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Micro Gravity Experiment of Variable Speed Control Moment Gyro at MG-LAB

Kuniyuki Omagari1 and Saburo Matunaga2 Tokyo Institute of Technology, Tokyo, 152-8552, Japan

Variable Speed Control Moment Gyro (VS-CMG) is a kind of CMG, which has its rotor speed controllable. This method increases degrees of freedom and makes it possible to control CMG in null space easily. On the other hand, another use of VS-CMG is focused in this paper, which uses only one VS-CMG to realize a line of sight control of a small spacecraft. This paper describes experimentally evaluation of the control logic to decrease the angular velocity of a spacecraft using a VS-CMG. A VS-CMG which was used in this experiment was developed for pyramid array of 4CMGs, based on two designing parameters, which are also described. In this paper, development of experiment setup and result are explained.

Nomenclature A = Jacobean Matrix of pyramid array of 4-CMGs h = angular momentum vector of spacecraft with a VS-CMG hs = h in the s direction ht = h in the t direction hg = h in the g direction h = angular momentum of a CMG wheel IWS = inertial matrix of a CMG wheel J = inertial matrix of the spacecraft including CMG β = skew angle of pyramid array γ = gimbal angle of CMG ω = angular velocity vector of spacecraft ωs = ω in the s direction ωt = ω in the t direction ωg = ω in the g direction Ω = angular rate of CMG wheel

I. Introduction ONTROL Moment Gyro (CMG) has studied and implemented for many years for attitude control device of large space platform such as ISS, because CMG generates high output torque and has large angular momentum

capacity. However, it had not been easily developed for small satellites because its control algorithm to avoid singularity is very complex and sometimes difficult.

Variable Speed Control Moment Gyro (VS-CMG) is a kind of CMG, which has its rotor speed controllable. This method increases degrees of freedom and makes it possible to control CMG in null space easily because degree of freedom of the pyramid array of 4-CMGs is eight. On the other hand, another use of VS-CMG is focused in this paper, which is only one VS-CMG to realize a line of sight control of a small satellite.

Authors are developing high performance and very small VS-CMG. Small satellites sometimes need high performance attitude controller but they usually need not to work so long period as for a decade. Although CMG has

C

1 Graduate Student, Mechanical and Aerospace Engineering, 2-12-1-I1-63 Ishikawadai, omagari@lss.mes.titech.ac.jp, student member AIAA. 2 Associate Professor, Department of Mechanical and Aerospace Engineering, 2-12-1-I1-63 Ishikawadai, Meguro-ku, Senior Member AIAA.

AIAA/AAS Astrodynamics Specialist Conference and Exhibit21 - 24 August 2006, Keystone, Colorado

AIAA 2006-6650

Copyright © 2006 by Omagari.Kuniyuki. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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complicated mechanism and easily malfunctions, short mission term of such small satellite is suitable for them. Test model of VS-CMGs was developed as a 4-skewed pyramid array. This was designed with appropriate design method we proposed assumed to be carried in the micro satellite of about 50kg class to accomplish the prompt attitude maneuver. And they were experimentally evaluated by the authors through two ground experiments, which are the 2-dimensional air floating attitude orientation experiment and the experiment using 3-dimensional ball bearing mounted attitude dynamics simulator. Design process and evaluation tests will be described in the third chapter.

This paper deals with the case of only a VS-CMG to be used, to be also evaluated. So, that was tested in the micro gravity drop experiment, which was conducted in MG-LAB, Japan. The objective of this experiment is to demonstrate the controllability of line of sight control using a Variable Speed CMG. CMG is usually used with 4 skewed units, but this experiment was conducted using only a unit. Conventional CMG has just one DOF per unit, on the other hand VS-CMG can control both wheel and gimbal motors. So, directional control of spacecraft can be realized with 1 unit VS-CMG. Only one VS-CMG control system drastically decreases the system weight and power consumption and best suits for agile maneuver missions of micro satellites.

The evaluation test was conducted this year. However, because the test was very short program, we only confirmed that a spacecraft with a VS-CMG can decrease its angular velocity.

In the experiment, we conducted angular rate damping control introduced by Yoon and Tsiotras1. A separation mass of about 3 kilograms including one VS-CMG and control and measurement system is to be separated in the drop capsule while about 4-seconds free fall. In the microgravity environment, one VS-CMG is controlled to suppress the rotation of the separation mass and gyroscopes measure its rotational rate. As a result, it was confirmed that one VS-CMG was able to make attitude rate of the separation mass less than 0.06 radians per second.

In this paper, VS-CMG control method is explained at first and the experiment system of the microgravity drop experiment in the 4th chapter. Finally, the result of angular rate damping control experiment is described.

II. Equation of Motion and the VS-CMG control The dynamics equations of a spacecraft with a VS-CMG are derived by Yoon and Tsiotras in the literature1.

( )( ) 21 ˆˆˆˆ

ˆˆˆˆ

uIuIIIJ

IIIIJJ

WSWSWScg

WSWSWScg

stsgωω

stsgωωω

−Ω−Ω++×−=

Ω−Ω−Ω++×−=

γ

γγ

&

&&&& (1)

where, the control input is

Ω

=

≡ &

&γ

2

1

uu

u (2)

The control logic to decrease ω toward zero is shown below.

sWS

WSt

IkuIku

ωω

22

11

=Ω=

(3)

This control logic can be proved to decrease the angular velocity using Lyapunov’s method. Here, we consider

the general case in which inertia matrix described in the Gimbal-Frame has full elements because in this experiment, the spacecraft carrying a VS-CMG is not necessarily axisymmetric.

=

ggtgsg

tgttst

sgstss

JJJJJJJJJ

J (4)

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Lyapunov function candidate is shown as

ωω JV T

21

1 = (5)

Because inertia matrix is symmetric matrix, derivative of Lyapunov function becomes

( )( )21

1

ˆˆˆˆ

uIuI

IIIIJ

JV

sWSWSt

WSWSWScgT

T

ωω

γγ

−Ω−=

Ω−Ω−Ω++×−=

=

stsgωωω

ωω&&&

&&

(6)

If the control input is described in (3), derivative of Lyapunov function is equal to or less than zero. So this control input can decrease the angular velocity of the spacecraft.

However, if derivative of Lyapunov function gets zero system may stay at an equilibrium which is not desired. Conditions in which the system stays at the equilibrium can be written as these equations.

0

0=

=Ω

sWS

WSt

IIω

ω (7)

There are two possibilities, 1) ωt = 0, ωs = 0, and 2) Ω = 0, ωs = 0. 1) In the case, angular velocity and angular momentum in the Gimbal frame become gω ˆgω= , gtsh ˆˆˆ gts hhh ++= (8)

Then, using the equation of motion (1) without input, the followings are required in order to permanently satisfy

the equations (7). 0== ts hh (8)

Except for very special case, these conditions are equal to [ ]Tggg Jh /00,0 ==Ω ω (10) The very special case is only when 0,0 ≠−=Ω= gsgWStg JIJ ω (11) We don’t care this case in this paper.

2) The other case, we have to consider the existence of undesired equilibrium when

0=Ω (12) As a result, we have to take care of undesired equilibrium when angular velocity of flywheel is zero and the

other requirements exist. In other case, we can use the control algorithm to decrease angular velocity described above.

Whether these undesired equilibriums are stable or not is not proved, however, it is important that we don’t have to deal with the undesired equilibrium when the wheel is rotating.

The simple case when the spacecraft is inertially axisymmetric about axis g is described in the literature1. In the paper, it was also proved that the undesired equilibrium is not stable and the proposed control input can globally decrease the angular momentum.

In the micro gravity experiment, this control input is implemented and tested.

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III. Motivation and Design Parameters of CMG In this section, how to determine the size of CMG is described. This paper describes attitude control using a VS-

CMG, however, it is explained in more general case. First, the advantages of CMG use for micro satellite are introduced. Here, a micro satellite carrying 4 CMGs is used as an example.

The science satellite mission varies widely from a small-scale experiment conducted by few laboratories to a

worldwide scale experiment. Especially, a small satellite is suitable for a small-scaled science mission. Using CMG for attitude control of a small satellite, prompt observation can be realized. In this design process, we assume that 90 degrees Rest-to-Rest maneuver should be done within 10 seconds. When this satellite is 40kg and the maximum moment of inertia of the satellite is 1kgm2, a necessary torque will be 0.035Nm.

A. Designing Parameters To design CMG, necessary output torque and maximum angular momentum not to be saturated should be

properly determined. In the paper, they are evaluated using two parameters, which are Manipulability and Mean maximum angular momentum2.

Though the output torque generated by entire CMG array cannot be simply expressed, the average output torque in a certain configuration of the gimbals angle can be estimated as follows.

γγ && hmAAhT T == )det( (13) where,

)det( TAAm = (14) is called Manipulability, which means the average gain of the system. This value becomes almost 1 in many

configurations in pyramid array of 4-CMGs. The larger each angular momentum h is, the more the torque gain increases.

Enough torque cannot be output when the average gain becomes small, and there is a possibility of which the control becomes impossible or difficult. It is said singular point and the torque cannot be output about a certain axis. A variety of arrays and the control methods have been researched for such singular problems of the CMG system.

Next, angular momentum is described. Maximum angular momentum means the maximum value of angular momentum to which the CMG array can be absorbed. Maximum angular momentum envelop can be calculated and is found that it can not become sphere. Therefore, maximum angular momentum to be accumulated differs with its direction.

Here, Mean maximum angular is assumed to be simply the average of any directions. The average can be numerically calculated, however, we propose such typical “maximum angular momentum” as

hh )cos1(2 β+≈ (15) Using manipulability, required torque per unit becomes, 035.0>γ&hm (16) Mean maximum Angular momentum of the pyramid array

is described in (15). Then, the demand angular momentum per unit becomes, 2.0)cos1(2 >+ βh (17) To satisfy output torque and angular momentum

requirements, the size of a wheel is determined. Where, required gimbal rate limit of 0.25rad/s can be

determined by equation (17). While gimbal rate is limited within this level, gimbal motor only has to achieve velocity control input.

This example, the motor is used for wheel which has maximum speed of 4,000 rpm when no load and maximum

torque of 3mNm. For gimbal motors, 159:1 gears are combined. The size of whole system becomes 200mm x 200mm x 150mm. To control full 3-axis using this CMG, volume of entire system is requested to be 5,000cm3,

Fig. 1 Momentum Envelop of pyramid array

Numerically calculated

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which is a half of the case using 3 reaction wheels system. Weight becomes 330g a unit and more for motors, gimbal and the control circuit.

Though it is said that CMG need more electric power than RW and has internal disturbance, CMG use can greatly reduce the size and weight of whole system.

B. Test model Here, development of test model of CMG pyramid array is described. Performances of this test model are based

on the pyramid array described in the former chapter. The CMG unit is composed of motor for the wheel, motor for gimbals, slip ring, motor driver, and the processing

computer. The optical encoder is installed in the motor, and the rotational speed can be measured. A small DC motor manufactured by Faulhaber is used for the motor for the wheels and for gimbals. The weight

of this motor is 27g. 159:1 gears are installed on the motor for gimbals. TITech DriverII, which was developed in Tokyo Institute of Technology, is used for the motor driver. The

processing computer is H8S/2626 manufactured by Renesas Technology. To control the motor for the wheels and for gimbals, 4 microcomputers are needed. These 4 computers are connected with Controller Area Network (CAN).

The motor driver installs various sensors and A/D converter and pulse counter are required to read the sensors. H8S/2626 can also be used as A/D converter and counter.

Then the pyramid array of 4-CMGs was developed. Total weight became 6.4kg. The size is 450mm x 450mm x 150mm, which is much larger than that estimated before because it was not able to miniaturize the control circuits and motor drivers. The output torque is nominally 35mNm when limiting gimbal rate within 0.25rad/s. Without limitation, in the case motors can’t be correctly controlled, output torque can be larger up to 210mNm depending on gimbal rate.

Fig. 2

Test model of a CMG unit and the pyramid CMG cluster Next, we conducted evaluation tests. As the method of simulating the microgravity environment, two systems

are introduced. One is the air floating 2-dimentional flat floor. It has advantage of very low friction between simulator and other environment. The other is 3-DOF attitude dynamics simulator developed for this experiment. It has advantage that it can rotate toward any direction.

C. Evaluation on the Flat Floor To evaluate the basic performance of this CMG, it was tested on the ground experiment simulator, which is

called “Dynamics and Intelligent control Simulator for satellite Cluster (DISC)”. DISC is a system that simulates dynamics of the spacecraft under 2-dimentional microgravity environments on the ground. DISC achieves a flat microgravity environment except for only air resistance and some friction by using the air floating pad.

Because air floating pad is not symmetry, the rotation occurs naturally even if DISC is on the flat floor. In the experiment, it is necessary to subtract this effect. Then, this torque is first calculated from the rotation profile of DISC on the flat floor.

This profile showed that it rotated 90 degrees in 15 seconds. At this time, the torque of about 35mNm generated by air pad. In the following experiments, the effect of this torque is subtracted.

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Because nominal output torque produced by the entire system of this CMG is only 35mNm, which is the same value as the force by air pad, the gimbals rate is unlimited up to 1.0rad/s to make the effect of CMG emphasized more clearly. The torque five times larger than nominal is generated. However, CMG is saturated in this case within one second.

Average 150mNm is expected as for the output torque. In Fig.3, line is the calculated attitude angle. And a circle is experiment data. It is considered that CMG can almost demonstrate the performance because reaching time to 90 degrees was almost the same as the expectation.

-20

0

20

40

60

80

100

120

0 5 10 15 20

Time [s]

Angl

e [

deg]

Fig. 3

DISC and the experiment result A circle on the figure indicates time when DISC rotates 90 degrees, which is on the expected line.

D. Evaluation with 3-Dimensional Dynamics Simulator To evaluate the basic performance of this CMG, it was also tested on the 3-DOF attitude dynamics simulator

developed for CMG experiment. The simulator consists of a low friction ball bearing, balance adjusters and sensors for attitude determination. The ball bearing was selected because of the system simplification. Although it is commonly said that the ball bearing makes larger friction than an air bearing, the effect of friction is assumed not to be as large as the CMG output torque. Also, we chose such kind of spherical bearing which brought friction close to the air bearing developed in recent years.

-Balancer The body of the simulator is supported with the spherical bearing, and center of gravity can be matched to the

ball center by moving adjusting weight. Then, the torque by the gravity causes no rotation regardless of the attitude of the simulator. These adjusters can be installed almost anywhere on the simulator.

-Sensors To acquire the angle information, Fiber Optic Gyro (FOG), which was manufactured by Japan Aviation

Electronics Industry is installed. And the acceleration sensor was installed to detect the direction of gravity directly. The roll angle and the pitch angle are derived from the direction of gravity, and the yaw angle is derived by using gyro with high accuracy.

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12Time [sec]

Ang

le [r

ad]

Fig.4 3-DOF Attitude Dynamics Simulator

The thin, pink line is calculated attitude using CMG dynamics and the bold, blue line is the attitude measured by gyroscope, which have gap because of friction.

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-Processing and Communications Processing and the communication of the sensor data are done by microcomputer H8/3069 by Renesas

Technology. The acquired data are sent to external PC using wireless LAN. The command from external PC to the CMG can be forwarded to it through this computer. Wireless LAN is used in order to free the effect of cables. The wireless modem is “Connect WI-ME” by Digi International. Both CMG data and sensor data are brought together to the external PC using this wireless network.

The attitude change operation around yaw axis was done by installed CMG, and a movement expected under a

microgravity environment using CMG data and an actual attitude acquired by FOG are compared. The bold line in Fig.4 is acquired data by FOG on the simulator and the thin line in this figure is expected

attitude change calculated using CMG data. They are almost the same but actual attitude change is smaller than desired change based on CMG data. It was easily considered that it was an effect of friction at the ball bearing. However, it is considered that the CMG can work as well as the desired performance.

The design process and experimentally evaluation of agile attitude control devices were described. There is a

problem in the design of CMG output torque because of drastically changing of its output torque depending on an internal gimbal configuration. In this section, a simplified method using two standard parameters, which are manipulability and mean maximum angular momentum were proposed and it was confirmed that the two parameters were suitable to use while designing CMG size based on two experiments.

IV. Micro Gravity Drop Experiment Setup In this section, microgravity drop experiment to test the control input introduced in the 2nd section is explained.

In the experiment, a VS-CMG developed in the former section is used. In the micro gravity experiment, a dummy satellite carrying a VS-CMG is separated in the drop capsule during

free-fall, and the control algorithm is verified. The electromagnet separation system is adopted to realize low disturbance and low speed separation.

The electromagnet separation mechanism consists of the holder part and the electromagnetism controller. The

holder part has two electromagnets, and holds the separation plate. To send a signal to the separation plate without contact, infrared rays LED is installed. Moreover, the electric power system (EPS) circuit is installed.

To degauss the electromagnets, the controller makes reverse-voltage at a short time. When the separation signal is received, a reverse-voltage will be added after 2.6 seconds because first 1.5 seconds, drop capsule does not guarantee the micro gravity. Reverse voltage time can be adjusted every 5msec. In this experiment, the voltage has been turned off applying a reverse-voltage during 50ms in the electromagnet.

Because the pushing force is not generated only by the demagnetization of the electromagnets, two springs are used. The force of pushing out of this spring is adjusted 1.7N or more, and the separation plate separates at a speed of 36mm/sec.

The separation plate is composed of the VS-CMG device and two control equipments. VS-CMG consists of the

wheel, and gimbal, and controls each of them with motor. The separation plate can be stabilized by proposed method. The control equipment is composed of EPS&Gyro Box and CMG Controller Box. EPS&Gyro Box installs the

lithium-ion battery, gyroscope for attitude measurement, a microcomputer which generates CMG control input and and collect data, and the EPS. Gyroscope measures the rotational speed of three axes in 50Hz, which is recorded in the memory. CMG Controller Box has electric circuits that control two motor drivers, which were developed for pyramid array of CMGs described in the former section and used in this experiment, too. The control history is sent to EPS&Gyro Box, and recorded in the memory.

The coordinate of the separation plate, which is B-Frame, is defined in Fig. 5. Gimbal Frame is defined as

follows.

3

21

21

ˆˆ

cosˆsinˆˆsinˆcosˆˆ

bg

bbt

bbs

=

+−=

+=

γγ

γγ

(18)

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CMG

Control Box

3

2

1

Fig. 5

Separation plate including a VS-CMG and two boxes Body Frame is shown in this figure

Fig. 6

Over view of Separation plate, a VS-CMG and two control boxes

I/FBOX

Li-ion

Battery

Ir Rx

Base PlateMagnet

Controller

CMGGyro

Laser Displacement Sensor

CH1,2from MGLAB

Analog Data

MGLAB Tokyo Tech

Fig. 7

Experiment system block diagram

B-Frame

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Fig.8 shows an overview of the capsule for micro gravity experiments. The experiments are conducted at MGLAB in Japan. MGLAB (Micro-Gravity

Laboratory) has a vertical 150m underground vacuum tube. This enables to realize good-quality microgravity environment for about 4.5s. A drop capsule decelerates and stops at a breaking area with friction dampers. The detail of the vacuum drop tube is as follows:

Drop way: vacuum free-fall capsule Free-fall area 100m, breaking area 50m Micro-gravity time: about 4.5 second Gravity: 10-4G level

V. Result of the Drop Experiment At the beginning, by changing the wheel speed during micro gravity the attitude was measured with gyroscope.

Next, the attitude was measured by gimbaling with the wheel rotated. The former is the same method as a Reaction Wheel, and the latter is the same method as classical CMG.

The output torque in the RW mode is calculated to be 7.9mNm, and is also calculated to rotate the separation plate at the speed of 0.15 rad/s. The gyroscope at this time indicated 0.15 rad/s, and the RW mode was confirmed to have the performance the same as nominal parameter.

The torque of 67.8mNm in the CMG mode was also calculated and to rotate the separation plate at 1.27 rad/s. The gyroscope at this time indicated 1.18 rad/s, and the CMG mode was confirmed to have almost the same performance as nominal. This little gap is the one based on the nonlinearity when CMG works largely.

The experiment to decrease the angular velocity of the separation plate using a VS-CMG was conducted. The

angular velocity is measured by gyroscope and controller uses it as feedback loop. The control input is as shown in the equations (3). Moment of inertia of the wheel and nominal wheel speed of

the CMG are as follows. Moreover, the coefficient was provided as follows.

72

21

2

10*5.2

10*2.1/450

00015.0

=

=

=Ω

=

k

ksradkgmIWS

(19)

Because the small computer was used for the controller, in order to reduce calculation cost, the gimbal angle was

assumed to be always small, and following assumption (20) are correct. 21 , ωωωω ≈≈ ts (20) The experiment was conducted in the following steps. First, the wheel starts to rotate three minutes before the

separation, and it reaches 4300 rpm. The separation signal is sent from the capsule at the same time of fall, and the separation plate will separate in 2.6 seconds. At this time, it is already micro gravity in the capsule.

Next, to make initial condition, separation plate is given the angular velocity by gimbaling the rotating wheel. Afterwards, the angular velocity control starts when internal clock passes 2 seconds and ends at 3 second.

The angular velocity measured by gyroscope is shown in Fig. 9. Fig. 10 shows the wheel speed and the gimbal angle. Because the angular velocity in s axis is negative, in order to rotate the plate toward positive direction, the wheel is decelerating. And it was confirmed that the angular velocity in s axis gets nearly zero. Similarly, gimbal of the CMG worked well to decrease the angular velocity in t axis.

Fig. 8Drop capsule used for MG-LAB experiment

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From these results, it was confirmed that the angular velocity had decreased less than 0.06 rad/s. The standard deviation of the gyroscope is actually 0.0068 rad/s, which is 10 times better, however, since controller handles data with 8bits, accuracy gets worse than 0.027 rad/s. It means that the control input was able to decrease the angular velocity within 3-σ.

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

2 2.2 2.4 2.6 2.8 3

Time [sec]

Angu

lar

velo

city

[rad/s]

s

t

g

Fig. 9

Angular velocity measured by gyroscope, decreased to zero

250

300

350

400

450

500

2 2.2 2.4 2.6 2.8 3Time [sec]

Wheel ra

te [

rad/

s]

0

0.1

0.2

0.3

0.4

0.5

0.6

2 2.2 2.4 2.6 2.8 3

Time [sec]

Gim

bal A

ngl

e [

rad]

Fig. 10

Wheel rate and Gimbal angle

VI. Conclusion In this paper, angular rate damping control was tested in the micro gravity drop experiment. A separation plate of

about 3 kilograms including one VS-CMG is not axisymmetry, the angular rate damping control was checked in more general case. It was confirmed to work well except for very special case, and the experiment system actually worked well. In the microgravity environment, one VS-CMG was controlled to suppress the rotation of the separation plate and gyroscopes measured its rotational rate. As a result, it was confirmed that one VS-CMG was able to decrease angular velocity of the separation plate.

References 1Yoon, H., Tsiotras, P., “Spacecraft Angular Velocity and Line-of-Sight Control Using A Single-Gimbal Variable-Speed

Control Moment Gyro” AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, California, AIAA 2005-6393, 2005.

2K. Omagari, T. Usuda and S. Matunaga, “Research of Control Momentum Gyros for Micro-satellites and 3-DOF Attitude Dynamics Simulator Experiments,” Proceedings of the 8th International Symposium on Artificial Intelligence, Robotics and Automation in Space, Munich, Germany, 5-8 September, ESA-SP603, 2005.