The Phillips Laboratory at Edwards AFB has constructed a test bed for the validation and comparison of modeling and control theories for the dynamics and control of flexible multibody systems. This project is called the Planar Articulating Controls Experiment (PACE). This paper presents the experimental apparatus for PACE and the problem formulation. An in-depth analysis on DC motor dynamics was also performed

Das, Alok

Kwak, Moon K.

Smith, Monty J.

English

NASA Technical Reports Server

N94-14650
PACE: A Test Bed for the Dynamics and
Control of Flexible Multibody Systems
Moon K. Kwak, Monty J. Smith and Alok Das
The USAF Phillips Laboratory
OLAC PL/VTSS
Edwards AFB, CA 93523
Abstract
The Phillips Lal)oratory at Edwards AFB has constructed a test bed for the validation
and comparison of modeling and control theories for tile dynamics and control of flexible
multibody systems. This project is called the Planar Articulating Controls Experiment
(PACE). This paper presents the experimental apparatus for PACE and the problem for-
mulation. All in depth analysis oll DC motor dynamics was also performed.
1. Introduction
The Air Force remains active ill space systems, and hardware, such as space robots,
rotorcraft and spacecraft, consists of subsystems which can be described as flexible multi-
bodies. The dynamics and contro[ of flexible multibody systems has been of interest for
many years. (Refs. l-ll ). Identifying, lno(leling and controlling such systems using various
theories with confidence has also become an important issue. At present, a real need exists
for the validation and comparison of various modeling and control theories based on an
actual hardware experiment, ltowever, compared to theoretical developments and number
of computer programs available, experimental verification has never been conducted. To
this end, the Phillips Laboratory at Edwards AFB has constructed a flexible multibody
structure which consists of 2 flexible beams connected in series with motors at both the
hub and the elbow joint. Figure 1 shows the multibody body structure named the Planar
Articulating Controls Experiment (PACE).
2. Experimental Apparatus
Figure 2 shows the PACE control loop which includes 2 flexible arm manipulator, var-
ious sensors and actuators, amplifiers, an AC-100 data acquisition controller and the VAX
workstation. Actuators and sensors are connected to D/A and A/D interfaces of the AC-100
controller through amplifiers. Sixteen channels are available on each D/A and A/D inter-
faces. The VAX 3100 workstation controls the AC-100 data acquisition controller with the
ISI real-time monitor software which includes MatrixX, Autocode and Interactive Animation
module.
The motion of the multibody test article is constrained to horizontal motion on a 14
foot square granite table. An air compressor is used to activate an air bearing, which allows
the whole system to float on air so that friction forces do not exist between the support
plate and the granite table. The shoulder motor is fixed at the center of the granite slab
and the elbow motor is located at the junction of two beams. Thus, the arms can be driven
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https://ntrs.nasa.gov/search.jsp?R=19940010177 2020-06-16T19:42:34+00:00Z
through some trajectory using tile DC motors.
Sensors for PACE include:
° Encoders count the change of a square wave; its resolution is 2540 cycles per revolution.
A differential interface converts the encoder output to the number of changes in the
data acquisition time interval, which is proportional to the angular velocity of the
motor shafts. Tachometers are not being used currently due to their inaccuracy in
measurements, as reported by the manufacturer, PMI company.
2. Lasers trace tile positions of two arms. JPL is designing and testing the hardware
implementation.
3. Accelerometers will measure accelerations of arbitrary points of interest on the struc-
ture.
4. Piezoceramic Sensors will measure strains along beams.
Actuators for PACE include:
1. PMI DC motors provide primary torques to slew the arms. Both motors have a gear
box.
2. Piezoceramic actuators will suppress vibrations of the arms.
3. Reaction wheels (Optional) will apply a secondary moment to suppress vibrations
of the arms.
The fl'ee body diagram for PACE, seen in Fig. 3, can be divided into 4 components; 2
DC motors and 2 flexible beams with lip masses at both ends. The dynamics of DC motors
should be incorporated into the dynamics of the whole system. Modeling of the PMI DC
motor with a gearbox is not an easy task since the gear box of DC motor causes noise,
backlash and power loss.
3. Problem Formulation
Before the integration of the components of PACE, DC motor identification was per-
formed using the unit-step and sine-sweep response tests. Tim sine-sweep response of the
elbow, shown in Fig. 5, illustrates the dominant effect of static fl'iction torque on the system
response. Based on these tests, the mathematical model includes mass moment of inertia,
viscous and Coulomb damping and static fl'iction. Thus, the equation of motion for the
shoulder motor is given as
n_I_._8,÷ C_i + C_ ._gn(_,)= n(T_ - T.I)- T, (I)
whilethe elbow motor isdescribedas
n2I_,,_2 + C_2 + C_ sgn(_2) = n(T_ - T_!) - T2 (2)
526 i
where n is the gear reduction ratio, Ism and Iem are the mass moment of inertias of the
shoulder and elbow motors, respectively, 81 and 02 are the angular displacements of each
motor relative to motor housings, C_, and Cev represent the viscous damping coefficients
of each motor, Csc and Cec represent the Coulomb frictions of each motor, Ts and Te are
the motor torques, T<[ and Tef represent tile static friction torques of each motor, and
7'1 and T2 represent the torques transferred to each arm of the shoulder and the forearm,
respectively. Note that the subscripts s and e denote the shoulder motor and the elbow
motor, respectively. The static friction torques, T_] and Tel, are expressed in terms of the
motor torques, T_ and Te.
-T;*/ if Ts < -T;_;T,I = T_ if-T;*/ _< T, < T;'/; (3)
W;*f if Ts > T;5.
-T;*/ if T_ < -T_;Tel = T, if-T;'f _< :/'e _< T;'f;
* T*Tel if Te > el"
Based on the circuits of the DC motors and the servo amplifiers, we can express the motor
torque in terms of the input voltage to the servo amplifier
Zs = I(sT(OsVs + t_s)
Tc --- -l(eT(O_eVe + fie) (4)
where K_T and I(eT are motor constants, as, ae and _, and J3e are constants of servo am-
plifiers, and I_ and 1_ are the input voltage to the servo amplifiers, respectively. Equations
(3) and (4) relate the output voltages of the AC-100 controller to the motor torques of DC
motors. Note that the minus sign is added in Eq. (4) because of the direction. Parameters
of the PMI DC motors were identified independently due to errors in the manufacturer data.
The identification results for the shoulder and elbow motors are tabulated in Tables 1 and
2. The material properties of each arm, listed in Fig. 5, will be identified in the near future.
Equations of motion for PACE are derived using the Lagrangian approach (Ref. 12).
Since each beam is represented by a distributed parameter system, the resulting equations
have the form of hybrid equations, i.e., the combination of ordinary differential equations
and partial differential equations. For the numerical shnulation and control design, the
elastic displacements are discretized with the assumed-mode technique, resulting in high-
order nonlinear ordinary differential equations. Thus, recalling Eqs. (1) and (2), we may
write the following state equation for the whole system
± = f(x,F) (5)
where
-- and
x = [01 qT e._ qT 0, dlT 82 itT ]T
F = [l,_v T Á/eVTIT
(6)
(7)
527
in whichx is the state,F is the controlvector,ql and q2 representhe generalizedcoor-
dinatesfor the elasticvibrationof eacharm, and vl and v2 are the input voltageto the
amplifiersof piezoceramicactuatorsand reactionwheelsmountedon eachbeam,respec-
tively.
Thenonlinearsensorequationsare
y = g(x,±) (8)
wherey consistsof the encoderoutputs,output voltagesof piezoceramicsensorsand ac-
celerometers.
The dynamicanalysisof PACEwill beperformedusingboth commercialandin-house
algorithms.
4. Control Design
The VAX workstation is equipped with integrated software for data acquisition and
control, the Real-Time Monitor Control. Fortran or C subroutines can be incorporated into
the real-time control of PACE. The control objectives of PACE are to drive the arms to a
certain position with a specified line of sight in minimum time and to suppress vibrations
simultaneously based on sensor measurements. The authors are performing a survey of
possible control techniques such as neural network control, nonlinear control and adaptive
control techniques that can be applied to PACE. The difficulty of finding a control algorithm
for PACE is in the inherent nonlinearity of the system, including the structural, sensor and
actuator dynamics.
5. Summary and Conclusions
The experimental apparatus for PACE has been described in detail. The current con-
figuration enables us to verify the numerical results of modeling and control theories for
flexible multibody systems experimentally. Presently, both sensors and actuators are still
being mounted to the PACE structure, and system identifications of its components must
continue to be performed. However, in the near future, PACE will be the ideal test bed for
researchers studying the dynamics and control of flexible multibody systems.
References
1. Meirovitch, L. and Iiale, A. L., "Synthesis and Dynamic Characteristics of Large Struc-
tures with Rotating Substructures," Proceedings of the IUTAM Symposium on the Dy-
namics of Multi-Body Systems, (Editor: K. Magnus), Springer-Verlag, Berlin, 1978,
pp. 231-244.
2. Hollerbach, J. M., "A Recursive Lagrangian Formulation of Manipulator Dynamics and
a Comparative Study of Dynamics Formulation Complexity," IEEE Transactions on
Systems, Man, and Cybernetics, Vol. SMC-10, No. 11, 1980, pp. 730-736.
528
3. Huston,R. L., "Flexibility EffectsinMultibodySystemDynamics,"Mechanics Research
Communications, Vol. 7, No. 4, 1980, pp. 261-268.
4. tluston, R. L., "Multi-Body Dynamics Including tile Effects of Flexibility and Compli-
ance," Computers and Structures, Vol. 14, No. 5-6, 1981, pp. 443-451.
5. Book, W. J., "Recursive Lagrangian Dynamics of Flexible Manipulator Arms," The
International Journal of Robotics Research, Vol. 3, No. 3, 1984, pp. 87-101.
6. Yoo, W. S. and Ilaug, E. J., "Dynamics of Articulated Structures. Part I. Theory,"
Journal of Structural Mech<mics, Vol. 14, No. l, 1986, pp. 105-126.
7. Yoo, W. S. and ][aug, E. J., "Dynamics of Articulated Structures. Part II. Computer
Implementation and Applications," Journal of Structural Mechanics, Vol. 14, No. 2,
1986, pp. 177-189.
8. Changizi, K. and Shabana, A. A., "A Recursive Formulation for the Dynamic Analysis
of Open Loop Deformable M ultibody Systems," Journal of Applied Mechanics, Vol. 55,
1988, pp. 687-693.
9. Shabana, A. A., "On the Use of the Finite Element Method and Classical Approximation
Techniques in the Non-linear Dynamics of Muitibody Systems," International Journal
of Non-Linear Mechanics, Vol. 25, No. 2, 1990, pp. 153-162.
10. Meirovitch, L. and Kwak, M. K., "Rayleigh-Ritz Based Substructure Synthesis for Flex-
ible Multil)ody Systems," AIAA Journal, Vol. 29, No. 10, Oct. 1991, pp. 1709-1719.
11. Meirovitch, L. Stemple, T. and Kwak, M. K., "Dynamics and Control of Flexible Space
Robots," presented at the Symposium on Mechanical Systems with Time- Varying Topol-
ogy, CSME Mechanical Engineering Forum 1990, June 3-9, 1990, Toronto, Canada.
12. Kwak, M. K. and Meirovitch, L. "A New Approach to the Maneuvering and Control of
Flexible Multibody Systems," Journal of Guidance, Control and Dynamics (to appear).
529
ShoulderMotor Unit
_ 60
l,m 1.043 × 10 -4 kg m 2
C,v 0.829 N m/rad/s
Csc 1.097 N m
KsT 0.084 N m/A
t_, 1.7189 A/V
/J_ 0.1590 A
0.030 N m
Table 1. Data for the Shoulder Motor (PMI S9M4II)
Elbow Motor
60
0.278 x 10 -4
Unit
0.012
kg m 2
C_. 0.073
C_c 0.423 N rn
h,r 0.030 N rn/A
ae 1.5,179 A/V
/_ 0.0289 A
N m
N m/rad/s
Table 2. Data for the Elbow Motor (PMI $6M411)
530
Fig. 1. The Planar Articulating Controls Experiment (PACE) Test Article
PACE
Actuator Signal
Sensor Signal
Amplifier
VAX Workstation
A/D D/A
AC-100
Controller
Fig. 2. The Control Loop for the PACE
531
Shoulder
Shoulder Motor
Beam
Forearm
Elbow
Elbow Motor
Bcam
Fixed End
Fig. 3. The Free Body Diagram for the PACE
0
Encoder Oulpu!
Voltage in
I0
Fig. 4. The Sine-Sweep Test of the Elbow Motor
532
Shoulder
ms = 0.872 k 9
]j = 13.664 x 10 -4 k 9 m 2
0.047 m
O.l12m
1st Beam Elbow
rT_l = 0.532 kg/m
Eln = 11.413 N m 2
]l = 161.589 x 10 -4 kg m 2
0.714 m
me = 4.280 kg
]e = 122.982 x 10 -4 kg m 2
 0023m
"1
0.165 m
Forearm 2nd Beam Fixed End
m I = 1.731 kg
]I = 81.912 x 10 -4 kg m 2
@
0.057 m -_ 14-
r
0.165 m
Ih2 = 0.531 kg/m
EIz = II.275 N m 2
]2 = 161.208 x 10 -4 kg m 2
0.714 m
md = 1.038 kg
],t = 15.244 x 10 -4 kg m z
0.050 m
0.009 m
Fig. 5. The Material Properties for the PACE
533



PACE: A test bed for the dynamics and control of flexible multibody systems

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