KR100778098B1 - Moment gyros'cluster for spacecraft three axis attitude control - Google Patents

Abstract

A moment gyro cluster for three axis attitude control of an artificial satellite is provided to improve torque performance by using an MPP(Moore-Penrose Pseudoinverse) driving law. A moment gyro cluster is mounted with a predetermined rotation angle(sigma) between 0° and 360°. Sequential torque inputs are applied as much as rotation amounts of an artificial satellite along an axis direction using a new pyramid shape which the moment gyro cluster is mounted with the predetermined rotation angle. Torque inputs corresponding to x, y, and z axes are sequentially applied in accordance with an artificial satellite attitude movement range in respective axes such that an artificial satellite attitude movement is performed.

Description

Moment Gyros'Cluster for Spacecraft Three Axis Attitude Control}

1 is a pyramid shape using four conventional control moment gyros,

2 is an improved pyramid shape using four control moment gyros according to the present invention.

The present invention is to improve the three-axis attitude control of the satellite using the control moment gyro by placing four control moment gyro (CMG) in a pyramid shape. In addition, as a solution to the problem of occurrence of singularity of the conventional pyramid shape developed at home and abroad, it does not use the conventional driving law but relates to a control moment gyro cluster for satellite three-axis attitude control to improve the conventional pyramid shape.

The present invention relates to a configuration of a control moment gyro cluster required to change a posture to a desired position when performing a mission of a satellite, and a reaction wheel, which is one of the conventional satellite core actuators, generates a greater torque than a control moment gyro. There was a disadvantage of not being able to. That is, when comparing the control moment gyro with the reaction wheel, the control moment gyro can generate the same torque performance more efficiently than the reaction wheel. As a result, overseas control moment gyroscopes, which generate high torque and improve the maneuverability of satellites, are being applied to large satellites such as space stations. In the future, control moment gyroscopes can guarantee the dynamics of all low-orbit satellites. Will act as a core driver.

It is necessary to solve the singularity, the most serious problem that can occur when trying to control the 3-axis attitude of the satellite using the control moment gyro. Here, the singularity refers to the fact that the torque no longer occurs in the desired direction when the gimbal angle of the control moment gyro reaches a certain combination.

)에서의 회전각을 나타낸다. 이러한 김벌각 회전에 의해 생기는 각속도가 각운동량 벡터(

)와 조합되어 4개의 제어 모멘트 자이로는 각각 자이로스코픽 토크를 발생시킨다. 그런데 이 토크를 명령하는 것은 인공위성의 외부제어루프이고, 이 토크명령을 입력으로 받아 이에 맞는 4개의 김벌 각속도 조합을 출력하는 것은 내부제어루프이다. 이 토크입력에 해당되는 김벌 각속도를 출력할 수 없을 때가 특이점에 빠진 상태이다. 종래의 기술은 이러한 특이점에서 회피하고자 여러 가지 구동법칙을 제안하였고, 이러한 구동법칙들은 각각의 고유한 특징과 장단점을 가지고 있다.As shown in Fig. 1, the conventional pyramid shape of the square pyramid introduces four control moment gyros as redundancy. The gimbal angles (δ ₁ , δ ₂ , δ ₃ , δ ₄ ) are respectively fixed gimbal axes (

Represents the rotation angle at). The angular velocity generated by this gimbal angle rotation is the angular momentum vector (

In combination with the four control moment gyroscopes each generate gyroscopic torque. However, this torque command is the external control loop of the satellite, and it is an internal control loop that receives this torque command as an input and outputs four gimbal angular velocity combinations. The singular point is when the gimbal angular velocity corresponding to this torque input cannot be output. The prior art has proposed various driving laws to avoid these singularities, and these driving laws have their own characteristics and advantages and disadvantages.

In order to solve the above-mentioned problems, the present invention is to avoid the singularity by changing the pyramid shape, not by the conventional singular point avoidance driving law. Thus, not only the conventional technology corresponding to the singular point avoidance driving law can be applied as it is, but also the control moment gyro for satellite 3-axis attitude control that can avoid the internal singularity by applying only Moore-Penrose Pseudoinverse driving law and not singular point avoidance driving law. The purpose is to provide a cluster.

On the other hand, the new pyramid shape proposed by the present invention has a disadvantage compared to the conventional pyramid shape. However, these shortcomings may be negligible depending on the frequency of the rotation direction to be maneuvered during satellite operation. For example, if a low-orbit satellite wants to observe a specific position of the earth, torque in the x-axis is required based on the spacecraft reference frame of the satellite of FIG. 1. And the x-axis torque is necessary to capture other areas as well as the area on the orbit when the satellite passes orbit. Therefore, the frequency of the torque input in the x-axis direction is the most frequent among the torque commands of the satellite rotating in any axis. 1 corresponding to the conventional pyramid shape has a disadvantage in that it is not possible to continuously achieve the torque input in the x-axis direction and fall into an internal specific point, and thus may not fully utilize the performance of the control moment gyro. In order to overcome this disadvantage, the driving principle of singularity avoidance has been proposed in the related art, but the present invention provides a control moment gyro cluster for satellite three-axis attitude control, which proposes a method for avoiding internal singularity by improving the pyramid shape as shown in FIG. There is a purpose.

)를 유도하면,

상기 식에서 cσ=cosσ, sσ=sinσ, cβ=cosβ, sβ=sinβ, cδ_i=cosδ_i, sδ_i=sinδ_i이며, β는 (0°~ 90°사이의 비틀림각) 이고, x,y 및 z는 위성체기준좌표축, δ₁ 내지 δ₄는 (제어 모멘트 자이로의 0°~ 360° 사이의 김벌각)이고, 제어 모멘트 자이로의 김벌각이 모두 0인 상태(δ=[0 0 0 0]deg)에서는 임의의 회전각 (σ)에 대해 각운동량 값이

을 만족하고, x-y평면에 임의의 회전각(σ)으로 4개의 제어 모멘트 자이로 클러스터를 대칭되도록 장착함으로써 달성된다.In order to achieve the above object, the control moment gyro cluster for satellite three-axis attitude control according to the present invention, the control moment gyro (CMG) cluster is rotated mounted at any rotation angle (σ) between 0 ° and 360 ° Angular momentum vector for the reference coordinate system of the satellite in the new pyramid shape

),

And wherein cσ = cosσ, sσ = sinσ, cβ = cosβ, sβ = sinβ, cδ i = cosδ i, sδ i = sinδ i, β is, x, y and a (a twist angle of between 0 ° ~ 90 °) z is the satellite reference coordinate axis, δ₁ to δ₄ (the gimbal angle between 0 ° and 360 ° of the control moment gyro), and when the gimbal angle of the control moment gyro is all zero (δ = [0 0 0 0] deg) The angular momentum value for any rotation angle (σ)

Is achieved by mounting the four control moment gyro clusters symmetrically in the xy plane at any rotational angle σ.

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Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings.

2 is an improved pyramid shape using four control moment gyros according to the present invention.

)를 유도하면 다음과 같다.As shown in FIG. 2, the improved arrangement of the control moment gyro cluster for satellite triaxial attitude control according to the present invention is different from that of the conventional reference coordinate system shown in FIG. 1. That is, the arrangement of the four control moment gyroscopes is to rotate the reference frame of the satellite by an arbitrary rotation angle σ around the z axis of FIG. 1 in a fixed state. In other words, this means a case where four control moment gyroscopes are rotated by an arbitrary rotation angle σ while the satellite is fixed. In the new pyramid shape of FIG. 2, the angular momentum vector for the reference coordinate system of the satellite (

) Is derived as follows.

여기에서 cσ=cosσ, sσ=sinσ, cβ=cosβ, sβ=sinβ, cδ_i=cosδ_i, sδ_i=sinδ_i, β는 (0°~ 90°사이의 비틀림각) 이고, δ₁ 내지 δ₄는 (제어 모멘트 자이로의 0°~ 360° 사이의 김벌각)이며, x,y 및 z는 위성체기준좌표축을 의미한다.
중요한 것은 도 2에 도시한 바와 같이, 제어 모멘트 자이로의 김벌각이 모두 0인 상태(δ=[0 0 0 0]deg)에서는 임의의 회전각 (σ)의 값에 관계없이 항상

을 만족한다는 점이다.
즉, 상기와 같이 각운동량 벡터를 유도한 결과는 종래의 피라미드 형상을 포함하여 위성 기준좌표계에 대한 제어 모멘트 자이로의 배치 피라미드 형상을 더욱 일반화시킨 것이며, 이는 x-y평면에 임의의 회전각(σ)으로 4개의 제어 모멘트 자이로 클러스터(CMG#1,CMG#2,CMG#3,CMG#4)를 장착할 수 있음을 의미한다.

Here cσ = cosσ, sσ = sinσ, cβ = cosβ, sβ = sinβ, cδ i = cosδ i, sδ i = sinδ i, β is a (a twist angle of between 0 ° ~ 90 °), δ₁ to δ₄ is ( Gimbal angle between 0 ° and 360 ° of the control moment gyro), and x, y and z are the satellite reference coordinate axes.
Importantly, as shown in FIG. 2, in the state where the gimbal angles of the control moment gyros are all zero (δ = [0 0 0 0] deg), regardless of the value of an arbitrary rotation angle σ

Is satisfied.
That is, the result of deriving the angular momentum vector as described above is a generalization of the arrangement pyramid shape of the control moment gyro with respect to the satellite reference coordinate system, including the conventional pyramid shape, which is 4 at an arbitrary rotation angle (σ) in the xy plane. This means that the control moment gyro clusters CMG # 1, CMG # 2, CMG # 3, and CMG # 4 can be mounted.

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On the other hand, if the gimbal axis vector is expressed in terms of the reference coordinate system of the satellite,

'의 관계를 이용하며 이는 자코비안 행렬(J)의 각 열벡터 성분으로 표시할 수 있다. 그 결과는 다음 식에 나와 있다.And the torque vector is'

'Can be expressed as each column vector component of the Jacobian matrix (J). The result is shown in the following equation.

This result can be applied to the following equation which is Moore-Penrose Pseudoinverse driving law that can finally calculate gimbal angular velocity.

는 4개 제어 모멘트 자이로의 김벌각속도 벡터(

)를 나타내고 τ는 위성의 기준좌표계에 대한 토크벡터(

)로서 토크입력에 해당된다.
이렇게 일반화된 식에서 z축을 중심으로 한 임의의 회전각인 σ의 값을 예로 들어본다. σ가 0°이면 도 1의 종래의 피라미드 형상이 되고, σ가 -45 ° 이면 도 2의 본 발명에 해당되는 새로운 피라미드 형상이 된다. 그리고, σ가 -45 °인 형태로 위성체에 4개의 제어 모멘트 자이로를 배치하면, x축 방향 토크입력에 대해 Moore-Penrose Pseudoinverse 구동법칙을 적용해도 내부특이점을 회피할 수 있다. 이는 종래의 피라미드 형상에 x축 방향 토크입력이 주어질 경우, Moore-Penrose Pseudoinverse 구동법칙이 내부특이점을 피할 수 없다는 단점을 극복한 것이다.
이를 구체적으로 설명하면, 도 1 과 도 2에 공통적으로 h= 15Nms, β=53.13°로 유지하고, 임의의 회전각 (σ)를 도 1에는 σ가 0°와 도 2에 σ가 -45°로 적용하여 Moore-Penrose Pseudoinverse 구동법칙을 적용하게 되면, 도 1의(종래의 피라미드형상) 경우 내부특이점을 만나기 전까지만 토크를 발생시키게 되어 도 1의 경우에는 -10Nm의 일정한 출력토크를 1.2초밖에 발생시키지 못하며 위성체의 회전속도가 극히 제한적으로 작용하여 3sec동안 2.6°까지 회전하게 되고, 반면에 도 2의 경우 상기 Moore-Penrose Pseudoinverse 구동법칙을 적용하게 되면, 내부특이점을 거치지 않아도 -10Nm의 일정한 출력토크를 약 4.5sec 동안 발생시킬 수 있어 위성체의 회전이 10sec동안 30°를 회전가능하게 하여 결국 z축을 중심으로 한 임의의 회전각(σ)가 0°에서 임의의 회전각(σ)가 -45° 만큼 축 이동시켜 새로운 피라미드 형상(도 2)으로 배치시킴으로 위성체의 자세기동능력이 개선되는 것을 확인할 수 있게 된다.From here

Is the gimbal angular velocity vector of the four control moment gyros.

) And τ is the torque vector (

) Corresponds to torque input.
In this generalized example, take the value of σ, which is an arbitrary rotation angle around the z-axis. When σ is 0 °, the conventional pyramid shape of FIG. 1 is obtained, and when sigma is -45 °, a new pyramid shape corresponding to the present invention of FIG. If four control moment gyroscopes are arranged on the satellite in the form of sigma -45 °, even if the Moore-Penrose Pseudoinverse driving law is applied to the torque input in the x-axis direction, the internal specific point can be avoided. This overcomes the disadvantage that the Moore-Penrose Pseudoinverse driving law cannot avoid the internal special points when the conventional pyramid shape is given the x-axis torque input.
Specifically, in Fig. 1 and Fig. 2, h = 15 Nms and β = 53.13 ° are kept in common, and any rotation angle σ is 0 ° in Fig. 1 and σ is -45 ° in Fig. 2. When the Moore-Penrose Pseudoinverse driving law is applied, the torque is generated until the internal specific point of FIG. 1 (conventional pyramid shape) is met. In the case of FIG. 1, the constant output torque of -10Nm is only 1.2 seconds. Since the rotation speed of the satellite is extremely limited, it rotates to 2.6 ° for 3 sec. On the other hand, in the case of FIG. 2, if the Moore-Penrose Pseudoinverse driving law is applied, a constant output of -10 Nm is required even without passing through an internal specific point. Torque can be generated for about 4.5 sec so that the rotation of the satellite can rotate 30 ° for 10 sec, so that any rotation angle (σ) around the z axis is 0 ° and any rotation angle (σ) is -45. Axis shifted by ° By placing the new pyramid shape (Fig. 2), it is possible to confirm that the attitude maneuverability of the satellite is improved.

Application of the technique of the present invention solves the problem that the conventional pyramid shape does not overcome for one-way torque input while still following the characteristics of the conventional pyramid shape in which four control moment gyros are arranged symmetrically. That is, even when the arbitrary rotation angle σ of FIG. 2 is -45 °, the control moment gyroscope is disposed in a symmetrical state on the xy plane, so that the y-axis torque input also overcomes the conventional pyramid shape (FIG. 1). The problem of not being able to fall into an internal special point can be solved by using the present invention of FIG. 2. On the other hand, the z-axis torque input is excluded from the object of the present invention because there is no problem that the performance of the control moment gyro is not sufficiently exhibited in both Figs.

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Since the present invention proves that an internal specific point can be avoided for one direction torque input, when the present invention is applied to a control moment gyroscope, a sequential rotation of the satellite body is possible. That is, as shown in FIG. 2 of the present invention for the satellite to be rotated in any axis as well as the torque input in one direction, if the control moment gyro is disposed, the torque input is sequential as much as the satellite is intended to rotate in each axial direction. This can be introduced. For example, the torque input corresponding to the x-axis (roll axis), y-axis (pitch axis), and z-axis (yaw-axis) of FIG. After rotating the shaft, apply it to the yaw rotation, etc.).

While the present invention has been illustrated and described with respect to preferred embodiments, the invention is not limited to the above-described embodiments, and is commonly used in the field of the invention without departing from the spirit of the invention as claimed in the claims. Anyone with a variety of variations will be possible.

According to the present invention described above, when the arrangement of the control moment gyro applied to the conventional pyramid shape, there was a problem of falling into the internal specific point, but solved by arranging it in the new pyramid shape of the present invention. Thus, the performance of four control moment gyros has been improved.

In addition, the present invention can reduce the driving law calculation amount by applying only Moore-Penrose Pseudoinverse, which is the simplest driving law, to the one-way torque input, thereby avoiding internal specific points. Therefore, the possibility of applying it to a real satellite is very high. Furthermore, if we want to avoid internal singularities in all directions, we have opened the possibility of applying the conventional singular point avoidance driving law to the new pyramid shape.

Claims (5)

A control moment gyro cluster for satellite three-axis attitude control, wherein the control moment gyro cluster is rotated and mounted at an arbitrary rotation angle σ between 0 ° and 360 °. The control moment gyro cluster of claim 1, wherein Angular momentum vector for the reference coordinate system of the satellite (

)

Satisfying And (a twist angle of between 0 ° ~ 90 °) wherein cσ = cosσ, sσ = sinσ, cβ = cosβ, sβ = sinβ, cδ _i = cosδ _i, sδ _i = sinδ _i and β is 1 to 4 4 Control moment gyro clusters (CMG # 1, CMG # 2, CMG # 3, CMG # 4), x, y and z are the satellite reference coordinate axes, and δ₁ to δ₄ are the latitudes between 0 ° and 360 ° of the control moment gyro. Bee angle) When the gimbal angles of the control moment gyro are all zero (δ = [0 0 0 0] deg), the angular momentum value for the arbitrary rotation angle (σ)

Control moment gyro cluster for satellite three-axis attitude control, characterized in that to satisfy. The method of claim 2, Gimbal axis vectors for four control moment gyro clusters

When satisfying, The torque vectors of the four control moment gyro clusters are '

' Becomes When the torque vector is represented by each column vector component of the Jacobian matrix J,

Control moment gyro cluster for satellite three-axis attitude control, characterized in that. The method of claim 2, A control moment gyro cluster for satellite triaxial attitude control, characterized in that an arbitrary rotation angle σ is -45 °. The method according to any one of claims 1 to 4, Using a new pyramid shape in which the control moment gyro (CMG) cluster is rotated and mounted at an arbitrary rotation angle (σ), when the satellite body introduces sequential torque input as much as it wishes to rotate in each axial direction, That is, by applying torque inputs corresponding to the x-axis (roll axis), y-axis (pitch axis) and z-axis (yaw-axis) sequentially according to the satellite attitude start range in each axial direction, A control moment gyro cluster for satellite 3-axis attitude control.

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