The Spacecraft Control Laboratory Experiment (SCOLE) was conceived to provide a physical test bed for the investigation of control techniques for large flexible spacecraft. The control problems studied are slewing maneuvers and pointing operations. The slew is defined as a minimum time maneuver to bring the antenna line-of-sight (LOS) pointing to within an error limit of the pointing target. The second objective is to rotate about the LOS within the 0.02 degree error limit. The SCOLE problem is defined as two design challenges: control laws for a mathematical model of a large antenna attached to the Space Shuttle by a long flexible mast; and a control scheme on a laboratory representation of the structure modelled on the control laws. Control sensors and actuators are typical of those which the control designer would have to deal with on an actual spacecraft. Computational facilities consist of microcomputer based central processing units with appropriate analog interfaces for implementation of the primary control system, and the attitude estimation algorithm. Preliminary results of some slewing control experiments are given

Williams, Jeffrey P.

English

NASA Technical Reports Server

SLEW MANEUVERS ON THE SCOLE
LABORATORY FAC IL ITY
N87-24511
Jeffrey P. Williams
Spacecraft Control Branch
NASA Langley Research Center
Hampton, Va.
851
https://ntrs.nasa.gov/search.jsp?R=19870015078 2020-03-20T11:03:25+00:00Z
INTRODUCTION
The Spacecraft Control Laboratory Experiment (SCOLE) has been
conceived to provide a physical test bed for the investigation of
control techniques for large flexible spacecraft. The control problems
to be studied are slewing maneuvers and pointing operations. The slew
is defined as a minimum time maneuver to bring the antenna
line-of-sight (LOS) pointing to within an error limit of the pointing
target. The second control objective is to rotate about the line of
sight and stabilize about the new attitude while keeping the LOS error
within the 0.02 degree error limit. The SCOLE problem is defined as two
design challenges. The first challenge is to design control laws for a
mathematical model of a large antenna attached to the Space Shuttle by
a long flexible mast. The second challenge is to design and implement a
control scheme on a laboratory representation of the structure modelled
in the first part [I]. Control sensors and actuators are typical of
those which the control designer would have to deal with on an actual
spacecraft. Computational facilities consist of micro-computer based
central processing units with appropriate analog interfaces for
implementation of the primary control system, and the attitude
estimation algorithm.
This report gives preliminary results of some slewing control
experiments which demonstrate the capabilities of the recently
completed experimental facility.
* EXPERIMENT CONCEIVED TO PROVIDE A COMMON "DESIGN CHALLENGE
FOR INTERESTED INVESTIGATORS
* SLEWING AND POINTING CONTROL PROBLEM
* USES ANTENNA LIKE STRUCTURAL CONFIGURATION AND INERTIAL
SENSORS AND ACTUATORS
* VARIETY OF SENSOR AND ACTUATOR TYPES
- Accelerometers, rate sensors, optical position
- Thrusters, crag, reaction wheel
* MULTI-MICROPROCESSOR BASED COMPUTING
* WILL DEMONSTRATE EFFECT OF APPLYING RIGID-BODY CONTROL LAW
TO A FLEXIBLE STRUCTURE USING THRUSTERS ONLY
852
SLEW MANEUVER ON THE SCOLE
The primary purpose of this paper is to demonstrate the capability
of the laboratory facility to fulfill the requirements of the second
part of the Design Challenge presented by Taylor and Balakrishnan [i].
That requirement is for an accessible laboratory experiment which will
allow the study of slewing maneuver of flexible spacecraft.
A 20 degree single axes minimum-time slew using the reflector
mounted thrusters is presented. An ad-hoc control scheme which allows
the maneuver to be completed without exciting the ist bending mode of
the mast is also demonstrated. No theoretical analysis is offered to
justify the performance of the controller or to generalize the
technique to other flexible structures.
PART TWO OF SCOLE DESIGN CHALLENGE (Taylor, Balakrishnan)
* SLEW 20 DEGREES USING THRUSTERS
WILL DEMONSTRATE AD-HOC CONTROL LAW TO SLEW WITHOUT
EXCITING Ist BENDING MODE
SCOLE LABORATORY FACILITY IS PROVIDED AS A TEST-BED
FOR EVALUATION OF CONTROL LAWS FOR
LARGE FLEXIBLE STRUCTURES.
IMPLEMENTATION OF A CLASSICAL RIGID BODY BANG-BANG
SLEWING CONTROL LAW DEMONSTRATESD THAT FLEXIBLITY
OF THE SCOLE APPARATUS WILL PRESENT CONTROL
CHALLENGES SUFFICIENT FOR IDENTIFYING CONTROL DESIGN
METHODOLOGIES WHICH MAY BE APPLIED TO FUTURE LARGE
FLEXIBLE SATELLITES
IMPLEMENATION OF AN AD-HOC CONTROLLER FOR VIBRATION
ACCOMMODATION DEMONSTRATED THAT FLEXIBILITY OF THE
STRUCTURE CAN BE SUPPRESSED
853
SCOLE LABORATORY APPARATUS 
The laboratory experiment shown in the figure attempts to 
implement the definition of the modelling and control design challenge 
within reasonable limits of the lg, atmospheric environment. The 
experimental facility exhibits the essential SCOLE characteristics of a 
large mass/inertia connected to a small mass/inertia by a flexible 
beam. Some trades are made in terms of structure, sensors, actuators, 
and computational capability in order to develop the experiment in a 
timely and cost effective manner. To this end, the basic structure is 
made of homogeneous continuous elements connected by welds and 
mechanical fasteners. The sensors are aircraft quality rate sensors 
and servo accelerometers. The Shuttle attitude will be determined 
through a combination of inertial measurements and optical sensing 
%echniques. The Shuttle control moments are provided by a pair of 
2-axis control moment gyros (CMG’s). Mast mounted control torques can 
be applied by a pair of two-axis reaction wheels. Reflector based 
forces are provided by solenoid actuated jets. Reflector mounted 
torque devices are a trio of high authority reaction wheels. 
qRl  
OF 
854 
STRUCTURES
The SCOLE is comprised of three basic structures, the Shuttle, the
mast, and the reflector panel. The assembly of these individual
components and the global reference frame are shown in the figure.
The Shuttle planform is made from a 13/16 inch steel plate and
has overall dimensions of 83.8 by 54.0 inches. Its total weight is
501.7 pounds. The Shuttle's center of mass is located 3.4 inches below
the experiment's point of suspension, and 26.8 inches forward of the
tail edge.
The mast is 120 inches long. It is made from stainless-steel
tubing and weighs 4.48 pounds. One-inch thick manifolds are mounted to
the mast at each end.
The reflector panel is hexagonal in shape, made from welded aluminum
tubing, and weighs 4.76 pounds. It is located 126.6 inches below the
SCOLE's point of suspension. The center of the reflector is located at
12.0 inches in the x direction and 20.8 inches in the y direction from
the end of the mast.
BASIC SCOLE STRUCTURE
Shu.le:
13/16 in. steel plate
501
Y
Mast:
3/4 x .049 in. stainless steel tube
4.48 Ib
Reflector:
314 x .0625 in. weldedaluminum tube
4.76 Ib
855
ORIGli$hL FX*215 IS 
SUSPENSION GIMBAL OF POOR QUALITY 
The complete system is suspended from an eleven-foot cable 
attached at the system center of gravity via a universal joint. The 
positive z-axis of the Shuttle is pointed up, thus minimizing the 
static bending of the antenna mast. The suspension point shown in the 
figure is a two-degree-of-freedom gimbal for pitch and roll rotations 
with yaw rotation supplied by the suspension cable. The estimated 
break-out torque of the gimbal is 0.1 ft-lb. The gimbal is fixed to 
the Shuttle plate, and the system center-of-gravity is made to coincide 
with the center-of-rotation by means of an adjustable counter balance 
system. 
856 
SLEW CONTROL LAW
The slewing of a rigid body spacecraft has long been accom-
plished with a simple on-off control algorithm which can be
derived by examining the phase-plane solution of the simple
forced-double-integrator dynamical system. Such a system will describe
a parabolic path in the phase plane. The particular path is a function
of the initial conditions and the applied torque. If one formulates
the final condition problem by specifying zero attitude and zero
attitude rate at the final time, backward solution of the equations of
motion shows that the approach to the origin must follow the
skew-symmetric parabolic curves shown in the figure. These lines will
be called the control switching curves. For a given initial condition,
the starting command to drive states of the body toward one of the
switching curves may be determined by inspection. When the states
intersect one of the curves, the control command will change sign and
the states will then be driven to zero. This algorithm is shown to be
minimum-time by Bryson and Ho in reference 2. If the effectiveness of
the torquers is mis-estimated, the controller will still converge to
zero, but more than one switch will be required. Also, to allow for
practical implementation, a dead-band must be included so that the
control command may be set to zero when sufficient attitude performance
is achieved.
Such a control law is implemented on the SCOLE by using the
reflector mounted thrusters for the control torque. The Shuttle rate
sensor and accelerometers are used to estimate attitude rate and
attitude by ignoring pendulumn motion of the suspension system. The
cold air thrusters on SCOLE have about 0.2 lb force output and are
approximately i0 ft from the center of rotation. Their rise time is
about 0.032 seconds.
* FOR A SIMPLE RIGID BODY SLEW ABOUT ONE AXIS,
le = tu
* THE MINIMUM TIME MANEUVER IS GIVEN BY (Bryson & Ho):
u = +1 if _O_sign.(6) < -2 t/I e or
if _Zsign(O) = -2 t/I e and e > 0
u = -1 if _sign(O) > -2 t/I 0 or
if _)_sign(_)) = -2 t/I 0 and e < 0
4_
U =-]
ic U_- I
* FOR IMPLEMENTATION:
() derived from rate sensor
0 derived from accelerometers by ignoring pendulumn effects
857
DAMPING CONTROL LAW
For a cantilevered end condition, that is to say, no rigid-body
motion, a vibration suppression control law which uses the reflector
mounted rate sensor and the thrusters may be derived. The control law
is simply to command thrust opposite the sign of the velocity component
parallel to thrust axes at the point of attachment of the thrusters.
This control will cause a linear decay of the controllable vibration
modes.
For implementation on the SCOLE, the velocity of the center of the
reflector (attachment point of the thrusters) is estimated by
calculating the cross product:
_v =_r xH
where X is the position vector of the thrusters with
respect to the rate sensor mounted on the corner of the
reflector and H is the output vector of the rate sensor.
Here again, a dead-band is required so that the thrusters will turn off
when the state origin is reached.
SUPPRESS BENDING MODE VIBRATIONS OF MAST/REFLECTOR
FOR CANTILEVERED END CONDITIONS SIMPLE COLLOCATED FEED-BACK
WILL SUFFICE:
U = - sign (velocity of thrusters)
÷ Thrust
o Velocity
0 ÷
FOR IMPLEMENTATION, VELOCITY OF THRUSTERS IS DERIVED FROM
REFLECTOR MOUNTED ANGULAR RATE SENSOR BY CALCULATING:
V=rxw
_ m
where V_ is the thruster velocity, r is the postition vector
of the thrusters w.r.t, the angular rate sensor, and w is
the output angular rate sensor.
858
AD-HOC SLEW CONTROLLER
Observation of the structural configuration indicates that the
first mode of motion for the system will be a bending mode which will
have the Shuttle and the reflector bending towardeach other. A
command to slew would tend to excite this mode. To suppress the
flexible motion would require a thruster command which is contrary to
the desired attitude motion. To resolve this dilemma, use is made of
the position dead-band for the bang-bang slew control law and the rate
dead-band of the vibration suppression control law. By combining the
thrust commands for the two controllers, a semi-consistent control
command can be determined. A semi-consistent command is one which has
the sign and magnitude of at least one of the individual commands. To
determine the semi-consistent command, one must first recognize that
the thruster can have one of three states:-l, O, or +i. If the two
commands have opposite signs, they are inconsistent and the only control
choice is to command zero thrust. If the signs are the same, or if
one command is zero and one is non-zero, then the command to the
thrusters should be the sign of the sum of the individual commands.
Admittedly, this technique does not account for more than one flexible
mode, but recall that the stated purpose of the paper is to demonstrate
the capability of the laboratory facility, not to develop new control
theory.
DETERMINE CONTROL COMMMANDS FOR BOTH CONTROL LAWS
SIMULTANEOUSLY
- IF COMMANDS CONFLICT ( ARE OF OPPOSITE SIGN ),
TURN THRUSTERS OFF
9 18A.G- /
_..,,.,,I DANG / Us
---+1 stewF--I
_r_lve"°cltYI I u
.r_leeeD-BacK I---i_
D_DAMPIN6 I "_
NO MODAL DECOUPLING ATTEMPTED
- THAT IS TO SAY, OUTPUTS OF SENSOR ARE USED DIRECTLY
MUST RECOGNIZE THAT NO THEORY IS PRESENTED TO PREDICT
PERFORMANCE OR GENERALIZE THIS TECHNIQUE TO OTHER
FLEXIBLE STRUCTURES
859
SENSORS 
The sensors for the experiment consist of threeservo- 
accelerometers and two, three-axis rotational rate sensing units. 
The power supplies for these sensors are mounted on the Shuttle plate 
to minimize the number of large gauge wires which must cross the 
universal joint suspension point. Only a single 115 VAC cable and 
thirty-three signal wires cross the universal joint. The wires for the 
sensors are routed on the Shuttle and along the mast. 
SHUTTLE MOUNTED ACCELEROMETERS 
The Shuttle-mounted accelerometers shown in the figure sense the 
x,y, and z accelerations of the Shuttle and gravity. The output of the 
x and y accelerometers are used to determine attitude angle by 
neglecting pendulumn effects of the suspension system. These sensors 
are distributed away from the suspension point to aid inertial attitude 
estimation. 
nearly flat up to 350 Hz. Linearity is within .17% of the full-scale 
output. 
The accelerometers have a frequency response which is 
860 
The reflector-mounted rate sensor package, shown in the extreme 
left of the figure, senses three axis angular rates at the reflector 
end of the mast. This information is used for the vibration suppression 
control law. 
The control forces on the reflector are provided by solenoid 
actuated cold gas jets. The thrusters are mounted in the center of 
the reflector and act in the x-y plane. The jets are supplied by a 
compressed air tank mounted on the Shuttle. The pressurized air 
travels through the mast to the solenoid manifold which gates the air 
flow between the regulated supply tank and the thrusters. Thrust is 
initiated by opening the solenoid with a discrete command. 
86 1 
SHUTTLE RATE SENSORS 
The rotational rate sensors are three axis aircraft 
quality instruments. The frequency response is approximately flat to 1 
Hz and -6 db at 10 Hz. Linearity is about 0.6% full scale. The 
range is 60 deg/sec for the yaw and pitch axes and 360 deg/sec 
for roll. The threshold is 0.01 deg/sec. 
The Shuttle-mounted rate sensor package shown in the figure, 
senses three axis rigid body angular rates of the Shuttle plate. These 
dataareused for the slewing control law. 
862 
COMPUTER SYSTEM
The main computer for control law implementation will be a
micro-computer based on the Motorola M68000 microprocessor. The
computer has 2.0 Mbyte of random access memory and a 40 M-byte hard
disk. The operating system is based on UNIX with C, Fortran and Pascal
compilers available for applications programming. The computer has 12
serial ports and one parallel port. Terminals are connected on two of
the ports and an answer-only modem is attached to another. One port is
used for an originate only modem. A line printer is attached to
another port.
Analog interfaces consist of a four-bit output-only discrete
channel, eight digital-to-analog converters and sixty-four
analog-to-digital converters. All converters are 12 bit devices with a
range of +/-10v.
/_ "_'' _ 4.8 KBAUD
[);/'0"i] _ 5EHIAL I ,1111,,,,
I J THRUSTERS
REACTION WHEELS •
ACCELEROMETERS,
RATE SENSORS
OPTICAL ATTITUDE SENSOR
IBM PC
CONTROLLER CMG COMMANDS
863
EXPERIMENTAL RESULTS
The effect of applying the rigid-body bang-bang slewing control
law to a flexible structure without taking that flexibility into
account is demonstrated in the top four time histories. The data
presented are, from top to bottom: the Shuttle roll attitude estimate,
the Shuttle roll rate estimate, the reflector roll rate measurement,
and the thruster command perpendicular to the roll axis. The control
law is demonstrated by applying an external torque during the first
five seconds with the control disabled. After approximately 20 degrees
of attitude error is built up, the control was enabled. The reduction
of the attitude error and first switch of the thrust command proceeds
essentially as expected for a simple double integrator plant. The
oscillation of the attitude during the period from twelve to twenty-two
seconds is due to an under estimate of the control effectiveness of the
thrusters. Note however that the attitude error continues to decrease.
The structural dynamics and control problem addressed by the SCOLE
Design Challenge are evident in the oscillation of the Shuttle and
reflector roll rates. After the attitude error has become very small
at about nineteen seconds it is apparent that the flexible mode is
completely unstable and would eventually lead to structural failure.
The effectiveness of the ad-hoc controller in accomplishing the
slew without exciting the flexible motion is shown in the bottom four
time histories. The same variables are plotted here as above. In this
case, the consistency comparison between the slew command and the
vibration suppression command allows the slew command to take effect
only during short bursts which usually last only one sample period.
These pulses are sufficient to drive the attitude error to zero, but
the maneuver takes about six seconds longer than the slew only control
law. Note however, that the flexible motion is not appreciably excited
in this case. Also, because the attitude rates remain relatively small,
the attitude error remains relatively low. A final special
circumstance in this demonstration must be recognized - that is that
the initial condition of the plant had essentially zero excitation of
the flexible mode. If it had been excited prior to activation of the
control, it is possible that the slew would not have been accomplished.
864
RIGID BODY BANG-BANG SLEW ONLY
(thrust 0
I_ c°mmand). E' [ L__
i I I,
0 4 8
r i I I I
12 16 20 24
TIME (seconds)
BANG-BANG SLEW
_(Shuttle Lattitude) 0 _-_-___,__
-20
_ (Shuttle 0 _
rate) -
(reflector +I) rate) u I "I
& VIBRATION SUPPRESSION
f v
.. ha.. n..nfl...r,n..
(thrust 0 I
&I command)_
I
0
I _ I t I i I
8 12 16 20 24 28
TIME (seconds)
865
CONCLUSIONS
The SCOLE laboratory facility has been constructed to provide a
test-bed for the testing and evaluation of control laws for large
flexible structures. Implementation of a classical rigid body
bang-bang slewing control law has demonstrated that the combination of
flexiblity and control authority present on the SCOLE apparatus will
present control challenges sufficient for identifying control design
methodologies which may be applied to future large flexible satellites.
The implemenation of an ad-hoc controller for vibration
accommodation demonstrated that flexible motion of the structure can
be suppressed.
866
REFERENCES
° Taylor, L.W., Jr., and Balakrishnan, A. V.: A Laboratory Experiment
Used to Evaluate Control Laws for Flexible Spacecraft...NASA/IEEE
Design Challenge, Proceedings of the Fourth VPI&SU/AIAA Symposium
on Dynamics and Control of Large Structures, June 1983, pp.
311-318.
o Bryson, A.E., Jr., and Ho, Y.C.: Applied Optimal Control,
Optimization, Estimation, and Control, John Wiley & Sons, N.Y.,
1975.
867


Slew maneuvers on the SCOLE Laboratory Facility

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