drawings

Fig. 1 is a simulink module verification diagram in MATLAB of the adaptive sliding mode attitude stabilization control method of a flexible spacecraft of the present invention.

Detailed Description

The invention is further described with reference to the following description and embodiments in conjunction with the accompanying drawings.

A self-adaptive sliding mode attitude stabilization control method for a flexible spacecraft comprises the following steps:

1. adaptive sliding mode control law based on state feedback is designed for the measurable condition of flexible mode

Wherein W, D, G are positive definite diagonal matrix, l₀,l₁Is a positive number.

Step 1 design slip form surface

Selecting the following sliding mode switching surface function:

s＝w+Gq_v

and, prove that the above-mentioned hyperplane can guarantee the slip form movement is stable, namely the whole movement process of the system, can be stable in limited time.

And (3) proving that: the chosen Lyapunov function is as follows:

step2 design control law

The control is designed to have the following form:

u＝u_eq+u_h+u_n(1)

wherein u is_eqFor equivalent control of nominal system, u_dTo deal with system uncertainty; u. of_hThe method is used for ensuring that the sliding mode switching function can be converged to the sliding mode surface. The sliding mode control law canSo that the state of the system can move to the sliding mode surface s of 0 in a limited time from any initial point, i.e. s is w + Gq_vAnd can be maintained on the slip manifold.

The equivalent control u is designed as follows_eqLet us orderThe following can be obtained:

the nominal part of the system model from the second equation of the system model is:

substituting equation (3) into equation (2) yields the equivalent control law as follows:

to construct a control law u_dFirst, the following definitions are given:

where Ψ is related to △ J, ω, q because | | △ J | | | is bounded, there is a positive-valued function ρ (t, ω, q) that satisfies the following inequality:

||Ψ||≤ρ(t,ω,q)

where ρ (t, ω, q) is related only to t, ω, q.

First, the following assumptions are given:

suppose that: presence of normal number c₀,c₁Such that the following inequality holds:

ρ(t,ω,q)≤c₀+c₁||(ω^T,q^T)^T||.

based on the above assumptions, design u_dAs follows

Wherein,are respectively c₀,c₁And has an estimated value of

Wherein l₀,l₁Are all positive numbers.

Finally, design u_hThe following were used:

u_h＝-Ws-DF(s),

wherein W, D, G are positive definite diagonal matrices, and,

F(s)＝[f(s₁)f(s₂)f(s₃)]^T,

in the following, we will illustrate the control effect of the adaptive sliding mode control law based on state feedback by way of example.

Considering the nominal value J of the moment of inertia of a spacecraft with a flexible attachment₀Comprises the following steps:

the moment of inertia uncertainty factor △ J is:

rigid-flexible coupling matrix between flexible spacecraft and flexible accessories:

the vibration frequency of the flexible attachment is:

ω_n＝[0.7681,1.1038,1.8733,2.5496]

the vibration damping of the flexible attachment is:

ξ＝[0.005607,0.00862,0.01283,0.02516]

the parameters of the sliding mode controller based on state feedback are as follows:

G＝diag{0.2 0.2 0.2}；W＝diag{200 200 200}；D＝diag{200 200 200}

parameters of the sliding mode controller based on the observer are as follows:

the invention provides a self-adaptive sliding mode attitude stability control algorithm for a flexible spacecraft, which is designed aiming at the problem of attitude stability control of the flexible spacecraft with perturbation of rotational inertia. The algorithm aims to solve the problems of stable control of the attitude of the flexible spacecraft with uncertain rotational inertia and suppression of buffeting vibration of the flexible accessories. The invention adopts a quaternion method to express a kinematic equation of the attitude of the flexible spacecraft, establishes a complex spacecraft dynamical equation with a flexible accessory in a central rigid body and perturbation of rotational inertia, and provides a simplified flexible spacecraft attitude dynamical equation based on mixed coordinates. Then, a sliding mode attitude stabilizing controller is designed by utilizing a Lyapunov direct method, improvement and optimization are carried out aiming at the problem of buffeting in sliding mode control, an original switch function term in the sliding mode control is replaced by a positive and negative cut function, and flutter in a system is restrained. Finally, the validity of the designed control algorithm was verified using the simulink module in MATLAB, as shown in fig. 1.

The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (2)

1. A self-adaptive sliding mode attitude stability control method of a flexible spacecraft is characterized by comprising the following steps: firstly, establishing a system model of the flexible spacecraft based on quaternion as follows:

wherein q is₀,q_vA scalar part and a vector part which are attitude quaternions respectively, omega is the attitude angular velocity of the flexible spacecraft,

delta is a coupling matrix between the flexible portion of the flexible spacecraft and the rigid body main body; c and K are respectively a damping matrix and a rigidity matrix,

ω_niwhere i is 1,2, …, N is the natural frequency, ζ_iI is 1, …, and N is damping coefficient; j. the design is a square_mbIs the moment of inertia of the rigid body part and has J_mb＝J-δ^Tδ, wherein J ═ J₀+△J，J₀The method is characterized in that the method is a rotational inertia nominal value, △ J is a rotational inertia uncertain coefficient, the flexible spacecraft is provided with a flexible attachment, and the rotational inertia contains perturbation terms, and the following sliding mode switching function is designed:

s＝w+Gq_v

wherein G is a symmetrical positive definite matrix of 3 × 3;

the upper bound of uncertainty is estimated by the following adaptive law:

wherein, are respectively c₀,c₁And has an estimated value of

Wherein l₀,l₁Are all positive numbers;

the adaptive sliding mode attitude stability control law of design state feedback is as follows:

wherein W, D, G are positive definite diagonal matrixes,

l₀,l₁is a positive number.

2. The adaptive sliding mode attitude stabilization control method of a flexible spacecraft of claim 1, characterized in that: the switching function F(s) contained in the adaptive sliding mode attitude stability control law of state feedback is replaced by F₁(s)：

F₁(s)＝{f(s₁),f(s₂),f(s₃)}^T

Finally, the following adaptive sliding mode attitude stability control law is obtained:

wherein W, D, G are positive definite diagonal matrix, l₀,l₁Is a positive number, f(s)_i) I ═ 1,2,3, defined as follows: