CN105388902B - A kind of unusual bypassing method of control-moment gyro based on instruction Torque vector control - Google Patents

Abstract

A control torque gyro singularity avoidance method based on command torque vector adjustment. First, collect the frame angle vector of the control torque gyroscope group, and then calculate the Jacobian matrix of the control torque gyroscope motion equation, singularity value, command torque vector adjustment coefficient, and then according to the attitude The control torque command given by the controller obtains the control torque command adjustment vector and the zero-motion singularity avoidance intensity coefficient, and finally obtains the control torque gyro frame angular velocity command vector according to the control torque command adjustment vector and zero-motion singularity avoidance intensity coefficient to control the torque gyro frame angular velocity . The invention overcomes the situation that the torque command coincides with its specific direction when the frame is "locked" and cannot be separated, solves the problem of "locked" frame angle existing in the prior art in the process of singularity avoidance, and realizes the control torque Effective evasion of gyro singularity.

Description

A control torque gyro singularity avoidance method based on command torque vector regulation

technical field

The invention relates to the field of attitude determination and control of spacecraft, in particular to a method for avoiding singularity of a control moment gyro based on command moment vector adjustment.

Background technique

Agile spacecraft with attitude and fast maneuvering requirements generally use control moment gyroscopes as actuators. Due to the strong attitude maneuverability of the satellite, when the frame of the control moment gyro group moves to a certain configuration, it will approach and be in the singular state of the frame, which will cause the actuator to fail to output the three-axis control torque of the spacecraft as expected. In order to avoid the singularity problem of controlling the motion of the moment gyroscope frame, the existing technical methods are the zero-motion singularity avoidance method and the robust singularity avoidance method proposed for the singularity problem. Among them, the zero-motion singularity avoidance method can only realize the Hidden singularity avoidance is used for effective avoidance, and the robust singularity avoidance method is mainly aimed at the apparent singularity avoidance problem that cannot be solved by the zero-motion singularity avoidance method, but the latter will cause certain disturbances in the attitude of the spacecraft during the avoidance process compared with the former. Therefore, although the conventional zero-motion singularity avoidance and robust singularity avoidance algorithms can avoid this problem to a certain extent, the spacecraft will temporarily lose its attitude control ability due to the "locking" phenomenon of the control moment gyro frame structure in this method. affect attitude maneuverability.

When the conventional singularity evasion algorithm is adopted, the frame "locking" phenomenon is discovered and a reasonable mathematical explanation is obtained (Wie Bong, et.al., Singularity Robust Steering Logic for Redundant Single-Gimbal Control Moment Gyros, AIAA Guidance, Navigation, and Control Conference and Exhibit, Denver, 2000), relevant scholars have carried out research to avoid this phenomenon. Most of the follow-up research mainly improved the robust singularity avoidance algorithm. Among them, the most typical one is the American scholar Wie Bong, who adopted the technical approach of taking the off-diagonal Line elements are transformed into different forms of non-zero elements (Wie Bong, New singularity escape/avoidance steering logic for controlmoment gyro systems, Journal of Guidance Control and Dynamics, 28(5), 2005), especially the off-diagonal elements are And change to avoid the problem of frame locking, and applied for a number of patents (such as Wie B., et.al., Robust Singularity Avoidance in Satellite Attitude Control, U.S.Patent6,039,290,2000; Wie B., Singularity Escape/Avoidance Steering Logic for ControlMoment Gyro Systems, U.S. Patent No. 6, 917, 862, 2005. etc.). In the above-mentioned existing improved methods, in order to achieve singularity avoidance and at the same time minimize the disturbance of star attitude, it is necessary to select the multi-parameter simulation trial and error method in the algorithm. It is generally difficult to take into account the problems of singularity avoidance and small spacecraft attitude disturbance at the same time in follow-up research and improvement methods.

Contents of the invention

The technical problem solved by the present invention is: to overcome the deficiencies of the prior art, and to provide a singularity avoidance method based on the zero-motion singularity avoidance and robust singularity avoidance algorithm, which is based on the self-adjustment of the control torque instruction vector with the singularity measure, which can Prevent the system from entering the singularity or rapidly leaving from the singularity point, and avoid the phenomenon of "locking" of the frame structure of the control moment gyro.

The technical solution of the present invention is: a method for avoiding the singularity of the control torque gyro based on the command torque vector adjustment, comprising the following steps:

(1) Collect the frame angle vector δ of the control moment gyroscope group, and then calculate the Jacobian matrix J of the frame angular motion according to the control moment gyroscope motion equation;

(2) Calculate the singular metric value Sv as

Sv＝det(J J ^T )

Then the command torque vector adjustment coefficient υ is obtained as

When |υ|>υ _Limt , υ=sgn(υ)·υ _Limt , where k _tmpυ is the adjustment gain, D _s3 is the vector adjustment threshold, υ _Limt is the limit value of the vector adjustment coefficient, and sgn(υ) is the Symbolic operation of υ;

(3) According to the control torque command τ _c given by the attitude controller, the control torque command adjustment vector τ _cAd is obtained as

(4) When Sv<D _s1 , zero motion singularity avoidance strength coefficient

When D _s1 ≤ Sv < D _s2 , zero motion singularity avoidance strength coefficient

When Sv≥D _s2 , zero motion singularity avoidance strength coefficient α _s1 =0;

Among them, D _s1 is the activation threshold of robust singularity avoidance, D _s2 is the activation threshold of zero-motion singularity avoidance, C ₁ is the gain coefficient of zero-motion singularity avoidance strength, and α _s10 is the bias value;

(5) When Sv<D _s1 , robust singularity avoidance strength coefficient α _s2 =

When Sv≥D _s1 , the robust singularity avoidance strength coefficient α _s2 =0, where C ₂ is the robust singularity avoidance strength gain coefficient;

(6) According to the control torque command adjustment vector τ _cAd , the singularity avoidance strength coefficients α _s1 and α _s2 to obtain the control torque gyro frame angular velocity command vector for

Use the control torque gyro frame angular velocity command vector Adjust the angular velocity of the control moment gyroscope frame in the control moment gyroscope group, where H _cmg0 is the angular momentum of the control moment gyroscope, _I3 is the third-order identity matrix, is the partial derivative of Sv to the frame angle vector δ, and -1 is the sign of matrix inverse operation.

The value range of the adjustment gain k _tmpυ is -100≤k _tmpυ≤100 , the vector adjustment threshold D _s3 >0, the value range of the vector adjustment coefficient limit value _υLimt is _0≤υLimt <1, robust Singularity avoidance activation threshold D _s1 ＞0, zero motion singularity avoidance activation threshold D _s2 ≥D _s1 , zero motion singularity avoidance strength gain coefficient C ₁ ≥0, offset α _s10 ≥0, robust singularity avoidance strength gain coefficient C ₂ ≥0.

The step (5) further includes a limit value α _s20 , when α _s2 >α _s20 , α _s2 =α _s20 , wherein α _s20 >0.

Said k _tmpυ =2, D _s3 =0.7, υ _Limt =0.7, D _s1 =0.5, D _s2 =2.0, C ₁ =0.18, C ₂ =0.1, α _s10 =0, α _s20 =0.5.

The advantage of the present invention compared with prior art is:

(1) The present invention carries out the means of autonomous deflection adjustment to the direction and amplitude of the control torque command vector under the singularity of the control torque gyroscope frame through the command torque vector adjustment, and overcomes the torque command and its relationship with the frame when the frame is "locked". The situation that the specific directions coincide and cannot be separated solves the problem of "locking" the frame angle existing in the process of singularity avoidance in the prior art, and realizes the effective avoidance of the singularity of the control moment gyroscope, which has simple form, clear physical meaning and It has the advantages of easy parameter selection and strong engineering applicability;

(2) The present invention solves the problem that the polarity of the control torque command after the vector adjustment is opposite to that of the original command, which leads to crossing the singular surface back and forth by selecting the off-diagonal elements as the technical means of the antisymmetric matrix operator in the vector adjustment algorithm. Unable to escape the possibility of spacecraft attitude maneuver failure, and realize the control moment gyro frame in the follow-up control can be completely separated and away from the corresponding singular state;

(3) The present invention avoids the direct call of robustness at the initial stage of singularity through the design means of rational logic call, vector adjustment coefficient and avoidance strength coefficient continuous adjustment including zero-motion singularity avoidance, robust singularity avoidance and command torque vector adjustment algorithm. The singularity avoidance algorithm and the vector adjustment algorithm or the problem of disturbance to the star attitude caused by the adjustment coefficient and action strength mutation of each call algorithm, achieved the goal of little disturbance to the star attitude in the whole process of singularity avoidance.

Description of drawings

Fig. 1 is a flow chart of a method for avoiding the singularity of the control torque gyroscope based on the command torque vector adjustment of the present invention;

Fig. 2 is the control moment gyro frame angle curve that the present invention collects;

Fig. 3 is the singular value curve of the control moment gyroscope group configuration of the present invention;

Fig. 4 is a comparison diagram before and after adjustment of the output control torque command of the controller of the present invention;

Fig. 5 is the angular velocity command curve of the control moment gyro frame calculated by the present invention.

Detailed ways

Aiming at the deficiencies in the prior art, the present invention proposes a method for avoiding the singularity of the control torque gyro based on command torque vector adjustment. As shown in Figure 1, the method of the present invention includes a specific implementation process as follows:

1) Collect the frame angle vector δ of the control torque gyroscope group (the control torque gyroscope is composed of a constant speed momentum flywheel, a frame supporting the flywheel, and a frame rotation servo system, and is composed of the vector of the frame angles of each control torque gyroscope in the control torque gyroscope group. It is the frame angle vector of the control moment gyro group), and the Jacobian matrix J of the frame angular motion is calculated according to the motion equation of the control moment gyroscope (the description of the motion equation and the calculation of the Jacobian matrix can be found in: Paradiso JA, GlobalSteering of Single Gimballed Control Momemt Gyroscope Using a DirectedSearch, J. of Guidance, Control, and Dynamics, 15(5), 1992:1236-1244), the singularity measure Sv and the partial derivative of Sv with respect to the frame angle vector δ (For the specific algorithm of the partial derivative, please refer to the literature: Zhang Renwei, Satellite Orbit Attitude Dynamics and Control, Beijing University of Aeronautics and Astronautics Press, 1998: 293), and calculate the command torque vector adjustment coefficient υ from the singular value Sv, and The spacecraft controller gives the control torque command τ _c to carry out the vector adjustment operation to obtain the adjustment vector τ _cAd . Specifically:

(1) Sv is the determinant of the matrix J·J ^T , namely

Sv＝det(J J ^T )

Among them, J ^T is the transpose matrix of matrix J.

(2) Calculate the command torque vector adjustment coefficient υ from the singular value Sv as

If |υ|＞υ _Limt , limit the processing: υ=sgn(υ)·υ _Limt , where k _tmpυ (-100≤k _tmpυ ≤100) is the adjustment gain, and D _s3 (D _s3 >0) is Vector adjustment threshold, υ _Limt (0≤υ _Limt <1) is the limit value of the vector adjustment coefficient, sgn(υ) is the sign operation of υ, that is, when υ is greater than zero, it is 1, otherwise it is 0.

(3) Perform vector adjustment operation on the control torque command τ _c given by the attitude controller:

2) Calculate zero motion singularity avoidance strength coefficient α _s1 and robust singularity avoidance strength coefficient α _s2 . Specifically:

(1) The calculation formula of zero motion singularity avoidance strength coefficient α _s1 is

If Sv<D _s1 ,

If D _s1 ≤Sv<D _s2 ,

If Sv≥D _s2 , α _s1 =0;

Among them, D _s1 (D _s1 ＞0) is the activation threshold of robust singularity avoidance, D _s2 (D _s2 ＞0, and satisfying D _s2 ≥D _s1 ) is the activation threshold of zero motion singularity avoidance, C ₁ (C ₁ ≥0) is the zero-motion singularity avoidance strength gain coefficient, and the offset α _s10 ≥0.

(2) The calculation formula of robust singularity avoidance strength coefficient α _s2 is

If Sv<D _s1 ,

If Sv≥D _s1 , α _s2 =0

If the above calculation results satisfy α _s2 > α _s20 , then set α _s2 = α _s20 , where C ₂ (C ₂ ≥ 0) is the robust singularity avoidance strength gain coefficient, and α _s20 (α _s20 > 0) is α _s2 clipping value.

3) According to the control torque command given by the attitude controller, the vector τ _cAd is adjusted, the singularity avoidance strength coefficients α _s1 , α _s2 , and the zero-motion singularity avoidance and robust singularity avoidance methods are adopted to control the frame angular velocity command of the torque gyroscope group Calculate, specifically:

in, is the angular velocity command vector of the control moment gyro frame to be obtained, H _cmg0 is the angular momentum of the control moment gyro, I ₃ is the third-order unit matrix, is the partial derivative of Sv with respect to the frame angle vector δ (for the specific calculation formula, please refer to the literature: Zhang Renwei, Satellite Orbital Attitude Dynamics and Control, Beijing University of Aeronautics and Astronautics Press, 1998: P293), the upper right corner marked "-1" is a matrix Inverse symbol. The method of the present invention will be described in detail below in conjunction with the examples.

Embodiment 1: Use 6 control moment gyroscopes with angular momentum H _cmg0 =25Nms to form a system configured with pentagonal pyramid actuators to perform +45°/-45° (roll/pitch) dual-axis combined maneuvering from zero attitude. In order to make the control moment gyro group configuration more likely to approach the singular state, only five control moment gyros are used to participate in the attitude maneuver control of the spacecraft, and the frame angle of the control moment gyroscope 1 is locked at 0° and does not participate in the control. A control torque gyro singularity avoidance method based on command torque vector regulation is specifically implemented as follows:

Setting parameters: k _tmpυ =2, D _s3 =0.7, υ _Limit =0.7, D _s1 =0.5, D _s2 =2.0, C ₁ =0.18, C ₂ =0.1, α _s10 =0, α _s20 =0.5.

The following steps are the implementation process in a control cycle when the method of the present invention is applied:

1) Acquisition of control moment gyroscope frame angle vector:

δ = [0.0 0.5450689 -0.46850 2.57336 0.57771 1.30145] ^T (rad);

The command torque output by the spacecraft controller is:

τ _c = [0.04125 0.03748 -0.65202] ^T ;

According to the equation of motion, it can be calculated as follows:

Sv=0.69644;

υ=0.007116;

2) Calculation of zero motion and robust singular motion avoidance strength coefficient:

α _s1 =0.16845669, α _s2 =0.

3) According to τ _cAd , α _s1 , α _s2 , adopt zero-motion singularity avoidance and robust singularity avoidance methods to control the frame angular velocity command of the moment gyroscope group for

The results of the whole process of attitude maneuver application are shown in Fig. 2 to Fig. 5. Among them, Fig. 2(a), Fig. 2(b), Fig. 2(c), Fig. 2(d), Fig. 2(e) and Fig. 2(f) show the collected control torque gyros 1-6 frame angle (unit: degree); from Figure 3, it can be seen that the singularity value of the frame decreases during the attitude maneuver of the spacecraft and triggers the vector adjustment singularity avoidance algorithm, and the singularity measure will increase under the action of the avoidance algorithm; 4, it can be seen that under the action of adjustment, the control torque vector will be deflected in direction and adjusted to a certain extent. Among them, Fig. 4(a), Fig. 4(b) and Fig. 4(c) respectively show the original control torque vector and The components of the vector-adjusted control torque vector on the three axes of star roll, pitch and yaw (unit: Nm), and the solid line is the component of the control torque vector of the original control torque vector on the three axes of star roll, pitch and yaw , the dotted line is the component of the vector-adjusted control moment vector on the three axes of star roll, pitch, and yaw; it can be seen from Fig. 5 that when the singular value is small, the change of the frame angular velocity command calculated is more severe than the singular value When the value is large, the change is not large, which shows that the method of the present invention has good singularity avoidance characteristics. Among them, Figure 5(a), Figure 5(b), Figure 5(c), Figure 5(d), Figure 5(e ), 5(f) respectively give the frame angular velocity command (unit: degree/second) for controlling moment gyroscopes 1 to 6; it can be seen from the experimental verification that the method of the present invention can effectively avoid when approaching the singularity state, and overcome the The "locked" situation of the frame angle in the conventional singular avoidance method ensures the good performance of the system maneuvering.

The content that is not described in detail in the description of the present invention belongs to the well-known technology of those skilled in the art.

Claims (4)

1. A singularity avoidance method of a control moment gyroscope based on instruction moment vector adjustment is characterized by comprising the following steps:

(1) collecting a frame angle vector delta of a control moment gyro group, and then calculating a Jacobian matrix J of frame angular motion according to a control moment gyro motion equation;

(2) calculating singular metric value Sv of

Sv＝det(J·J^T)

Further obtaining a command torque vector regulation coefficient upsilon as

When | υ |>υ_LimtWhen v is sgn (v) or v_LimtWherein k is_tmpυTo adjust the gain, D_s3Adjusting the threshold value, upsilon, for a vector_LimtRegulating a coefficient amplitude limit value for a vector, and carrying out sign operation on sgn (upsilon) by taking upsilon;

(3) according to a control moment instruction tau given by an attitude controller_cObtaining a control moment instruction regulation vector tau_cAdIs composed of

(4) determining zero-motion singularity avoidance strength coefficient α according to singularity metric value Sv_s1robust singular evasion intensity coefficient alpha_s2for zero motion singularity avoidance intensity coefficient α_s1，

When Sv<D_s1Time, zero motion singularity avoidance intensity coefficient

When D is present_s1≤Sv<D_s2Time, zero motion singularity avoidance intensity coefficient

When Sv ≧ D_s2time, zero motion singularity avoidance intensity coefficient α_s1＝0；

Wherein D is_s1Starting threshold for robust singularity avoidance, D_s2Starting threshold for zero motion singularity avoidance, C₁gain coefficient of singularity avoidance intensity for zero motion, α_s10Is an offset;

(5) avoidance intensity coefficient alpha for robust singularity_s2When Sv is<D_s1Robust singularity avoidance intensity coefficient

When Sv ≧ D_s1robust singular avoidance intensity coefficient alpha_s20, wherein C₂Gain coefficients for robust singularity avoidance strength;

(6) adjusting vector tau according to control moment instruction_cAdsingularity avoidance intensity coefficient α_s1and alpha_s2Obtaining the angular velocity instruction vector of the control moment gyro frameIs composed of

Angular velocity command vector using control moment gyro frameAdjusting the angular velocity of the control moment gyro frame in the control moment gyro group, wherein H_cmg0For controlling moment gyro angular momentum, I₃Is an identity matrix of the order of 3,the partial derivative of Sv to the frame angle delta, and-1 is the sign of the matrix inversion operation.

2. The control moment gyro singularity avoidance method based on instruction moment vector adjustment according to claim 1, wherein: the adjusting gain k_tmpυK is not less than-100_tmpυLess than or equal to 100, vector adjusting threshold D_s3>0, vector regulation coefficient limit value upsilon_LimtHas a value range of 0 to upsilon_Limt<1, robust singularity evasion starting threshold D_s1>0, zero-motion singularity avoidance starting threshold D_s2≥D_s1Zero motion singularity avoidance strength gain coefficient C₁not less than 0, offset α_s10Not less than 0, gain coefficient C of robust singular evasion strength₂≥0。

3. the control moment gyro singularity avoidance method based on instruction moment vector regulation as claimed in claim 1 or 2, wherein the step (5) further comprises the step of applying a robust singularity avoidance intensity coefficient α to the robust singularity avoidance intensity coefficient α_s2limiting when alpha is_s2>α_s20when is α_s2＝α_s20wherein the clipping value α_s20>0。

4. The control moment gyro singularity avoidance method based on instruction moment vector regulation as claimed in claim 1 or 2, wherein: k is as described_tmpυ＝2、D_s3＝0.7、υ_Limt＝0.7、D_s1＝0.5、D_s2＝2.0、C₁＝0.18、C₂＝0.1、α_s10＝0、α_s20＝0.5。