CN103941741A - Method for determining controlled quantity of angular speed of control moment gyro frame on basis of zero movement - Google Patents

Abstract

Provided is method for determining the controlled quantity of the angular speed of a control moment gyro frame on the basis of zero movement. Aiming at the control problems of a control moment gyro group, the position of a current frame angle is measured firstly, the current frame angle is compared with a nominal frame angle to obtain deviation between the current frame angle and the nominal frame angle, and a low-speed frame instruction of a return nominal frame angle is designed according to the deviation. Then the control instruction of the obtained return nominal frame angle is projected to a null space where the control moment gyro frame moves. Finally, the controlled quantity of the angular speed of the control moment gyro frame is ultimately obtained by combining a traditional method for obtaining the angular speed instruction of a low-speed frame on the basis of a Jcobian matrix and a method of singular circumvention. According to the method for determining the controlled quantity of the angular speed of the control moment gyro frame on the basis of the zero movement, under the condition that astral postures are not influenced, a control moment gyro returns to a frame nominal position smoothly, the control moment gyro can maintain a good structure, and the method is quite suitable for a control system of a maneuvering satellite with external disturbance effects or with multiaxis high angles.

Description

Control-moment gyro frame corners speed control method for determination of amount based on zero motion

Technical field

The invention belongs to spacecraft guidance, navigation and control field, relate to a kind of control method of control-moment gyro.

Background technology

The satellite with fast reserve demand generally adopts control-moment gyro (CMG) group as topworks, makes it have the ability of the axis of rolling and pitch axis multiaxis rapid attitude maneuver.Because the control-moment gyro quantity of working in topworks is greater than 3 conventionally, therefore for topworks, it has infinite multiple frame corners position and separates under zero momentum.But under these frame corners positions, the resultant moment characteristic of CMG output is different.To comprise the unusual good moment output requirement of evading in order realizing, conventionally to expect that satellite low speed frame corners in the time of attitude stabilization will remain near given nominal value.

The control method of existing CMG under the slow-speed of revolution, lacks the control strategy that returns nominal position.Therefore, outer disturb effect when satellite exists, or after experience attitude maneuver moves low speed framework wide-angle, the low speed frame corners position after celestial body attitude stabilization often remains on new equilibrium position, cannot return the nominal position of original design.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, a kind of frame corners speed controlled quentity controlled variable acquisition methods that returns nominal position based on definite CMG of zero motion is provided, avoid low speed frame corners under the outer effect of disturbing or after large angle maneuver to depart from nominal position and remain on other equilibrium positions, guarantee that CMG has good configuration.

Technical solution of the present invention is: the control-moment gyro frame corners speed control method for determination of amount based on zero motion, comprises the steps:

(1) measure the real-time frame corners δ of control-moment gyro;

(2) calculate real-time frame corners δ and the frame corners nominal value δ of control-moment gyro ₀between error delta δ=δ ₀-δ;

(3) adopt formula ${\stackrel{\·}{\mathrm{\δ}}}_M=\mathrm{\γ}(I_n-J^T{({\mathrm{JJ}}^T+\mathrm{\α}{I}_n)}^{-1}J)\mathrm{\Δ\δ}$ Calculating control-moment gyro frame corners gets back to and δ ₀the corresponding required frame corners speed controlled quentity controlled variable in position wherein J=Acos δ-Bsin δ, A, B are the 3 × n matrix relevant with the installation of control-moment gyro, the i list of matrix A shows that frame corners is angular momentum unit's direction vector of 90 i control-moment gyros while spending, the i list of matrix B shows that frame corners is angular momentum unit's direction vector of 0 i control-moment gyro while spending, I _nn dimension unit matrix, the number that n is control-moment gyro, γ is back nominal potential coefficient, and for being greater than 0 numerical value, the size of γ has determined that control-moment gyro frame corners gets back to the speed of nominal position, and it is faster that γ more returns speed, and α is the unusual coefficient of evading;

(4) according to the control moment T expecting _c, adopt formula resolve and obtain corresponding frame corners speed controlled quentity controlled variable h in formula ₀for the angular momentum of single control-moment gyro;

(5) adopt formula ${\stackrel{\·}{\mathrm{\δ}}}_N=\mathrm{\β}(I_n-J^T{({\mathrm{JJ}}^T+\mathrm{\α}{I}_n)}^{-1}J)\frac{\∂D}{\∂\mathrm{\δ}}$ Calculate singular point and evade controlled quentity controlled variable in formula, β is zero kinematic coefficient that singular point is evaded, and for being more than or equal to 0 numerical value, has determined the size of β with the distance of singular point, and the value of the nearlyer β of odd dissimilarity is larger, D=det (JJ ^t);

(6), according to the result of step (3)～step (5), obtain the controlled quentity controlled variable of final control-moment gyro frame corners speed ${\stackrel{\·}{\mathrm{\δ}}}_d={\stackrel{\·}{\mathrm{\δ}}}_c+{\stackrel{\·}{\mathrm{\δ}}}_N+{\stackrel{\·}{\mathrm{\δ}}}_M.$

The present invention's advantage is compared with prior art: existing CMG control method, and in control procedure, often make CMG low speed framework depart from nominal position, cause the variation of CMG configuration and weakening of control ability.The inventive method is for the satellite control system of CMG group control, a kind of frame corners method for control speed that returns nominal position based on zero motion is proposed, the method adopts the form of resolving of zero motion, CMG is moved towards nominal frame corners place along the angular velocity direction of no-output moment, thereby avoid, because low speed frame corners after the effect of disturbing or large angle maneuver departs from nominal position, guaranteeing that CMG has good configuration outward.

Brief description of the drawings

Fig. 1 is the FB(flow block) of the inventive method.

Embodiment

As shown in Figure 1, be the FB(flow block) of the inventive method, key step is as follows:

(1) the low speed frame corners δ of measurement CMG;

(2) error between measured value and the nominal value of the low speed frame corners of calculating CMG,

Δδ＝δ ₀-δ

Wherein δ ₀for the nominal value of the low speed frame corners of CMG;

(3) calculate the frame corners speed command that returns nominal position based on zero motion.Method is to utilize the quality of Δ δ as assessment CMG configuration, constantly by framework configuration again, and does not cause that during this period additional gyroscopic couple, the adjustment of this configuration again can be referred to as idle running, can be solved by following gyroscopic couple calculating formula:

$T_c=\stackrel{\·}{H}=J\stackrel{\·}{\mathrm{\δ}}{H}_0$

T _cfor control moment, angular Momentum H differentiate, H ₀for the angular momentum of single control-moment gyro.J=Acos δ-Bsin δ, A, B are the 3 × n matrix relevant with the installation of control-moment gyro, the i list of matrix A shows that frame corners is angular momentum unit's direction vector of 90 i control-moment gyros while spending, and the i list of matrix B shows that frame corners is angular momentum unit's direction vector of 0 i control-moment gyro while spending.

This formula solution has two parts:

$\stackrel{\·}{\mathrm{\δ}}={\stackrel{\·}{\mathrm{\δ}}}_T+{\stackrel{\·}{\mathrm{\δ}}}_N$

In formula, for there being the rotary speed instruction of moment output, and for idle running instruction, meet following equation:

$\left\{\begin{array}{c}J{\stackrel{\·}{\mathrm{\δ}}}_T=\frac{1}{H_0}{T}_c\\ J{\stackrel{\·}{\mathrm{\δ}}}_N=0\end{array}\right.$

The second formula in above formula can solve by generalized inverse theorem:

${\stackrel{\·}{\mathrm{\δ}}}_N=\mathrm{\ϵ}(I_n-J^T{\left({\mathrm{JJ}}^T\right)}^{-1}J)u$

Be idle running instruction, in formula, u is n-dimensional vector undetermined, I _nbe n dimension unit matrix, ε is coefficient (according to the concrete physical significance difference of u, can be referred to as singular point and evade zero kinematic coefficient (being written as β), return nominal potential coefficient (being written as γ) etc.).In the time of u=Δ δ, idle running instruction the direction that framework is reduced along Δ δ is moved, thereby makes CMG configuration reply nominal position.

The angular velocity instruction of returning nominal position is rewritten as follows:

${\stackrel{\·}{\mathrm{\δ}}}_M=\mathrm{\γ}(I_n-J^T{({\mathrm{JJ}}^T+\mathrm{\α}{I}_n)}^{-1}J)\mathrm{\Δ\δ}$

In formula, γ is back nominal potential coefficient, and its size has determined that control-moment gyro frame corners gets back to the speed of nominal position, makes its very fast nominal position of replying if will strengthen back the control of nominal position, gets larger positive number, otherwise gets less positive number; α is the coefficient of evading setting for unusual, and in the time that CMG configuration singularity degree is greater than A, α gets 0, otherwise gets the positive number that is greater than 0, and the concrete value of A is normally chosen between 0.1～0.5.

(4) traditional based on Jcobian Matrix Solving low speed frame corners speed command by try to achieve, utilize robust Pseudoinverse algorithm to be in the hope of its expression formula:

Unusually evade instruction be to occur unusually for fear of configuration in CMG control procedure, its basic ideas that solve are also to utilize idle running instruction, produce to evade instruction and make configuration depart from singular point under the condition that does not produce extra moment.Definition singular measure is D=det (JJ ^t), this index is for the tolerance of the quality of real-time assessment configuration, and for making CMG configuration become large along the gradient direction of singular measure, the known expression formula for the unusual idle running instruction of evading is ${\stackrel{\·}{\mathrm{\δ}}}_N=\mathrm{\β}(I_n-J^T{({\mathrm{JJ}}^T+\mathrm{\α}{I}_n)}^{-1}J)\frac{\∂D}{\∂\mathrm{\δ}};$

with had the algorithm of comparative maturity, algorithm principle and concrete derivation can lists of references " satellite orbit and attitude dynamics and control " (Zhang Renwei, publishing house of BJ University of Aeronautics & Astronautics, 1998.8).

(5) the frame corners speed command that returns nominal position based on zero motion that to sum up, step (3) calculates step (4) is traditional based on Jcobian Matrix Solving low speed frame corners speed command and the instruction that solves of unusual bypassing method due to with be all a kind of idle running instruction in essence, can not affect the effect that CMG controls, there is the characteristic of linear, additive, therefore can be directly and be added fusion, thereby obtain the CMG low speed frame corners speed controlled quentity controlled variable of the inventive method

The content not being described in detail in instructions of the present invention belongs to those skilled in the art's known technology.

Claims (1)

1. the control-moment gyro frame corners speed control method for determination of amount based on zero motion, is characterized in that comprising the steps:

(1) measure the real-time frame corners δ of control-moment gyro;

(2) calculate real-time frame corners δ and the frame corners nominal value δ of control-moment gyro ₀between error delta δ=δ ₀-δ;

(3) adopt formula ${\stackrel{\·}{\mathrm{\δ}}}_M=\mathrm{\γ}(I_n-J^T{({\mathrm{JJ}}^T+\mathrm{\α}{I}_n)}^{-1}J)\mathrm{\Δ\δ}$ Calculating control-moment gyro frame corners gets back to and δ ₀the corresponding required frame corners speed controlled quentity controlled variable in position wherein J=Acos δ-Bsin δ, A, B are the 3 × n matrix relevant with the installation of control-moment gyro, the i list of matrix A shows that frame corners is angular momentum unit's direction vector of 90 i control-moment gyros while spending, the i list of matrix B shows that frame corners is angular momentum unit's direction vector of 0 i control-moment gyro while spending, I _nn dimension unit matrix, the number that n is control-moment gyro, γ is back nominal potential coefficient, and for being greater than 0 numerical value, the size of γ has determined that control-moment gyro frame corners gets back to the speed of nominal position, and it is faster that γ more returns speed, and α is the unusual coefficient of evading;

(4) according to the control moment T expecting _c, adopt formula resolve and obtain corresponding frame corners speed controlled quentity controlled variable h in formula ₀for the angular momentum of single control-moment gyro;

(5) adopt formula ${\stackrel{\·}{\mathrm{\δ}}}_N=\mathrm{\β}(I_n-J^T{({\mathrm{JJ}}^T+\mathrm{\α}{I}_n)}^{-1}J)\frac{\∂D}{\∂\mathrm{\δ}}$ Calculate singular point and evade controlled quentity controlled variable in formula, β is zero kinematic coefficient that singular point is evaded, and for being more than or equal to 0 numerical value, the size of β has determined the distance with singular point, and the value of the nearlyer β of odd dissimilarity is larger, D=det (JJ ^t);

(6), according to the result of step (3)～step (5), obtain the controlled quentity controlled variable of final control-moment gyro frame corners speed ${\stackrel{\·}{\mathrm{\δ}}}_d={\stackrel{\·}{\mathrm{\δ}}}_c+{\stackrel{\·}{\mathrm{\δ}}}_N+{\stackrel{\·}{\mathrm{\δ}}}_M.$