CN102033491B

CN102033491B - Method for controlling flexible satellite based on feature model

Info

Publication number: CN102033491B
Application number: CN2010102979615A
Authority: CN
Inventors: 孟斌; 吴宏鑫; 杨孟飞
Original assignee: Beijing Institute of Control Engineering
Current assignee: Beijing Institute of Control Engineering
Priority date: 2010-09-29
Filing date: 2010-09-29
Publication date: 2012-08-22
Anticipated expiration: 2030-09-29
Also published as: CN102033491A

Abstract

The invention relates to a method for controlling a flexible satellite based on a feature model, which is characterized in that the time dimension, the sampling time and the parameters M and m are determined according to the kinetic equation of the flexible satellite; the coefficient range of the feature model is determined according to each obtained variable; the parameters of the feature model are identified by utilizing a gradient method; and a control law is designed according to the coefficients of the feature model obtained through the identification, and the attitude angle of the flexible satellite is controlled through the kinetic equation that the control law is fed back to the flexible satellite. The method has the advantages that the time dimension and the sampling period of the flexible satellite are introduced; the change rate of the flexible satellite is depicted; the bottleneck problem of the feature modeling of the flexible satellite is solved; the expression of the parameter range of the feature model of the flexible satellite is provided; the parameter property of the feature model is qualitatively researched; the boundary of the parameters of the feature model is relative to the sampling period, the modeling error, the system order and the change rate of the system from the given parameter range; and the theoretical foundation of the self-adaptive control based on the feature model is laid for the flexible satellite. The method is suitable for the feature model of the attitude kinetics of an aircraft so as to lay the foundation for the aircraft based on the attitude control of the feature model.

Description

Flexible satellite control method based on feature model

Technical Field

The invention relates to a satellite control method, in particular to a flexible satellite control method based on a characteristic model, and belongs to the technical field of satellite control.

Background

The full-coefficient self-adaptive control method based on the characteristic model is provided by Wu Hongxin academy, and after more than 20 years of research, important progress is made in theory and application, and a set of self-adaptive control theory and method with strong practicability is formed. The method needs less identification parameters, can ensure the transient performance and the steady-state performance of a closed-loop system, and has strong robustness and adaptivity. Particularly, the theoretical thought and the engineering main points of the method are creatively applied to airship return reentry control, and the parachute opening precision of the method reaches the world advanced level.

The basic idea of the full-coefficient self-adaptive control method based on the characteristic model is that firstly, the characteristic model of the system and the parameter range thereof are established, and then the full-coefficient self-adaptive control law is designed according to the characteristic model parameters. In general, a characteristic model of a system is described by a coefficient-bounded second-order time-varying difference equation. In the adaptive control design based on the feature model, firstly, a coefficient range of a second-order time-varying difference equation is determined, then an initial identification value is selected from the range, and the identification result of each step is projected into the range, so that the determination of the coefficient range is one of the key problems of the control method based on the feature model. The problem of determining the parameter range of the characteristic model of the linear steady system is solved, and for a nonlinear system, the problem is always a bottleneck for restricting the design of full-coefficient adaptive control.

The method for converting nonlinear systems in special forms into a second-order time-varying difference equation set is disclosed in nonlinear golden section adaptive control, Wu hong Xin, Wang Ying Chun Shu, astronavigation newspaper publication (2002, 23 (6): 1-8.2) and multivariate linear time-varying system characteristic models and adaptive fuzzy control methods, and the Udon hong Xin publication (2005, 26 (6): 677 and 681.) have the defects that the method is only suitable for the nonlinear systems in special forms to be considered and modeling errors are not considered. The method for determining the parameter boundary of the flexible satellite characteristic model under any modeling error provided by the invention has no method with complete practical significance.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art and provides a flexible satellite control method based on a feature model.

The technical solution of the invention is as follows: a flexible satellite control method based on a feature model is realized by the following steps:

in the first step, the time scale p of the flexible satellite dynamic equation is determined by using the formula (2),

wherein the flexible satellite kinetic equation is a formula set (1),

{\tilde{w}}_{s} = [\begin{matrix} 0 & - w_{z} & w_{y} \\ w_{z} & 0 & - w_{x} \\ - w_{y} & w_{x} & 0 \end{matrix}]

phi, theta, psi denote the pitch, yaw and roll attitude angles of the flexible satellite, [ w ]_x w_y w_z]^TRepresenting the coordinates of the angular velocity of the satellite relative to the orbital coordinate system in a body coordinate system, w_s、Respectively representing the angular velocity array and the anti-symmetric array, eta, of the flexible satellite central body_l、η_rModal coordinate arrays, ξ, of the left and right sun wings of a flexible satellite, respectively_l、ξ_rThe modal damping coefficients of the left and right solar wings of the flexible satellite respectively, F_sl、F_srThe coupling coefficients of the left and right solar wings and the central body of the flexible satellite, T_sRepresenting an array of external moments acting on a flexible satellite, I_sRepresenting the flexible satellite inertia matrix, x₁＝[φθψ]^TY denotes the flexible satellite output, w_l、w_rThe angular velocities of the left and right solar wings of the flexible satellite respectively,

f₁＝C(x₁)w_s，

g = I_{s}^{- 1},

u＝T_s，f＝f₂+gu，

M_{f_{1}} = \max | f_{1} |,

M_{f_{2}} = \max | f_{2} |,

M_u＝max|gu|；

secondly, determining a sampling time scale h by using a formula (3) and the time scale p obtained in the first step,

h = \frac{p}{d}, d > 5 - - - (3);

third step, using the formula set (4) and the parameter f determined in the first step₁、x₁、x₂G, obtaining f_1iWith respect to x_1j、x_2jAnd the upper bound M of g and the partial derivative of (c),

<math> <mrow> <mo>|</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> <mo>|</mo> <mo>≤</mo> <mi>M</mi> </mrow> </math>

<math> <mrow> <mo>|</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> <mo>|</mo> <mo>≤</mo> <mi>M</mi> </mrow> </math>

||g(k)||≤M (4)

wherein x₂＝w_s，i，j＝1，2，３，k＝1，2，…，f_1i、x_1i、x_2iDenotes f₁、x₁、x₂Row i of (1);

step four, determining a parameter M by using the formula (5) and the M obtained in the step three,

wherein N is_x> 0 denotes the Flexible satellite output y_iI is the upper bound of y, i is 1, 2, 3, epsilon is the modeling error, C_x＞0；

Fifthly, obtaining the coefficient range of the flexible satellite characteristic model by using a formula group (6) according to the sampling time scale h determined in the second step, the M determined in the third step and the parameter M determined in the fourth step,

|b_ij(k)|≤M²h²

wherein a is_i1、a_i2、b_ijCoefficients representing a characteristic model, b_ij∈R，j＝1，2，3，b_i＝[b_i1 b_i2 b_i3](ii) a Sixthly, utilizing gradient method to make coefficient a of characteristic model obtained from the fifth step_i1、a_i2、b_ijIdentifying to obtain the coefficient of the identified characteristic model

Seventhly, using the identified coefficient of the characteristic model obtained in the sixth step

The control rate of the formula (7) is composed,

wherein u is_i＝u_0i+u_Gi+u_Ii+u_Di，u_0iFor maintaining/tracking the control law u_GiFor golden section control rate, u_IiFor the logical integral control rate, u_DiIs a logical differential control rate;

and step eight, substituting the control rate determined in the step seven into the flexible satellite dynamics equation of the formula set (1) to control the pitch, yaw and roll attitude angles of the flexible satellite.

In the fourth step C_xThe determination of (a) is accomplished by the following steps,

A4.1、h²|h_il is a continuous function, and h²|h_iLess than or equal to epsilon to obtain | x_1iThe range of l is such that,

wherein

h is a sampling time scale, and epsilon is a modeling error;

a4.2, | x obtained according to A4.1_1iRange of | according to the formula | x_1i|≤C_xDetermination of C_xThe value of (c).

Compared with the prior art, the invention has the beneficial effects that:

(1) the time scale and the sampling period of the flexible satellite are introduced, the change rate of the flexible satellite is described, and the bottleneck problem of flexible satellite characteristic modeling is solved;

(2) the invention provides an expression of the parameter range of the flexible satellite characteristic model, qualitatively researches the parameter property of the characteristic model, and as can be seen from the given parameter range, the boundary of the characteristic model parameter is related to the sampling period, the modeling error, the system order and the system change rate, thereby laying a theoretical foundation for the flexible satellite adaptive control based on the characteristic model;

(3) the method is suitable for the characteristic modeling of the aircraft attitude dynamics, thereby laying a foundation for the attitude control of the aircraft based on the characteristic model;

(4) the method is simple and clear, and is suitable for engineering design.

Drawings

FIG. 1 is a flow chart of the present invention.

Detailed Description

The invention is realized by the following steps as shown in figure 1:

1. the time scale, the sampling time, and the parameters M and M are determined according to the kinetic equation of the flexible satellite.

The flexible satellite dynamics are:

wherein,

{\tilde{w}}_{s} = [\begin{matrix} 0 & - w_{z} & w_{y} \\ w_{z} & 0 & - w_{x} \\ - w_{y} & w_{x} & 0 \end{matrix}]

phi, theta, psi denotes the pitch, yaw, roll attitude angles of the satellite_x w_y w_z]^TRepresenting the coordinates of the angular velocity of the satellite relative to the orbital coordinate system in a body coordinate system, w_sAnd

representing the angular velocity array and the anti-symmetric array, eta, respectively, of the satellite central body_l，η_rThe modal coordinate arrays, xi, of the left and right solar wings respectively_l，ξ_rModal damping coefficients, F, of the left and right solar wings, respectively_sl，F_srThe coupling coefficients of the left and right solar wings and the central body, T_sRepresenting an array of external moments acting on the satellite, I_sRepresenting the satellite inertia matrix, x₁＝[φθψ]^TY denotes satellite output, w_l、w_rThe angular velocities of the left and right solar wings of the flexible satellite are respectively.

The time scale p is calculated as follows:

wherein,

f₁＝C(x₁)w_s，

g = I_{s}^{- 1},

u＝T_s，f＝f₂+gu

M_{f_{1}} = \max | f_{1} |,

M_{f_{2}} = \max | f_{2} |,

M_u＝max|gu|

the sampling time scale h is calculated as follows:

h = \frac{p}{d}, d > 5

m is f_1iWith respect to x_1j、x_2jThe partial derivative of (i, j ═ 1, 2, 3) and the upper bound of g, i.e.

<math> <mrow> <mo>|</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> </mrow> <msub> <mrow> <mo>&PartialD;</mo> <mi>x</mi> </mrow> <mrow> <mn>1</mn> <mi>j</mi> </mrow> </msub> </mfrac> <mo>|</mo> <mo>≤</mo> <mi>M</mi> <mo>,</mo> </mrow> </math>

<math> <mrow> <mo>|</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> <mo>|</mo> <mo>≤</mo> <mi>M</mi> <mo>,</mo> </mrow> </math>

||g(k)||≤M，i，j＝1，2，3，k＝1，2，…

Wherein x is₂＝w_s，f_1i，x_1i，x_2iDenotes f₁，x₁，x₂I is 1, 2, 3.

m is determined according to the following formula:

wherein N is_x> 0 denotes the system output y_iUpper bound of |, i ═ 1, 2, 3;

C_x> 0 is determined according to the following formula: note the book

<math> <mrow> <msub> <mi>h</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>Σ</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>&NotEqual;</mo> <mi>i</mi> </mrow> <mn>3</mn> </munderover> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>x</mi> <mo>·</mo> </mover> <mrow> <mn>1</mn> <mi>j</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </mfrac> <msub> <mi>f</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1,2,3</mn> </mrow> </math>

h²|h_iIf | is a continuous function, thenGiven a modeling error ε, the presence of C_x> 0, for i ═ 1, 2, 3, when | x_1i|≤C_xWhen h is present²|h_i|≤ε。

2. And determining the coefficient range of the characteristic model according to the variables obtained in the step 1.

Designing a set of nonlinear and compressive functions:

s_{i 1} (k) = \frac{y_{i} (k)}{y_{i} {(k)}^{2} + y_{i} {(k - 1)}^{2} + N_{x}}

s_{i 2} (k) = \frac{x_{1 i} (k - 1)}{y_{i} {(k)}^{2} + y_{i} {(k - 1)}^{2} + N_{x}}

s_{i 3} (k) = \frac{N_{x}}{y_{i} {(k)}^{2} + y_{i} {(k - 1)}^{2} + N_{x}}

and

f_{c, i} = S_{i} (k) s_{i 1} y_{i} (k) + S_{i} (k) s_{i 2} y_{i} (k - 1) + s_{i 3}^{m + 1}, i = 1,2,3

wherein,

the characteristic model is as follows:

{\tilde{y}}_{i} (k + 1) = a_{i 1} (k) {\tilde{y}}_{i} (k) + a_{i 2} (k) {\tilde{y}}_{i} (k - 1) + b_{i} (k) u (k), i = 1,2,3

wherein, a_i1，a_i2∈R，b_i＝[b_i1 b_i2 b_i3]，b_ije.R, j is 1, 2, 3, representing coefficients of the feature model,

express characterThe output of the eigenmodel, R, represents the real number set.

Y is given below₁＝x₁₁The rest states are similar. x is the number of₁₁The following differential equation is satisfied:

by derivation of the above formula, the result is obtained

<math> <mrow> <msub> <mover> <mi>x</mi> <mrow> <mo>·</mo> <mo>·</mo> </mrow> </mover> <mn>11</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mn>11</mn> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mn>11</mn> </msub> </mrow> </mfrac> <msub> <mover> <mi>x</mi> <mo>·</mo> </mover> <mn>11</mn> </msub> <mo>+</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mn>11</mn> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </mfrac> <mi>gu</mi> </mrow> </math>

Wherein,

<math> <mrow> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>Σ</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>2</mn> </mrow> <mn>3</mn> </munderover> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mn>11</mn> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>x</mi> <mo>·</mo> </mover> <mrow> <mn>1</mn> <mi>j</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mn>11</mn> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </mfrac> <msub> <mi>f</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </math>

discretizing the above formula and obtaining easily

<math> <mrow> <msub> <mi>x</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>2</mn> <msub> <mi>x</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <mi>h</mi> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mn>11</mn> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mn>11</mn> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>h</mi> <mn>2</mn> </msup> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mn>11</mn> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </mfrac> <mi>gu</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>h</mi> <mn>2</mn> </msup> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </math>

Compressing function f_c，1Multiplying the last item of the above formula, and sorting to obtain

x₁₁(k+1)＝a₁₁(k)x₁₁(k)+a₁₂(k)x₁₁(k-1)+b₁(k)u(k)+e₁(k)

Wherein,

<math> <mrow> <msub> <mi>a</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>2</mn> <mo>+</mo> <mi>h</mi> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mn>11</mn> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mn>11</mn> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>h</mi> <mn>2</mn> </msup> <msub> <mi>S</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <msub> <mi>s</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msub> <mi>a</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>h</mi> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mn>11</mn> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mn>11</mn> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>h</mi> <mn>2</mn> </msup> <msub> <mi>S</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <msub> <mi>s</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msub> <mi>b</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>h</mi> <mn>2</mn> </msup> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mn>11</mn> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mi>g</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </math>

e_{1} (k) = h^{2} h_{1} s_{13}^{m + 1}

wherein e₁(k) Representing the modeling error of the feature model. The modeling error | e can be known₁(k) And | < ε. Due to the fact that

|S_i(k)|≤m+1，i＝1，2，3，k＝1，2，…

From h₁Definition of (1), to know

And is easy to know s₁₁，s₁₂Are all less than 1, therefore

|b_ij(k)|≤M²h²，j＝1，2，3

3. And (3) identifying parameters of the characteristic model by using a gradient method according to the coefficient range of the characteristic model obtained in the step (2). (the specific identification method is described in Chongzhi, Xiao De cloud article "identification of Process" page 201 and 229.)

θ_i＝[a_i1，a_i2，b_i]^T，i＝1，2，3

Wherein λ is_i1，λ_i2And (3) in the identification process, limiting the identification result by using the parameter range given in the step (2) for adjusting the parameters.

And 4, designing a control law according to the coefficient of the characteristic model obtained by identification in the step 3.

The control law is as follows:

wherein,

u_i＝u_0i+u_Gi+u_Ii+u_Di，i＝1，2，3

u_Ii(k)＝u_Ii(k-1)-k_Iie_i(k)

u_Di(k)＝-k_Die_i(k)

l₁＝0.382，l₂＝0.618，e_i(k)＝y_i(k)-y_ri(k)，

k_Ii1＞＞k_Ii2＞0，

or,k_Ii1，k_Ii2，c_Di，l_Di，λ_0i，λ_Gito adjust the parameters as required, y_ri(k) To track an objective function. u. of_0i，u_Gi，u_IiAnd u and_Dithe control law is called maintenance/tracking control law, golden section control rate, logic integral control rate and logic differential control rate (the specific resolving method is shown in the fifth chapter of intelligent adaptive control based on feature model published by the scientific and technical publication 2009, wu hongxin, jun and jie yongchun).

5. And (4) feeding the control rate determined in the step (4) back to a flexible satellite dynamic equation recorded in the formula set (1) to control the pitch, yaw and roll attitude angles of the flexible satellite.

The invention is not described in detail and is within the knowledge of a person skilled in the art.

Claims

1. A flexible satellite control method based on a feature model is characterized by comprising the following steps:

wherein the flexible satellite kinetic equation is a formula set (1),

{\tilde{w}}_{s} = [\begin{matrix} 0 & - w_{z} & w_{y} \\ w_{z} & 0 & - w_{x} \\ - w_{y} & w_{x} & 0 \end{matrix}]

phi, theta, psi denotes the pitch, yaw and roll attitude angles of the flexure satellite, [ wx wy wz]^TRepresenting the coordinates of the angular velocity of the satellite relative to the orbital coordinate system in a body coordinate system, w_s、

Respectively representing the angular velocity array and the anti-symmetric array, eta, of the flexible satellite central body_l、η_rModal coordinate arrays, ξ, of the left and right sun wings of a flexible satellite, respectively_l、ξ_rThe modal damping coefficients of the left and right solar wings of the flexible satellite respectively, F_sl、F_srThe coupling coefficients of the left and right solar wings and the central body of the flexible satellite, T_sRepresenting an array of external moments acting on a flexible satellite, I_sRepresenting the flexible satellite inertia matrix, x_l＝[φθψ]^TY denotes the flexible satellite output, w_l、w_rThe angular velocities of the left and right solar wings of the flexible satellite respectively,

f_l＝C(x₁)w_s，

g = I_{s}^{- 1},

u＝T_s，f＝f₂+gu，

M_u＝max|gu|；

h = \frac{p}{d}, d > 5 - - - (3);

||g(k)||≤M (4)

wherein x₂＝w_s，i，j＝1，2，3，k＝1，2，…，f_1i、x_1i、x_2iDenotes f₁、x₁、x₂Row i of (1);

|b_ij(k)|≤M²h²

wherein a is_i1、a_i2、b_ijCoefficients representing a characteristic model, b_ij∈R，j＝1，2，3，b_i＝[b_i1 b_i2 b_i3]，d＞5；

Sixthly, utilizing gradient method to make coefficient a of characteristic model obtained from the fifth step_i1、a_i2、b_ijIdentifying to obtain the coefficient of the identified characteristic model

Seventhly, using the identified coefficient of the characteristic model obtained in the sixth stepThe control rate of the formula (7) is composed,

2. The flexible satellite control method based on the feature model according to claim 1, wherein: in the fourth step C_xThe determination of (a) is accomplished by the following steps,

wherein

<math> <mrow> <msub> <mi>h</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>Σ</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>&NotEqual;</mo> <mi>i</mi> </mrow> <mn>3</mn> </munderover> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> <msub> <mover> <mi>x</mi> <mo>·</mo> </mover> <mrow> <mn>1</mn> <mi>j</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <msub> <mi>f</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mo>&PartialD;</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </mfrac> <msub> <mi>f</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1,2,3</mn> <mo>,</mo> </mrow> </math>

h is a sampling time scale, and epsilon is a modeling error;