Mechanical Modeling of an Actuated Platform

for Precision Pointing Control

Via Finite-element Analysis and Normal Mode Analysis

Eric U. Diaz, Gerardo Zarate, Helen Boussalis and Khosrow Rad

NASA SPACE Center URC, California State University, Los Angeles, 5151 State University Dr., Los Angeles, U.S.A.

Keywords: Finite-element Analysis, Normal Mode Analysis, Space Telescope.

Abstract: A large, segmented space telescope requires high precision and accuracy in its mirror shape to obtain clear

images. The Structures, Propulsion, and Control Engineering (SPACE) telescope testbed at the NASA

sponsored University Research Center of excellence must maintain a pointing control accuracy of 2 arc

seconds. A Peripheral Pointing Architecture (PPA) has been designed to demonstrate the Testbed’s pointing

accuracy. A Finite Element Analysis (FEA) model of the PPA is developed. Normal mode analysis is

performed to establish the PPA’s natural frequencies, mode shapes, and the mass and stiffness matrices.

Utilizing the H-infinity controllers developed to achieve figure maintenance, the pointing control of the

Testbed structure is achieved.

1 INTRODUCTION

Due to an ever increasing need to “see” further into

space, a new generation of space telescopes is

needed. Younger objects, receding from us at an

ever-faster rate, are red-shifted into the near infrared

where Hubble loses sensitivity (Stockman, 1997).

To meet this requirement the National

Aeronautics and Space Administration (NASA) will

replace the Hubble Space Telescope with the James

Webb Space Telescope (JWST), previously known

as the Next Generation Space Telescope (NGST).

This telescope consists of a very large light-

gathering primary mirror capable of detecting faint

signals from the first billion years, the period when

galaxies have been formed. The JWST will be

capable of detecting radiation whose wavelength lies

in the range of 0.6 to 20 mm. Furthermore, the

JWST will be able to see objects 400 times fainter

than those currently studied with large ground-based

infrared telescopes such as the Keck Observatory.

Due to the size and weight limitations associated

with current launch vehicles, the Next Generation

Space Telescopes will employ segmented reflectors.

Although multiple-mirror designs have many

advantages, a number of major difficulties are

associated with this technique. Due to atmospheric

disturbances, the mirrors can be easily misaligned

and figure maintenance, as well as, precision

pointing of the telescope cannot be achieved.

Therefore, to accomplish figure maintenance and

precision pointing of the large segmented structure,

design of sophisticated controllers is necessary to

study the control of such large segmented optical

systems, in 1994, NASA established the SPACE

Laboratory at California State University, Los

Angeles (CSULA). One of the major goals of this

Laboratory is to design and fabricate a testbed that

resembles the complex dynamic behavior of a

segmented space telescope, (Boussalis et al., 1995),

(Boussalis, 1994), (Boussalis et al., 1996). The

SPACE center team of students and faculty work on

the development of control algorithms which will

accomplish the figure maintenance and precision

pointing of the control oriented SPACE testbed,

(Boussalis, 2002). Due to the symmetry of the

structure and the nature of the interconnections

among its subsystems, decentralized control

techniques are utilized.

The SPACE testbed utilizes an actuated laser

platform to demonstrate accomplishment of the

precision pointing and figure maintenance of the

complex structure, (Boussalis, 2005). Previous work

has shown the achievement of 1 micron RMS figure

maintenance of the segmented reflector. To

accomplish this requirement, a decentralized H-

infinity controller has been developed, (Morales et

al., 1999), and (Lim, 2011). To achieve the pointing

595

U. Diaz E., Zarate G., Boussalis H. and Rad K..

Mechanical Modeling of an Actuated Platform for Precision Pointing Control - Via Finite-element Analysis and Normal Mode Analysis.

DOI: 10.5220/0004030305950599

In Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2012), pages 595-599

ISBN: 978-989-8565-21-1

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

of the SPACE testbed with accuracy of 2 arc

seconds, the team is investigating the use of the

already established controllers (Morales et al.,

1999), (Lim, 2011). To utilize the existing control

law, first, the actuated laser platform is modeled

using finite element techniques.

2 BACKGROUND

2.1 SPACE Testbed

The SPACE testbed shown in Fig. 1 emulates a

Cassegrain telescope of 2.4-meter focal length with

performance comparable to an actual space-borne

system. The system's top-level requirements include

figure maintenance of the primary mirror to within 1

micron RMS distortion with respect to a nominal

shape of the primary mirror, and precision pointing

with accuracy of 2 arc seconds, (Boussalis et al.,

1996), (Boussalis, 2005), (Desai et al., 2011).

Figure 1: SPACE Testbed.

The SPACE testbed consists of a primary mirror,

a secondary mirror and a lightweight flexible truss

structure. The primary mirror (mounted on the

support truss) consists of seven hexagonal panels,

each 101 cm in diameter. The six peripheral panels

are actively controlled in the three degrees-of-

freedom by 18 linear electromagnetic actuators (3

actuators per active panel), and the seventh panel is

used as a reference. A set of 18 edge sensors are

used to provide measurements of relative

displacement and angle of the panels (3 sensors per

active panel). The Testbed’s active secondary mirror

is a six-sided pyramidal mirror used to reflect the

light from the primary mirror to the central plane

and is attached to the primary by a tripod. The entire

Testbed is supported by a triangular isolation

platform made of aluminum honeycomb core with

stainless steel top and bottom skin, (Morales, 2001).

2.1.1 Figure Maintenance

Unlike a monolithic primary mirror, a segmented

reflector, such as the JWST or the SPACE testbed,

requires an active control system to maintain the

desired optical performance. Active control of the

Testbed reflector panels was achieved using a set of

decentralized H-infinity controllers. Fig. 2 shows the

closed loop response results, (Morales et al., 1999),

using this control scheme under decentralized

control. It is anticipated that system model being

developed will allow the development of a new H-

infinity controller for pointing precision that can be

incorporated with the current figure maintenance

controller as a 7

local subcontroller to demonstrate

both figure maintenance and pointing precision

simultaneously.

It is evident that figure maintenance is achieved

using the decentralized control scheme described in

(Boussalis et al., 1996), (Boussalis, 2002), (Lim,

2011).

Figure 2: Closed loop response.

2.1.2 Peripheral Pointing Architecture

The SPACE telescope testbed is required to perform

precision pointing while maintaining the parabolic

shape of the primary mirror. In order to achieve

precision pointing of the Testbed with accuracy of 2

arc seconds, a Peripheral Pointing Architecture

(PPA) has been designed. The PPA structure is

shown in Fig. 3 (left).

The PPA uses an assembly of six lasers as shown

in Fig. 3 (right) to simulate the object of study. Each

laser corresponds to its own separate panel and

optical detector. The laser assembly sits on a

motorized tip/tilt platform and the laser source

coincides with the rotation, or gimbal, point of the

platform.

Since the laser source lies on the rotation point of

the platform, there is no translation or displacement

ICINCO 2012 - 9th International Conference on Informatics in Control, Automation and Robotics

596

of the source. When the motorized platform is tipped

or tilted, the source is stationary, while only the laser

beams direction are affected.

Using the distance from the platform’s rotation

point to each actuator, (a

and a

for the actuator on

each respective axis), and the actuator displacement,

it is calculated that the platform moves an angle θ

from its zero position on the y-axis. The platform’s

normal vector also moves the same angle θ from the

positive z-axis.

Figure 3: SPACE Testbed PPA Laser Path (left) and

physical assembly (right).

3 FINITE ELEMENT MODEL

DEVELOPMENT

3.1 SolidWorks Model

A geometric model of the PPA is developed using

SolidWorks. The PPA structure is composed of six

lasers, six laser holders, a hexagonal plate, the top

platform, the Newport 37 platform, two Newport

linear actuators, and nine supporting rods.

The PPA is composed of two main parts which

consist of a controllable and a fixed part. The

controllable part is the top half section of the

structure where the actuators push upwards in a

linear fashion and where the Newport 37 platform

has its gimbal point. For simplicity and ease of

computation the fixed part of the PPA structure was

removed. To develop the PPA model, first the model

for each component is developed. The designed

geometry is saved as a parasolid file and imported

into Finite Element Modeling and Post Processing

(FEMAP).

3.2 FEMAP Model

Subsequently, a mesh analysis is performed by

importing the SolidWorks model into FEMAP. The

analysis performed on the model resulted with

250000 nodes and 150000 elements. The minimum

number of nodes and elements achieved while

keeping reasonably accurate results using solid

elements is 146000 nodes and 91000 elements..

In using plate and beam elements, as opposed to

solid elements, the number of nodes and elements of

the model can are reduced significantly. Using plate

elements and increasing the growth ratio and mesh

density the model is reduced to 5795 nodes and 4993

elements.

The PPA model is constrained at three points.

Two points for the linear actuators are constrained in

the x-axis and y-axis for translation and in the x, y,

and z axes for rotation. The gimbal point has a

pinned constraint meaning that it is cannot translate.

4 RESULTS

An initial analysis shows the frequency range for the

first 100 modes ranged from 56.7 Hz to 13.017 kHz

as shown in Fig. 4. A second analysis yielded similar

results, but were truncated to the first 20 modes

(approximately 1 kHz), to reduce the size of the

eventual state-space model, since it was determined

that higher frequencies would not be within the

operational range.

0 10 20 30 40 50 60 70 80 90 100

2000

4000

6000

8000

10000

12000

14000

Mode #

Frequency (Hz)

Frequency vs 100 Modes

Figure 4: Frequency of first 100 modes of platform.

The first group of mode shapes corresponds to

deformations of the laser holders followed by the

deformation of the platform. The deformations of

mode 4 at 126.2326 Hz and mode 10 at 261.7744 Hz

are shown in Fig. 5. This figure shows the

deformations of the laser holders in the first group of

frequencies followed by the more rigid platform at

higher frequencies.

Mechanical Modeling of an Actuated Platform for Precision Pointing Control - Via Finite-element Analysis and Normal

Mode Analysis

597

(a) (b)

Figure 5: Mode 4, 126.23 Hz (a). Mode 10, 261.77 Hz (b).

5 CONTROL DESIGN

Consider the linear time-invariant system given by

the following state equations,







uBAxx



NixCy

,,1, 

(1)

Where

x 

u 

and

y 

represent

the state, input and output respectively of the ith

local control station. A, B

and C

are real, constant

matrices. The results of the modal analysis are used

to determine the matrices A, B

and C

that will

describe the dynamics of the PPA structure.

For decentralized control, it is necessary to

determine n local feedback control laws that will

dynamically compensate for (1) in order to stabilize

the control loop, generating the following feedback

controllers:

iiii

yGzFz 



NivyKzHu

iiiiii

,,1, 

(2)

where

z 

and

v 

are the ith

subcontroller and local external input and F

, G

, H

and K

are real, constant matrices. The standard two-

block mixed-sensitivity H-infinity technique,

(Morales et al., 1999), will be applied to accomplish

a pointing accuracy of 2 arc seconds to the final

reduced and validated state-space model.

6 CONCLUSIONS

An FEA model of an actuated laser platform used

for pointing control of a segmented telescope testbed

is developed. Modal analysis is performed on the

FEA model which calculates the natural frequencies,

mode shapes, degrees of freedom, and eigenvalues

of the structure. Further research is to be undertaken

to define which nodes are desirable and which nodes

are unnecessary in order to be able to perform

Guyan Reduction to reduce the size of the model for

practical implementation. The process described

here streamlines the process of modeling a

motorized platform from mechanical model (CAD,

SolidWorks, etc) to a preliminary, albeit enormous,

state-space model for the implementation of

controllers.

REFERENCES

H. S. Stockman, 1997. “The Next Generation Space

Telescope Visiting a Time When Galaxies Were

Young”.

H. Boussalis, Z. Wei, and M. Mirmirani, 1995. “Dynamic

Performance Modeling and Decentralization of A

Segmented Reflector Telescope,” IASTED Conference

on Modeling and Simulation, Mexico.

H. Boussalis, 1994. “Decentralization of Large

Spaceborne Telescopes”, Proc. 1994 SPIE Symposium

on Astronomical Telescopes, Hawaii.

H. Boussalis, M. Mirmirani, A. Chassiakos, K. Rad, 1996.

“The Use of Decentralized Control in Design of a

Large Segmented Space Reflector”, Control and

Structures Research Laboratory, California State

University, Los Angeles, Final Report.

H. Boussalis, 2002. “The Use of Decentralized Control in

Design of A Large Segmented Space Reflector”,

Structure Pointing and Control Laboratory, California

State University, Los Angeles, Final Technical Report.

H. Boussalis, K. Rad, A. Khosafian, Y. Komandyan, 2005.

“Pointing Control Testbed for Segmented Reflectors”.

A. Desai, J. Alvarenga, H. Tarsaria, K. Rad, H. Boussalis,

2011. “Ray Tracing Visualization Using LabVIEW

for Precision Pointing Architecture of a Segmented

Reflector Testbed,” MED 2011, Corfu, Greece.

M. J. Morales, 2001. “Design and modeling of the SPACE

Tesbted,” M.S. Thesis, Department of Electrical

Engineering, California State University, Los Angeles,

Los Angeles, CA, USA.

M.J. Morales, M. Mirmirani, H. Boussalis, 1999. “Design,

Simulation & Control of a Segmented Reflector Test-

bed,” MED 1999, Haifa, Israel.

K. Lim, 2011. “Modelling and Overlapping Decentralized

Control of a Large Segmented Telescope Test-Bed,”

PhD Dissertation, University of Southern California,

Los Angeles, CA, USA.

K. J. Bathe, and E. L. Wilson, 1976. Numerical Methods

in Finite Element Analysis, 2nd Ed., John Wiley and

Sons.

C. H. Ih, H. C. Briggs, S. J. Wang, 1990. “3D Dynamic

Modeling and Simulation of a Precision Segmented

Reflector Telescope”, Proceedings of the 21st Annual

Pittsburgh Conference.

H. Ryaciotaki-Boussalis, H. C. Briggs, and C. H. Ih, 1991.

“Dynamic Performance Modeling and Stability

Analysis of a Segmented Reflector Telescope,”

Proceedings of the 1991 Automatic Control

Conference.

ICINCO 2012 - 9th International Conference on Informatics in Control, Automation and Robotics

598

A. C. Carrier, 1990. “Modeling and Shape control of a

Segmented-Mirror Telescope,” Ph.D. dissertation,

Dept. Aeronautics and Astronautics, Stanford Univ.,

Stanford, CA.

R. D. Cook, 1981. Concepts and Applications in Finite

Element Analysis, 2nd Ed., John Wiley and Sons.

R. Bishop, and D. C. Johnson, 1981. The Mechanics of

Vibration, Cambridge University Press.

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Mode Analysis

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