JP5556782B2 - Satellite attitude control device - Google Patents

Description

The present invention relates to an attitude control device for an artificial satellite that performs attitude control using a CMG (Control Moment Gyro) mounted on the artificial satellite.

In the attitude control device for satellites that uses multiple conventional single gimbal CMGs (CMG is an abbreviation for control moment gyro), the attitude control torque required to control the attitude of the satellite is converted to the CMG gimbal angular velocity. To do. This conversion uses an inverse Jacobian matrix that relates the CMG gimbal angular velocity and the attitude control torque.

At this time, there is a situation where the CMG gimbal angular velocity cannot be obtained from the attitude control torque, and this is generally called a CMG singular state. In order to avoid the situation in which the angular velocity cannot be obtained, the inverse matrix of the Jacobian matrix is obtained so that an approximate inverse matrix can be obtained even when the CMG is in a singular state (for example, Patent Documents). 1).

JP 2002-506773 A (pages 6-7, FIG. 1)

As described in Patent Document 1, when performing attitude control of an artificial satellite, the CMG becomes a singular state, and an inverse matrix of the Jacobian matrix that relates the CMG gimbal angular velocity and the attitude control torque of the artificial satellite is obtained. Not a problem. This problem can be expressed as follows.

ここでτは３次元のベクトル、dθ/dtはのCMG数をｎとすればｎ次元のベクトルであり、Ａは両者を関係づける３×ｎ次の行列であり、ヤコビ行列と呼ばれる。 When the attitude control torque of the satellite is τ, the CMG gimbal angle is θ, and the gimbal angular velocity is dθ / dt, the following relationship holds between the attitude control torque τ and the gimbal angular velocity dθ / dt (Equation (1 )).

Here, τ is a three-dimensional vector, dθ / dt is an n-dimensional vector when the number of CMGs is n, and A is a 3 × n-order matrix that relates the two and is called a Jacobian matrix.

ここで右肩添字のＴは転置、−１は逆行列をとる操作を示す（以下同様）。 When performing feedback attitude control of an artificial satellite, it is necessary to obtain the CMG gimbal angular velocity dθ / dt from the attitude control torque τ. If the rank of the Jacobian matrix A is 3, it can be obtained as follows (formula ( 2)).

Here, the right subscript T indicates transposition, and -1 indicates the operation of taking the inverse matrix (the same applies hereinafter).

However, the rank of the Jacobian matrix A varies depending on the CMG gimbal angle. In particular, when the CMG is called singular, the rank of the Jacobian matrix A becomes 2 or less, and the inverse matrix of the above equation cannot be obtained. This is the same even when the CMG is nearly singular. Specifically, if the condition number of the Jacobian matrix A is 10 or more, the inverse matrix of the above equation can be obtained, but the value is When it becomes excessive, the value of the gimbal angular velocity dθ / dt also becomes excessive, causing trouble.

CMG singular states, including those close to singularities, are a state where CMG singular states often appear, which is a major technical issue in the attitude control system of satellites using CMG. Has always been a problem.

In fact, various attempts have been made to approximate the inverse of the Jacobian matrix in the singular state of CMG. One of the typical methods is the method described in Patent Document 1 described above. According to this method, the CMG gimbal angular velocity dθ / dt is obtained from the attitude control torque τ as follows (formula (3)).

Here, κ is an arbitrary positive constant that allows an inverse matrix to be obtained even when CMG is in a singular state, I is a unit matrix, and P is a matrix that gives a minute disturbance so that CMG can avoid a singular state. Yes, with the following form:

Here, ε _i (t) (i = 1, 2, 3) is a term giving a time-varying minute disturbance, and has a function of avoiding CMG staying in a singular state. ε _i (t) is given by, for example, the following equation (5).

In this method, the constant κ and the matrix P are added to the conventional Jacobian matrix to prevent the gimbal angular velocity dθ / dt from diverging when the CMG enters the singular state, and to prevent the CMG from remaining in the singular state. It is avoiding.

These have a certain effect in the singular state of CMG, but constants that can be arbitrarily set like κ and ε _i are included in the calculation, and the effect also varies depending on how to give it However, there is no clear guidance on how to give it, and it is determined on a trial and error basis.

Further, κ can prevent the gimbal angular velocity dθ / dt from diverging in the singular state of the CMG, but the posture control torque τ to be realized may be significantly different from the posture control torque applied from the posture control system. Furthermore, an effect of avoiding CMG from staying in a singular state by ε _i can be expected, but there is no guarantee that it is always effective, and there may be a situation where ε _i is used to stay in a singular state.

As described above, in such an attitude control device for an artificial satellite, when the CMG is in a singular state, from the attitude control torque τ of the artificial satellite so as to avoid the singular state accurately and reliably. It does not provide a means for obtaining the CMG gimbal angular velocity dθ / dt.

In addition, there are many parameters that can be set arbitrarily, and they must be determined by trial and error in consideration of the moment of inertia of the satellite, the angular momentum of the CMG, the upper limit of the CMG gimbal angular velocity, etc. In order to apply this method, there were problems such as requiring many prior verifications.

  The present invention has been made to solve the above-mentioned problems, and the attitude of an artificial satellite that can reliably and accurately determine the gimbal angular velocity from the attitude control torque even when the CMG is in a singular state. The purpose is to obtain a control device.

An attitude control device for an artificial satellite according to the present invention includes a rotor that rotates around a rotor axis, and a gimbal that rotates the rotor around a gimbal axis orthogonal to the rotor axis, and is mounted on the artificial satellite. Multiple CMGs, a gimbal control unit that controls the rotation of the gimbal of the CMG, an attitude control unit that controls the attitude of the satellite, and the attitude control torque that is the output of the attitude control unit is decomposed into CMG gimbal angular velocities The steering control unit, and in the steering control unit, when the CMG is close to a singular state, the CMG's micro gimbal angle is calculated from the relationship between the satellite's micro angular momentum change and the CMG's micro gimbal angle change. The change is obtained, and the CMG gimbal angular velocity obtained from the obtained minute change of the CMG gimbal angle is used as the output of the steering control unit.

According to this invention, in a plurality of CMGs, even when the CMG is in a singular state, the solution of the minute gimbal angle change is obtained based on the nonlinear relationship between the minute angular momentum change and the minute gimbal angle change. Thus, it is possible to reliably obtain a solution for the minute gimbal angle change. In addition, even if the CMG is in a singular state, the change in the gimbal angle can be minimized, and it is possible to naturally avoid that the CMG stays in the singular state.

It is a conceptual diagram of CMG which is an attitude control actuator for an artificial satellite used in the present invention. It is a conceptual diagram which shows an example in case multiple CMG is arrange | positioned to an artificial satellite. It is a block diagram which shows the structure of the attitude | position control apparatus of the artificial satellite in this invention. It is a flowchart which calculates | requires the micro gimbal angle change of CMG from the micro angular momentum change of the artificial satellite by Embodiment 1 of this invention. FIG. 10 is a flowchart when an approximate solution is obtained by developing the minute angular momentum change to the second order term when obtaining the minute gimbal angle change of the CMG from the minute angular momentum change of the artificial satellite according to the second embodiment of the present invention. It is a flowchart at the time of calculating | requiring analytically a solution by developing a minute angular momentum change to a quadratic term when calculating | requiring the minute gimbal angle change of CMG from the minute angular momentum change of the artificial satellite by Embodiment 3 of this invention.

Embodiment 1 FIG.
FIG. 1 is a conceptual diagram of a single gimbal CMG that is an attitude control actuator for an artificial satellite used in the present invention. The CMG is composed of a wheel that rotates at high speed around the spin axis and a gimbal shaft that rotates the rotation axis of the wheel. The wheel has a certain amount of angular momentum around the spin axis due to high-speed rotation of the wheel, but by rotating the direction of the angular momentum around the gimbal axis, a large reaction torque acts on the satellite body, and this torque is used for attitude control .

FIG. 2 shows an example in which a plurality of CMGs are arranged on an artificial satellite. Usually, about 4 CMGs are arranged on the artificial satellite as shown in this figure, and the attitude control of the artificial satellite is realized by operating these CMGs in cooperation. In the case of FIG. 2, each CMG is arranged at the bottom of the quadrangular pyramid, so it is called a pyramid arrangement, and is one of typical arrangement examples of the CMG.

FIG. 3 shows an example of a block diagram of an attitude control device for an artificial satellite according to the present invention. When the attitude target value 2 of the artificial satellite is given, the attitude control unit 3 performs feedback control so that the attitude angle of the artificial satellite approaches the attitude target value 2 from the deviation between the attitude target value 2 and the attitude angle of the artificial satellite. Do. The attitude control torque of the satellite can be obtained as an output of the attitude control unit 3. In order to realize this attitude control torque, it is necessary to cause a desired reaction torque to act on the satellite body by the movement of the gimbal angle of the CMG. There is. For this purpose, the steering control unit 4 gives the angular velocity of the CMG gimbal angle and the target value of the angle, and the present invention relates to this steering control unit 4.

The following linear relationship exists between the attitude control torque τ (third-order vector) of the artificial satellite and the CMG gimbal angular velocity dθ / dt (n-order vector). However, since the Jacobian matrix is a function of the gimbal angle θ, it will be expressed as A (θ) below in order to clarify it.

In the above equation (6), when the CMG is in a singular state, the Jacobian matrix A (θ) has a rank of 2 or less, and thus the gimbal angular velocity dθ / dt that realizes the attitude control torque τ cannot be obtained.

On the other hand, if the angular momentum of the entire CMG is h, h is also a function h (θ) of the gimbal angle θ, and the above equation can also be expressed by the following equation.

Here, a short time during which the attitude control torque τ is regarded as constant is defined as a minute time Δt. The interval of the minute time Δt varies depending on the band of the attitude control system, but can be considered as a value of about 0.2 to 0.3 seconds. If the gimbal angle change during this minute time Δt is Δθ, the following equation (8) is obtained.

In the present invention, when the CMG is in a singular state and the gimbal angular velocity dθ / dt cannot be determined from the attitude control torque τ, the minute change Δθ of the gimbal angle is determined based on the above equation.

  This will be described in more detail based on the flowchart of FIG. Since the above equation is a nonlinear equation with respect to Δθ, it cannot usually be solved analytically. However, if this nonlinear relationship obtained by extending the time to Δt in the above equation is used, the influence of second-order or higher-order microterms omitted in the linear relationship is included. It is possible to obtain a solution even if it is not possible.

If this solution is obtained by repeated calculation, it is necessary to first set an appropriate approximate value of the solution Δθ. This is S1. If this approximate value is Δθ _i , the angular momentum error Δh _err can be obtained by the following equation (9).

The calculation of the above equation corresponds to S2. If the magnitude of Δh _err can be regarded as 0 (zero), Δθ _i at this time can be adopted as a solution for Δθ. Further, when the magnitude of Δh _err cannot be regarded as 0 (zero), it is necessary to update the value of Δθ _i to make this value smaller. It is S3 that makes this determination.

の状態に近づけるようなΔθ_iを、Δθの更新値Δθ_i+1として用いる。この更新を行うのがS4である。Δｈ_errの大きさが十分に小さくなるまで、この更新を繰り返すことにより、十分な精度を有するジンバル角の変化量Δθが得られる。こうしてΔθが得られれば、ジンバル角速度dθ/dtは

として求めることができる。 If Δh _err is not small enough and needs to be updated,

Δθ _i that approaches the state of is used as the updated value Δθ _{i + 1} of Δθ. It is S4 that performs this update. By repeating this update until Δh _err becomes sufficiently small, a change amount Δθ of the gimbal angle having sufficient accuracy can be obtained. If Δθ is obtained in this way, the gimbal angular velocity dθ / dt is

Can be obtained as

  As described above, in the steering control unit 4, not the relationship between the conventional attitude control torque τ and the gimbal angular velocity dθ / dt, but Δτ 2 between τΔt, which is a minute time applied to the attitude control torque, and the minute gimbal angle change Δθ. Since the relation including the second and higher terms is used, the solution of Δθ can be obtained by the effect of the second and higher terms even when the linear relation including only the first order of Δθ cannot be obtained. Even when the CMG is in a singular state, it is possible to construct a highly reliable satellite attitude control device that does not diverge the gimbal angle of the CMG.

ここでH(θ)はヘッセ行列と呼ばれ、各成分を３次のベクトルとするようなｎ×ｎ行列となる。 Embodiment 2. FIG.
FIG. 5 is a flowchart for obtaining an approximate value of the minute change amount of the gimbal angle according to the second embodiment of the present invention. τΔt can be approximated by the following equation (12) by expanding the Taylor series of h (θ + Δθ).

Here, H (θ) is called a Hessian matrix, and becomes an n × n matrix in which each component is a third-order vector.

The first term on the right side of the above equation represents the linear relationship between the normal attitude control torque τ and the gimbal angular velocity dθ / dt, and the second term on the right side represents the second-order nonlinear term. This relationship corresponds to S6 in FIG. In the second embodiment, a method of deriving a value of Δθ that satisfies this relationship based on this relationship will be described below. Since this relationship is a non-linear relationship including a second-order term of Δθ that is an n-th order vector, it is not easy to analytically give a solution although it is a second order.

上式の計算を行うのがS8にあたる。 Therefore, also in this case, the solution is obtained by repeated calculation, and an approximate value of Δθ is first given as an initial value. This corresponds to S7 in FIG. The approximate value in this case may be set to Δθ = 0 (zero) or an appropriate minute amount. Next, an angular momentum error Δh _err is obtained by the following equation using this approximate value as Δθ _i .

The calculation of the above equation corresponds to S8.

If the magnitude of Δh _err can be regarded as 0 (zero), Δθ _i at this time can be adopted as a solution for Δθ. Further, when the magnitude of Δh _err cannot be regarded as 0 (zero), it is necessary to update the value of Δθ _i to make this value smaller. This determination is made in S9.

ただし記号†は擬似逆行列を表す。この更新を行うのがS10である。 If Δh _err is not sufficiently small and needs to be updated, an updated value Δθ _{i + 1} of Δθ is obtained by the following equation (14).

The symbol † represents a pseudo inverse matrix. This update is performed in S10.

By repeating this update until the magnitude of Δh _err becomes sufficiently small, a change amount Δθ of the gimbal angle having sufficient accuracy can be obtained for the relation including the quadratic term of Δθ. In this case, since the target equation includes only a second-order nonlinear term, it is easier to obtain a solution than a general nonlinear case.

Since this method approximately obtains Δθ that realizes Δh _err = 0 (zero), if it is used in the process of executing the flowchart of FIG. 4, it includes a final second-order nonlinearity. The solution of the equation can be obtained efficiently.

Specifically, an approximate value of Δθ that realizes Δh _err = 0 (zero) is required in S1 and S4 of the flowchart of FIG. 4, and the flowchart of FIG. 5 is executed at that step. As a result, Δθ satisfying τΔt = h (θ + Δθ) −h (θ), which is the original purpose, can be obtained in a short time.

As described above, in the invention according to the second embodiment, the equation to be obtained is limited to the terms up to the second order of Δθ, and the solution of Δθ is obtained within that range. It is also possible to efficiently obtain a solution of an equation including a third-order term, and to reliably obtain a solution of the gimbal angular velocity in a short time even when the CMG is in a singular state.

ここで上式はｎ次元ベクトルΔθに関する３個の連立方程式である。 Embodiment 3 FIG.
FIG. 6 is a flowchart for obtaining an approximate value of the minute change amount of the gimbal angle according to the third embodiment of the present invention. As described above, τΔt can be approximated by the following equation (15) by developing Taylor series of h (θ + Δθ).

Here, the above equation is three simultaneous equations concerning the n-dimensional vector Δθ.

This relationship is shown in S12 of FIG. 6, which is the same as S6 of FIG. Normally, this equation is a complex quadratic equation in which each component of Δθ is coupled, and therefore cannot be easily solved. From the viewpoint of mounting, it is a general method to use iterative calculation as shown in FIG. It becomes.

However, if the higher-order algebraic equations are solved, the above equation can be treated analytically. Since the above equation has three components, there are three components of Δθ necessary to satisfy the above equation. This is defined as a dependent variable Δθ _{D in} Δθ. On the other hand, since the remaining (n-3) components of Δθ are components whose values can be set independently, this is set as an independent variable Δθ _I. This step corresponds to S13. A value can be arbitrarily set for this independent variable Δθ _I , but for example, 0 (zero) may be set. The part where this value is set is S14.

At this time, by using mathematical means to simplify solution calculation such as Gröbner basis (for example, Masayuki Noro, Kazuhiro Yokoyama, “Gröbner basis calculation basics”, The University of Tokyo Press, 2003) The solution calculation of the three simultaneous equations shown in S12 can be reduced to solving the following three algebraic equations. One is an 8th-order algebraic equation for one component of Δθ _D. The remaining two are first-order algebraic equations for the remaining two components of Δθ _D. Here, in the solution calculation of the remaining two algebraic equations, the solution of the former 8th-order algebraic equation is used.

Therefore, if these three algebraic equations are solved, a solution can be obtained without using iterative calculation. This step is S15. Thus, although a solution for Δθ is obtained, the solution for Δθ _D also varies depending on the setting of the value of Δθ _I , so the solution is evaluated to determine whether it is satisfactory. The step for doing this is S16. This may be evaluated by, for example, the magnitude of the solution of Δθ (norm of Δθ).

If the solution is not desirable, the value of Δθ _I is updated so that the size of the solution of Δθ is reduced, but the step of doing this is S17. However, with this method, an analytical solution that satisfies the equation shown in S12 can be obtained, so that the value of Δθ _I need not be updated. For example, if the size of the solution of [Delta] [theta] obtained by the initial value of [Delta] [theta] _I have satisfactory step S17 can be omitted.

As described above, in the invention according to the third embodiment, the equation to be obtained is limited to terms up to the second order of Δθ, and an analytical solution for Δθ is obtained within that range, so that CMG is not used without iterative calculation. Even in a singular state, a solution for the gimbal angular velocity can be obtained reliably in a short time.

Embodiment 4 FIG.
Next, the operation of the attitude control device according to the fourth embodiment will be described. When the CMG is in a singular state, the CMG gimbal angle change Δθ that realizes a minute angular momentum change that integrates the attitude control torque of the artificial satellite with a minute time Δt is found to be a singular state in which the CMG is difficult to pass. In some cases, a situation may occur in which the value of Δθ is not necessarily minute. In this case, since this Δθ is realized between Δt, the magnitude of Δθ / Δt becomes excessive, and the gimbal angular velocity may exceed the upper limit value of the hardware. In order to cope with such a situation, a threshold value δ is provided for the magnitude | Δθ | of the minute change Δθ of the gimbal angle. If | Δθ |> δ, Δθ is corrected by the following equation (16).

When this Δφ is used instead of Δθ, the resultant attitude control torque τ is also corrected. This avoids the direction of torque that is difficult to avoid in the singular state, and as a result, the singular state is smoothly avoided.

  As described above, in the invention according to the fourth embodiment, when the CMG is in a singular state, from the minute angular momentum change of the artificial satellite (change in angular momentum during the minute time Δt in which the attitude control torque τ can be regarded as constant). The CMG gimbal angle change is obtained, and when the magnitude exceeds a certain threshold value, the magnitude is limited by the threshold value, so the attitude control torque to be realized is also modified to avoid a singular state. Even if the CMG is in a singular state where passage is difficult, it is possible to avoid the singular state naturally. Here, the CMG gimbal angle change is regarded as a vector and its size is limited, but the same effect can be obtained even if a threshold is set for each CMG gimbal angle change. it can.

  1 CMG, 2 attitude target values, 3 attitude control units, 4 steering control units, 5 gimbal control units, 6 CMG gimbal dynamics, 7 satellite attitude dynamics.

Claims (4)

A rotor that rotates around the rotor axis, and a gimbal that rotates the rotor around a gimbal axis orthogonal to the rotor axis, and a plurality of CMGs mounted on an artificial satellite;
A gimbal control unit for controlling rotation of the gimbal of the CMG;
An attitude control unit for controlling the attitude of the artificial satellite;
A steering control unit that decomposes the attitude control torque, which is an output of the attitude control unit, into a CMG gimbal angular velocity,
In the steering control unit, when the CMG is close to a singular state, the CMG minute gimbal angle change is obtained from the relationship between the minute angular momentum change of the artificial satellite and the minute gimbal angle change of the CMG. A satellite attitude control device characterized in that the CMG gimbal angular velocity obtained from the change in gimbal angle is used as the output of the steering control unit. The above-mentioned minute gimbal angle change used when obtaining the CMG gimbal angular velocity as the output of the steering control unit is based on the relationship between the minute angular momentum change of the satellite and the secondary term of the CMG minute gimbal angle change. 2. The attitude control device for an artificial satellite according to claim 1, wherein the attitude control device is obtained as an approximate value of a change in a minute gimbal angle of the CMG. The approximate value of the obtained minute gimbal angle change is based on the relationship between the minute angular momentum change of the satellite and the quadratic term of the CMG minute gimbal angle change, and the simultaneous algebraic equations relating the minute change of the CMG gimbal angle are analyzed. 3. The attitude control device for an artificial satellite according to claim 2, wherein the attitude control value is obtained by solving the problem. When obtaining the CMG's micro gimbal angle change from the satellite's micro angular momentum change, a threshold is set for the CMG's micro gimbal angle change amount, and the micro gimbal angle change amount exceeds a predetermined magnitude. The artificial satellite attitude control device according to claim 1, wherein the size of the artificial satellite is limited by a threshold value.

Images