CN105867406A - Assembly spacecraft closed loop feedback optimal control distribution method - Google Patents

Abstract

The invention relates to an assembly spacecraft closed loop feedback optimal control distribution method which is designed oriented to the problems of executing mechanism installation deviation, executing mechanism saturation and energy restriction of an assembly spacecraft. The assembly spacecraft closed loop feedback optimal control distribution method comprises the steps that firstly, an assembly spacecraft posture kinematic and dynamic model including executing mechanism installation deviation is established; secondly, an assembly spacecraft anti-saturation and posture stable controller is designed for the assembly spacecraft posture kinematic and dynamic model, and an assembly spacecraft three-axis virtual posture stable control instruction is obtained through solving; thirdly, an open loop optimal control distribution method is designed based on the virtual control instruction, and distribution is made to meet the restriction condition of energy optimum; finally, based on the open loop optimal control distribution method, the closed loop feedback optimal control distribution method is designed to reduce distribution errors brought by executing mechanism installation deviation. The assembly spacecraft closed loop feedback optimal control distribution method has the advantages of being high in reliability and low in energy consumption, and is suitable for control distribution among multiple executing mechanisms of the assembly spacecraft.

Description

Closed-loop feedback optimal control distribution method for combined spacecraft

Technical Field

The invention designs a closed-loop feedback optimal control distribution method for a combined spacecraft, which is mainly applied to attitude stability control of a novel space combined spacecraft in an energy optimal mode under the condition that an actuating mechanism has installation deviation and saturation limitation.

Background

The combined spacecraft is a spacecraft formed by combining two or more spacecraft units in a butt joint or capturing mode and the like according to the requirement of a space complex task, and the main combination types comprise rendezvous and butt joint of a large space station and a spacecraft, a waste satellite and a service satellite, a space debris and capturing satellite, a space robot and the like. The spacecraft is mainly used for completing complex space tasks with high difficulty, so that the requirement on the cooperative control precision among all space units is high. The realization of cooperative control of the combined spacecraft is a core technology which must be mastered by the world and the world in the future, and is also important competitiveness among the countries in the aerospace field.

Generally, the combined spacecraft is provided with a plurality of executing mechanisms, so that the available resources on the combined spacecraft are effectively utilized, the instructions executed by the executing mechanisms are reasonably distributed, and the control precision and reliability of the combined spacecraft are greatly improved. Due to the defects of the prior art, the installation deviation generally exists in the actuating mechanism installed on the spacecraft, the actuating mechanism is limited by the saturation factor and is constrained by the energy, and therefore the implementation of the optimal control distribution among multiple actuating mechanisms is a key technology under the constraints of considering the installation deviation, the saturation and the energy of the actuating mechanism.

The existing open-loop control distribution technology in the prior art considers the limits of energy and actuator saturation factors, but the method puts high requirements on the accuracy of the actuator, and the system can be stabilized on the basis of meeting the constraint condition only when the actual output torque of the actuator is completely equal to the ideal control torque. When the installation deviation of the actuating mechanism exists in the open-loop control distribution method, the control distribution error is greatly increased, the control performance of the combined spacecraft system is seriously influenced, and the existing control distribution method at the present stage can fail when the installation deviation, saturation and energy constraint of the actuating mechanism are considered at the same time.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: aiming at the problems of installation error and saturation limitation of an actuating mechanism of the combined spacecraft, the closed-loop feedback optimal control distribution method of the combined spacecraft is provided under the condition of energy constraint, the problem that the control precision of the combined spacecraft is reduced due to installation deviation of the actuating mechanism in attitude stability control is solved, the control precision of the combined spacecraft is improved, and meanwhile, the energy optimal control is realized.

The technical solution of the invention is as follows: an optimal control allocation method for an assembly spacecraft based on closed-loop feedback is shown in fig. 1, and the method comprises the following implementation steps:

firstly, establishing a combined spacecraft attitude kinematics and dynamics model containing uncertainty of an actuating mechanism:

$\left\{\begin{array}{c}\stackrel{\·}{q}=\frac{1}{2}(q_0\mathrm{\ω}+q\×\mathrm{\ω})\\ {\stackrel{\·}{q}}_0=-\frac{1}{2}{q}^T\mathrm{\ω}\\ J\stackrel{\·}{\mathrm{\ω}}=u\left(t\right)-\mathrm{\ω}\×J\mathrm{\ω}\\ u\left(t\right)=(D_0+\mathrm{\Δ}D)\mathrm{\τ}\left(t\right)\end{array}\right.$

wherein q and q₀Respectively are a four-element vector and a scalar of the attitude of the combined spacecraft, J is the moment of inertia of the combined spacecraft, omega is the attitude angular velocity of the combined spacecraft, u (t) is a three-axis virtual attitude stability control instruction of the combined spacecraft, tau (t) is the output of an actuating mechanism, D₀Is the nominal actuator distribution matrix and △ D is the error matrix representing actuator mounting variations.

Secondly, designing an anti-saturation attitude stability controller of the combined spacecraft based on the attitude kinematics and dynamics model of the combined spacecraft as follows:

u(t)＝-βu_maxq-(1-β)u_maxTanh[(ω+kq)/p²]

wherein u (t) is a three-axis virtual attitude stabilization control command of the combined spacecraft, and u_maxIs the upper bound of the control input, β is a value satisfying 0<β<1, Tanh (-) is a standard tangent function, ω is a combinationThe attitude angular velocity of the spacecraft is satisfied by that q is a four-element vector of the attitude of the spacecraft in combination, and p is a normal numberThe gain k is a function of time, and controls the switching of ω and q, and the change is as follows:

$\begin{array}{c}\stackrel{\&CenterDot;}{k}=-{\mathrm{\&gamma;}}_k\left(1-\mathrm{\&beta;}\right)u_{\max }{q}^T\{Tanh\&lsqb;\left(\mathrm{\&omega;}+kq\right)/p^2\&rsqb;+\\ Tanh\left(kq/p^2\right)\}-{\mathrm{\&gamma;}}_k{\mathrm{\&gamma;}}_{c}k\left(q^{T}q+{\mathrm{\&gamma;}}_d\right)\end{array}$

wherein, γ_k∈[0,1]And gamma_d∈[0,1]Is a normal number, γ_cIs a unit adjustment parameter.

Thirdly, based on the anti-saturation attitude stabilization controller, designing an optimization objective function of the open-loop optimal control distribution method as follows:

Θ＝arg min{||R₀W₀τ_act(t)||²+||R₁W₁[τ_act(t)-τ_d(t)]||²+||W₂[τ_act(t)-τ_act(t-T)]||²}

s.t.u_d(t)＝D₀τ_act(t)

wherein, W₀、W₁And W₂Respectively positive definite diagonal matrixes which express the weight among optimization targets; d₀Is a nominal actuator distribution matrix, u_d(t) u (t) andrespectively representing expected control commands and execution mechanism commands, u (t) is a three-axis virtual attitude stabilization control command in the second step,is the plus inverse of the nominal actuator allocation matrix, correspondingly, u_act(t) and τ_act(T) represents the actual control command and the actual actuator command, respectively, T is the system sampling time, R₀And R₁Also positively determined diagonal matrix for applying τ_act(t) and τ_d(t) is limited to the range allowed by the actuator and is defined as R₀＝diag(r₀)，R₁＝diag(r₁)，r₀And r₁Are respectively defined as follows:

$r_0=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)}{{\mathrm{\&tau;}}_{act}\left(t\right)}& {\mathrm{\&tau;}}_{act}\left(t\right)\&GreaterEqual;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\\ 1& {\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\&le;{\mathrm{\&tau;}}_{act}\left(t\right)\&le;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\\ \frac{{\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)}{{\mathrm{\&tau;}}_{act}\left(t\right)}& {\mathrm{\&tau;}}_{act}\left(t\right)\&le;{\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\end{array}\right.$

$r_1=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)}{{\mathrm{\&tau;}}_d\left(t\right)}& {\mathrm{\&tau;}}_d\left(t\right)\&GreaterEqual;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\\ 1& {\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\&le;{\mathrm{\&tau;}}_d\left(t\right)\&le;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\\ \frac{{\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)}{{\mathrm{\&tau;}}_d\left(t\right)}& {\mathrm{\&tau;}}_d\left(t\right)\&le;{\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\end{array}\right.$

wherein,andτ _act(t) are each τ_actUpper and lower bounds of (t), correspondingAndτ _d(t) are each τ_dThe upper and lower bounds of (t);

the open-loop optimal control distribution method meeting the condition constraint comprises the following steps:

t_act(t)＝Eτ_d(t)+Fτ_act(t-T)+Gu_d(t)

wherein,E＝(I-GD₀)W^-2(R₁W₁)²,G＝W^-1(D₀W^-1)⁺and I is a unit array.

Fourthly, based on the open-loop optimal control distribution method, an optimization objective function of the closed-loop feedback optimal control distribution method is designed as follows:

Θ＝arg min{||R₀W₀τ_act(t)||²+||R₁W₁[τ_act(t)-τ_d(t)]||²+||W₂[τ_act(t)-τ_act(t-T)]||²}

s.t.u_d(t)＝(D₀+△D)τ_act(t)

wherein, W₀、W₁And W₂Respectively positive definite diagonal matrixes which express the weight among optimization targets; d₀Is a nominal actuator distribution matrix, △ D is an error matrix representing actuator mounting tolerances_d(t) u (t) andrespectively representing expected control commands and execution mechanism commands, u (t) is a three-axis virtual attitude stabilization control command solved in the second step,is the plus inverse of the nominal actuator allocation matrix, correspondingly, u_act(t) and τ_act(t) represents the actual control command andthe actuator command, T is the system sampling time, R₀And R₁Also positively determined diagonal matrix for applying τ_act(t) and τ_d(t) is limited to the range allowed by the actuator and is defined as R₀＝diag(r₀)，R₁＝diag(r₁)，r₀And r₁Are respectively defined as follows:

$r_0=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)}{{\mathrm{\&tau;}}_{act}\left(t\right)}& {\mathrm{\&tau;}}_{act}\left(t\right)\&GreaterEqual;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\\ 1& {\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\&le;{\mathrm{\&tau;}}_{act}\left(t\right)\&le;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\\ \frac{{\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)}{{\mathrm{\&tau;}}_{act}\left(t\right)}& {\mathrm{\&tau;}}_{act}\left(t\right)\&le;{\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\end{array}\right.$

$r_1=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)}{{\mathrm{\&tau;}}_d\left(t\right)}& {\mathrm{\&tau;}}_d\left(t\right)\&GreaterEqual;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\\ 1& {\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\&le;{\mathrm{\&tau;}}_d\left(t\right)\&le;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\\ \frac{{\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)}{{\mathrm{\&tau;}}_d\left(t\right)}& {\mathrm{\&tau;}}_d\left(t\right)\&le;{\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\end{array}\right.$

wherein,andτ _act(t) are each τ_actUpper and lower bounds of (t), correspondingAndτ _d(t) are each τ_dThe upper and lower bounds of (t);

the closed loop feedback optimal control distribution method meeting the condition constraint comprises the following steps:

τ_act(t)＝Eτ_CA(t)+Fτ_act(t-T)+Gu_CA(t)

wherein,E＝(I-GD₀)W^-2(R₁W₁)²,G＝W^-1(D₀W^-1)⁺，u_CA(t)＝u_d(t)+e(t-T)＝u_d(t)+u_CA(t-T)-u_act(T-T), I is a unit matrix.

Compared with the prior art, the invention has the advantages that:

(1) the invention introduces closed loop feedback to reduce control distribution error caused by installation deviation of an actuating mechanism; firstly, designing an open-loop optimal control distribution method based on an anti-saturation attitude stability control instruction, and considering the saturation and energy constraint of an execution mechanism; closed loop feedback is introduced to reduce distribution errors caused by installation deviation of the actuating mechanism; the designed closed-loop feedback optimal control distribution method can realize attitude stabilization control of the combined spacecraft with minimum energy under the condition that the executing mechanism has installation deviation and saturation limitation, solve the problem that the control precision of the combined spacecraft is reduced due to the installation deviation of the executing mechanism in the attitude stabilization control, improve the control precision of the combined spacecraft, and simultaneously realize the optimal control of the energy.

(2) The invention also has the advantages of high reliability and low energy consumption, and is suitable for control distribution among a plurality of actuating mechanisms of the combined spacecraft.

Drawings

FIG. 1 is a design flow chart of a closed-loop feedback optimal control distribution method for a combined spacecraft of the present invention;

FIG. 2 is a design flow chart of an embodiment of the present invention.

Detailed Description

As shown in fig. 2, the implementation steps of the present invention are as follows (the implementation of the method is described below by taking an example of a combined spacecraft composed of a space obsolete microsatellite and a service satellite):

firstly, establishing attitude kinematics and dynamics models of a discarded microsatellite and a service satellite:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{q}=\frac{1}{2}(q_0\mathrm{\&omega;}+q\&times;\mathrm{\&omega;})\\ {\stackrel{\&CenterDot;}{q}}_0=-\frac{1}{2}{q}^T\mathrm{\&omega;}\\ J\stackrel{\&CenterDot;}{\mathrm{\&omega;}}=u\left(t\right)-\mathrm{\&omega;}\&times;J\mathrm{\&omega;}\\ u\left(t\right)=(D_0+\mathrm{\&Delta;}D)\mathrm{\&tau;}\left(t\right)\end{array}\right.$

wherein q and q₀The attitude four-element vector and scalar of the discarded microsatellite and service satellite combination respectively have initial values of q ═ 0.4, -0.4,0.2]^T，q₀＝0.8，Is the moment of inertia of the assembly of the waste microsatellite and the service satellite, omega is the attitude angular velocity of the assembly of the waste microsatellite and the service satellite, and the initial value is omega ═ 1, -1,0.5]rad/s, u (t) is the virtual control command, τ (t) is the actuator output,is a nominal actuator allocation matrix,is an error matrix representing the mounting deviation of the actuator, wherein α is 45 DEG, △ r_i＝0.1m，β_i＝15°，l＝0.24m。

And secondly, designing an anti-saturation attitude stabilization controller of the waste microsatellite and service satellite assembly based on the dynamics model established in the first step as follows:

u(t)＝-βu_maxq-(1-β)u_maxTanh[(ω+kq)/p²]

wherein u (t) is a three-axis virtual attitude stabilization control command of the discarded microsatellite and service satellite assembly, u_max2N · m is an upper bound of the control output, and β is 0.005 and satisfies 0<β<A constant of 1, q is an attitude four-element vector of the abandoned microsatellite and service satellite combination, and the initial value is q ═ 0.4, -0.4,0.2]^Tω is the attitude angular velocity of the assembly of the discarded microsatellite and the service satellite, and the initial value is ω ═ 1, -1,0.5]rad/s，P²Tanh (·) is a standard tangent function, 0.5. The gain k is a function of time, and controls the switching of ω and q, and the change is as follows:

$\begin{array}{c}\stackrel{\&CenterDot;}{k}=-{\mathrm{\&gamma;}}_k\left(1-\mathrm{\&beta;}\right)u_{\max }{q}^T\{Tanh\&lsqb;\left(\mathrm{\&omega;}+kq\right)/p^2\&rsqb;+\\ Tanh\left(kq/p^2\right)\}-{\mathrm{\&gamma;}}_k{\mathrm{\&gamma;}}_{c}k(q^{T}q+{\mathrm{\&gamma;}}_d)\end{array}$

wherein k (0) ═ 1,1]^T，γ_k＝10^-3radkg^-1m²And gamma_d＝10^-5，γ_c＝1kgm²s^-1。

Thirdly, designing an optimization objective function of the open-loop optimal control distribution method according to the saturation controller as follows:

Θ＝arg min{||R₀W₀τ_act(t)||²+||R₁W₁[τ_act(t)-τ_d(t)]||²+||W₂[τ_act(t)-τ_act(t-T)]||²}

s.t.u_d(t)＝D₀τ_act(t)

wherein,andpositive definite diagonal matrixes respectively representing the weight among all parts; d₀Is a nominal actuator distribution matrix, u_d(t) u (t) andrespectively representing the desired control command and the actuator command, u (t) is the three-axis virtual control command in the second step,is the plus inverse of the nominal actuator distribution matrix, u_d(t) and τ_d(t) represents a desired control command and an actuator command, respectively, and, correspondingly, u_act(t) and τ_act(T) represents an actual control command and an actual actuator command, respectively, and T ═ 0.5s is a system sampling time. R₀And R₁Also positively determined diagonal matrix for applying τ_act(t) and τ_d(t) limiting to performingWithin the range allowed by the mechanism, defined as R₀＝diag(r₀)，R₁＝diag(r₁). And r₀And r₁Are respectively defined as follows:

$r_0=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)}{{\mathrm{\&tau;}}_{act}\left(t\right)}& {\mathrm{\&tau;}}_{act}\left(t\right)\&GreaterEqual;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\\ 1& {\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\&le;{\mathrm{\&tau;}}_{act}\left(t\right)\&le;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\\ \frac{{\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)}{{\mathrm{\&tau;}}_{act}\left(t\right)}& {\mathrm{\&tau;}}_{act}\left(t\right)\&le;{\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\end{array}\right.$

$r_1=\left\{\begin{array}{cc}\frac{\stackrel{\&OverBar;}{{\mathrm{\&tau;}}_d}\left(t\right)}{{\mathrm{\&tau;}}_d\left(t\right)}& {\mathrm{\&tau;}}_d\left(t\right)\&GreaterEqual;\stackrel{\&OverBar;}{{\mathrm{\&tau;}}_d}\left(t\right)\\ 1& {\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\&le;{\mathrm{\&tau;}}_d\left(t\right)\&le;\stackrel{\&OverBar;}{{\mathrm{\&tau;}}_d}\left(t\right)\\ \frac{\mathrm{\&tau;}\left(t\right)}{{\mathrm{\&tau;}}_d\left(t\right)}& {\mathrm{\&tau;}}_d\left(t\right)\&le;{\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\end{array}\right.$

wherein,andτ _act(t) — 5N is each τ_actThe upper and lower bounds of (t), correspondingly,andτ _d(t) are each τ_dThe upper and lower bounds of (t).

The open-loop optimal control distribution method meeting the condition constraint comprises the following steps:

t_act(t)＝Eτ_d(t)+Fτ_act(t-T)+Gu_d(t)

wherein,E＝(I-GD₀)W^-2(R₁W₁)²,G＝W^-1(D₀W^-1)⁺and I is a unit array.

Fourthly, based on the open-loop control distribution method, an optimization objective function of the closed-loop feedback optimal control distribution method is designed as follows:

Θ＝arg min{||R₀W₀τ_act(t)||²+||R₁W₁[τ_act(t)-τ_d(t)]||²+||W₂[τ_act(t)-τ_act(t-T)]||²}

s.t.u_d(t)＝(D₀+△D)τ_act(t)

wherein,andrespectively positive definite diagonal matrixes which express the weight among optimization targets; d₀Is a nominal actuator distribution matrix, △ D is an error matrix representing actuator mounting tolerances_d(t) u (t) andrespectively representing the desired control command and the actuator command, u (t) is the three-axis virtual control command in the second step,is the plus inverse of the nominal actuator allocation matrix, correspondingly, u_act(t) and τ_act(T) represents an actual control command and an actual actuator command, respectively, T is a system sampling time, R is 0.5s₀And R₁Also positively determined diagonal matrix for applying τ_act(t) and τ_d(t) is limited to the range allowed by the actuator and is defined as R₀＝diag(r₀)，R₁＝diag(r₁)，r₀And r₁Are respectively defined as follows:

$r_0=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)}{{\mathrm{\&tau;}}_{act}\left(t\right)}& {\mathrm{\&tau;}}_{act}\left(t\right)\&GreaterEqual;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\\ 1& {\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\&le;{\mathrm{\&tau;}}_{act}\left(t\right)\&le;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\\ \frac{{\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)}{{\mathrm{\&tau;}}_{act}\left(t\right)}& {\mathrm{\&tau;}}_{act}\left(t\right)\&le;{\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\end{array}\right.$

$r_1=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)}{{\mathrm{\&tau;}}_d\left(t\right)}& {\mathrm{\&tau;}}_d\left(t\right)\&GreaterEqual;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\\ 1& {\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\&le;{\mathrm{\&tau;}}_d\left(t\right)\&le;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\\ \frac{{\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)}{{\mathrm{\&tau;}}_d\left(t\right)}& {\mathrm{\&tau;}}_d\left(t\right)\&le;{\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\end{array}\right.$

wherein,andτ _act(t) — 5N is each τ_actThe upper and lower bounds of (t), correspondingly,andτ _d(t) are each τ_dThe upper and lower bounds of (t);

the closed-loop optimal control distribution method meeting the condition constraint comprises the following steps:

τ_act(t)＝Eτ_CA(t)+Fτ_act(t-T)+Gu_CA(t)

wherein,E＝(I-GD₀)W^-2(R₁W₁)²,G＝W^-1(D₀W^-1)⁺，u_CA(t)＝u_d(t)+e(t-T)＝u_d(t)+u_CA(t-T)-u_act(T-T), I is a unit matrix.

Those skilled in the art will appreciate that the invention may be practiced without these specific details.

Claims (5)

1. A closed-loop feedback optimal control distribution method for a combined spacecraft is characterized by comprising the following steps:

(1) establishing a combined spacecraft attitude kinematics and dynamics model containing the installation deviation of an actuating mechanism;

(2) aiming at the attitude kinematics and dynamics model of the combined spacecraft, designing an anti-saturation attitude stability controller of the combined spacecraft, and solving to obtain a three-axis virtual attitude stability control instruction of the combined spacecraft;

(3) designing an open-loop optimal control distribution method according to the three-axis virtual attitude stability control instruction obtained by solving so that distribution meets constraint conditions of optimal energy;

(4) and (4) designing a closed-loop feedback optimal control distribution method based on the open-loop optimal control distribution method in the step (3), and reducing distribution errors caused by installation deviation of the actuating mechanism.

2. The closed-loop feedback optimal control allocation method for a spacecraft assembly according to claim 1, wherein: the combination spacecraft attitude kinematics and dynamics model of the step (1) is as follows:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{q}=\frac{1}{2}(q_0\mathrm{\&omega;}+q\&times;\mathrm{\&omega;})\\ {\stackrel{\&CenterDot;}{q}}_0=-\frac{1}{2}{q}^T\mathrm{\&omega;}\\ J\stackrel{\&CenterDot;}{\mathrm{\&omega;}}=u\left(t\right)-\mathrm{\&omega;}\&times;J\mathrm{\&omega;}\\ u\left(t\right)=(D_0+\mathrm{\&Delta;}D)\mathrm{\&tau;}\left(t\right)\end{array}\right.$

wherein q and q₀Respectively are a four-element vector and a scalar of the attitude of the combined spacecraft, J is the moment of inertia of the combined spacecraft, omega is the attitude angular velocity of the combined spacecraft, u (t) is a three-axis virtual attitude stability control instruction of the combined spacecraft, tau (t) is the output of an actuating mechanism, D₀Is the nominal actuator distribution matrix, ΔD is an error matrix representing actuator mounting variation.

3. The closed-loop feedback optimal control allocation method for a spacecraft assembly according to claim 1, wherein: the anti-saturation attitude stabilization controller of the combined spacecraft designed in the step (2) is as follows:

u(t)＝-βu_maxq-(1-β)u_maxTanh[(ω+kq)/p²]

wherein u (t) is a three-axis virtual attitude stabilization control command of the combined spacecraft, and u_maxIs the upper bound of the control input, β is a value satisfying 0<β<1, Tanh (-) is a standard tangent function, omega is the attitude angular velocity of the combined spacecraft, q is the four-element vector of the attitude of the combined spacecraft, p is a normal number, and the conditions are metThe gain k is a function of time, and controls the switching of ω and q, and the change is as follows:

$\begin{array}{c}\stackrel{\&CenterDot;}{k}=-{\mathrm{\&gamma;}}_k(1-\mathrm{\&beta;})u_{\max }{q}^T\{Tanh\&lsqb;(\mathrm{\&omega;}+kq)/p^2\&rsqb;+\\ Tanh(kq/p^2)\}-{\mathrm{\&gamma;}}_k{\mathrm{\&gamma;}}_{c}k(q^{T}q+{\mathrm{\&gamma;}}_d)\end{array}$

wherein, γ_k∈[0,1]And gamma_d∈[0,1]Is a normal number, γ_cIs a unit adjustment parameter.

4. The closed-loop feedback-based method for optimal control allocation of a combined spacecraft as claimed in claim 1, wherein: the optimization objective function for designing the open-loop optimal control distribution method in the step (3) is as follows:

Θ＝arg min{||R₀W₀τ_act(t)||²+||R₁W₁[τ_act(t)-τ_d(t)]||²+||W₂[τ_act(t)-τ_act(t-T)]||²}

s.t.u_d(t)＝D₀τ_act(t)

wherein, W₀、W₁And W₂Respectively positive definite diagonal matrixes which express the weight among optimization targets; d₀Is a nominal actuator distribution matrix, u_d(t) u (t) andrespectively representing expected control commands and execution mechanism commands, u (t) is the three-axis virtual attitude stabilization control command in the step (3),is the plus inverse of the nominal actuator allocation matrix, correspondingly, u_act(t) and τ_act(T) represents the actual control command and the actual actuator command, respectively, T is the system sampling time, R₀And R₁Also positively determined diagonal matrix for applying τ_act(t) and τ_d(t) is limited to the range allowed by the actuator and is defined as R₀＝diag(r₀)，R₁＝diag(r₁)，r₀And r₁Are respectively defined as follows:

$r_0=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)}{{\mathrm{\&tau;}}_{act}\left(t\right)}& {\mathrm{\&tau;}}_{act}\left(t\right)\&GreaterEqual;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\\ 1& {\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\&le;{\mathrm{\&tau;}}_{act}\left(t\right)\&le;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\\ \frac{{\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)}{{\mathrm{\&tau;}}_{act}\left(t\right)}& {\mathrm{\&tau;}}_{act}\left(t\right)\&le;{\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\end{array}\right.$

$r_1=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)}{{\mathrm{\&tau;}}_d\left(t\right)}& {\mathrm{\&tau;}}_d\left(t\right)\&GreaterEqual;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\\ 1& {\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\&le;{\mathrm{\&tau;}}_d\left(t\right)\&le;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\\ \frac{{\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)}{{\mathrm{\&tau;}}_d\left(t\right)}& {\mathrm{\&tau;}}_d\left(t\right)\&le;{\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\end{array}\right.$

wherein,andτ _act(t) are each τ_actUpper and lower bounds of (t), correspondingAndτ _d(t) are each τ_dThe upper and lower bounds of (t);

the open-loop optimal control distribution method meeting the condition constraint comprises the following steps:

t_act(t)＝Eτ_d(t)+Fτ_act(t-T)+Gu_d(t)

wherein,E＝(I-GD₀)W^-2(R₁W₁)²,

G＝W^-1(D₀W^-1)⁺and I is a unit array.

5. The closed-loop feedback-based method for optimal control allocation of a combined spacecraft as claimed in claim 1, wherein: the optimization objective function of the closed-loop feedback optimal control allocation method designed in the step (4) is as follows:

Θ＝arg min{||R₀W₀τ_act(t)||²+||R₁W₁[τ_act(t)-τ_d(t)]||²+||W₂[τ_act(t)-τ_act(t-T)]||²}

s.t.u_d(t)＝(D₀+ΔD)τ_act(t)

wherein, W₀、W₁And W₂Respectively positive definite diagonal matrixes which express the weight among optimization targets; d₀Is the nominal actuator distribution matrix and Δ D is the error matrix representing actuator mounting variation. u. of_d(t) u (t) andrespectively representing expected control commands and execution mechanism commands, u (t) is the three-axis virtual attitude stabilization control command in the step (3),is the plus inverse of the nominal actuator allocation matrix, correspondingly, u_act(t) and τ_act(T) represents the actual control command and the actual actuator command, respectively, T is the system sampling time, R₀And R₁Also positively determined diagonal matrix for applying τ_act(t) and τ_d(t) is limited to the range allowed by the actuator and is defined as R₀＝diag(r₀)，R₁＝diag(r₁)，r₀And r₁Are respectively defined as follows:

$r_0=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)}{{\mathrm{\&tau;}}_{act}\left(t\right)}& {\mathrm{\&tau;}}_{act}\left(t\right)\&GreaterEqual;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\\ 1& {\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\&le;{\mathrm{\&tau;}}_{act}\left(t\right)\&le;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\\ \frac{{\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)}{{\mathrm{\&tau;}}_{act}\left(t\right)}& {\mathrm{\&tau;}}_{act}\left(t\right)\&le;{\underset{\&OverBar;}{\mathrm{\&tau;}}}_{act}\left(t\right)\end{array}\right.$

$r_1=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)}{{\mathrm{\&tau;}}_d\left(t\right)}& {\mathrm{\&tau;}}_d\left(t\right)\&GreaterEqual;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\\ 1& {\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\&le;{\mathrm{\&tau;}}_d\left(t\right)\&le;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\\ \frac{{\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)}{{\mathrm{\&tau;}}_d\left(t\right)}& {\mathrm{\&tau;}}_d\left(t\right)\&le;{\underset{\&OverBar;}{\mathrm{\&tau;}}}_d\left(t\right)\end{array}\right.$

wherein,andτ _act(t) are each τ_actUpper and lower bounds of (t), correspondingAndτ _d(t) are each τ_dThe upper and lower bounds of (t);

the closed loop feedback optimal control distribution method meeting the condition constraint comprises the following steps:

τ_act(t)＝Eτ_CA(t)+Fτ_act(t-T)+Gu_CA(t)

wherein,E＝(I-GD₀)W^-2(R₁W₁)²,G＝W^-1(D₀W^-1)⁺，u_CA(t)＝u_d(t)+e(t-T)＝u_d(t)+u_CA(t-T)-u_act(T-T), I is a unit matrix.