DESIGN, MODELING, AND OPTIMIZATION OF A MECHANICALLY RECONFIGURABLE SMART REFLECTOR ANTENNA SYSTEM DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Hwan-Sik Yoon, M.S. * * * * * The Ohio State University 2002 Dissertation Committee: Approved by Dr. Gregory Washington, Adviser Dr. Giorgio Rizzoni _____________________________ Dr. Roberto Rojas Adviser Department of Mechanical Engineering ABSTRACT In this research, a new design and operation methodology of a reconfigurable dual offset contour beam reflector antenna (DCBRA) using a mechanically adjustable subreflector is presented. Based on the Cassegrain configuration, the fixed main reflector with a diameter of 1.25m is shaped for the continental U.S. (CONUS) beam pattern and the smaller subreflector is initially set up to have a hyperboloidal cut shape with an elliptical aperture of 30 cm by 70 cm. The subreflector is made with a thin flexible material such that it deforms by movement of a certain number of linear point actuators attached on the back surface. With the deformable subreflector, the electromagnetic field illuminating the main reflector can be changed leading to a different far-field radiation pattern. For the analysis, the finite element method (FEM) is applied to calculate the deformed shape of the subreflector from a given configuration and movement of actuators. The actuators are modeled as boundary condition and then the linear matrix equation is solved using LU decomposition technique. For the calculation of radiation pattern, Physical Optics (PO) is utilized for both the main reflector and the subreflector: PO-PO. After two separate codes are completed, a unified computation tool is developed by incorporating the PO-PO routine into the FEM code. ii For optimal and minimal usage of the actuators, two independent optimization problems are solved: Optimization of actuator placement and optimization of actuation values. Several actuator placement optimization techniques are proposed and implemented in the code. After actuator positions are determined, the optimal actuation value of each actuator needs to be determined. The objective function is defined as the sum of the squared error between the actual antenna gain and the desired gain at each point falling inside of a geometrical boundary in the u-v space. When implemented, it was observed that the Cyclic Coordinate Search method performs the best. Finally, as an example, generation of contour beams for four different geographic regions – CONUS, Australia, Brazil, and Afghanistan – is presented. The effect and result of various actuator placement optimization techniques are also presented and discussed. iii DEDICATION Dedicated to my parents for their love and support throughout my life iv ACKNOWLEDGMENTS I would first like to thank my advisor, Dr. Gregory Washington for his continuous support, patience, and guidance throughout this work. I would also like to thank Dr. Giorgio Rizzoni and Dr. Roberto Rojas for taking time out to participate in my dissertation committee. I would like to give a special thank to Dr. Wilhelmus Theunissen and Dr. Walter D. Burnside for helping me understand electrical aspects of antenna systems and allowing me to use their electromagnetic simulation code. I thank my fellow graduate students, Matthew Detrick and Peter Eyabi, for all their help and assistance during this research. I also thank all Korean students in Mechanical Engineering department at the Ohio State University for their advice and help. Finally, I would like to thank my family especially my wife whose continuous love and support made it possible for me to study abroad. v VITA February 24, 1971..............................Born – Seoul, Korea 1994...................................................B.S. Physics Education, Seoul National University, Seoul, Korea 1998...................................................M.S. Mechanical Engineering, The Ohio State University 1999 - present....................................Graduate Research Associate, The Ohio State University PUBLICATIONS Journal Publications 1. Yoon H.-S. and Washington G. N., 1998, “Piezoceramic Actuated Aperture Antennas,” Journal of Smart Materials and Structures, 7, pp.537-542 2. Theunissen W. H., Yoon H.-S., Washington G. N. and Burnside W. D., 1999, “Reconfigurable Contour Beam Reflector Antenna using an Adjustable Subreflector and an Adjustable Feed,” Microwave and Optical Technology Letters, 21(6), pp. 436- 446. 3. Yoon H.-S. and Washington G. N., 2000, “Modeling, Design and Zero Gravity Testing of a Doubly Curved Aperture Antenna,” Journal of Intelligent Material Systems and Structures, 10(2), pp. 141-148. 4. Yoon H.-S. and Washington G. N. and Theunissen, W. H., 2000, “Analysis and Design of Doubly Curved Piezoelectric Strip-Actuated Aperture Antennas,” IEEE Transaction on Antennas and Propagation, 48(5), pp. 755-763. vi 5. Theunissen, W. H., Yoon H.-S., Burnside, W. D., and Washington G. N., 2001, “Reconfigurable Contour Beam-Reflector Antenna Synthesis Using a Mechanical Finite-Element Description of the Adjustable Surface,” IEEE Transaction on Antennas and Propagation, 49(2), pp. 272-279. 6. Washington G. N., Yoon, H.-S., Angelino, M., and Theunissen, W. H., 2002, “Design, Modeling and Optimization of Mechanically Reconfigurable Aperture Antennas,” IEEE Transaction on Antennas and Propagation, 50(5), pp. 628-637. 7. Yoon, H.-S. and Washington G. N., 2002, “A Study on Shape Control of a Deformable Structure with an Application to a Mechanically Reconfigurable Reflector Antenna,” (Submitted to Journal of Spacecraft and Rockets) 8. Yoon, H.-S. and Washington G. N., 2002, “Modeling and Optimization of a Mechanically Reconfigurable Reflector,” (Submitted to IEE Proceedings Microwaves, Antennas and Propagation) Conference Presentations 1. Yoon, H. S. and Washington, G. N., 1998, “Piezoceramic Actuated Aperture Antennas,” Proceedings of SPIE Int. Conference on Smart Structures and Materials, 3328. 2. Yoon H. S. and Washington G. N., 1998, “Analysis of Doubly Curved Antenna Structures,” Adaptive Structures and Material Systems Symposium, ASME International Congress and Exposition, 57, pp. 225-229. 3. Theunissen W. H., Yoon H. S., Washington G. N., and Burnside W. D., 1999, “Mechanical Finite Element Diffraction Synthesis of Reconfigurable Contour Beams from Dual Offset Reflector Antennas,” IEEE Antennas and Propagation Society International Symposium, pp. 2348-2351. 4. Yoon, H. S. and Washington G. N., 1999, “Zero G Validation of Smart Aperture Antennas,” ASME International Congress and Exposition, 59, pp.239-243. 5. Yoon, H. S., Washington, G. N., and Theunissen, W. H., 2000, “Reconfigurable Contour beam generation using a Smart Subreflector Antenna System,” Proceedings of SPIE Int. Conference on Smart Structures and Materials. vii FIELDS OF STUDY Major Fields: Mechanical Engineering System Dynamics and Control. Smart Material and Adaptive Structures. viii TABLE OF CONTENTS Page ABSTRACT......................................................................................................................ii DEDICATION..................................................................................................................iv ACKNOWLEDGMENTS...................................................................................................v VITA ..............................................................................................................................vi LIST OF TABLES............................................................................................................xi LIST OF FIGURES..........................................................................................................xii CHAPTERS: 1. INTRODUCTION...................................................................................................1 2. LITERATURE REVIEW........................................................................................7 2.1 Mechanically Reconfigurable Antenna.......................................................7 2.2 Shape Optimization of Mechanical Structures..........................................14 3. ELECTROMAGNETIC SIMULATION OF ANTENNA...................................24 3.1 Geometry of the Offset Dual Reflector Antenna......................................24 3.2 Coordinate Systems of the Dual Reflector Antenna.................................27 3.3 Calculation of Radiation Pattern...............................................................31 3.4 Implementation of the Numerical Calculation..........................................35 4. FINITE ELEMENT ANALYSIS OF SUBREFLECTOR....................................45 4.1 Finite Element Analysis............................................................................45 4.2 Three-Node Triangular Shell Element......................................................46 4.3 In-Plane (Two-Dimensional) Motion........................................................48 4.4 Out-of-plane (Lateral) Deflection.............................................................55 ix 4.5 Composition of the Global Stiffness Matrix (Local to Global Coordinate Transformation).........................................................................................61 4.6 Implementation..........................................................................................63 5. Mathematical Analysis of Shape Optimization.....................................................66 5.1 Shape Optimization Using the Finite Element Method............................66 5.2 Shape Error Minimization.........................................................................71 5.3 Performance Optimization via Shape Optimization..................................73 5.4 Effect of Reduced Number of Actuators (Controlled Nodes)...................80 5.5 Example: One-Dimensional Bar with Three Elements.............................87 6. OPTIMIZATION OF ACTUATION VALUES.................................................108 6.1 Introduction.............................................................................................108 6.2 Multi-Variable Optimization Methods....................................................109 6.3 Cyclic Coordinate Search Method (Univariate Method)........................110 6.4 Conjugate Direction Set Method.............................................................112 6.5 Simulated Annealing Technique.............................................................117 7. OPTIMIZATION OF ACTUATOR PLACEMENT..........................................120 7.1 Introduction.............................................................................................120 7.2 Adding Actuators to Optimal Positions..................................................121 7.3 Removing Actuators From Less Influential Nodes.................................127 7.4 Optimal Repositioning of Actuators.......................................................128 8. RESULTS AND DISCUSSION.........................................................................132 8.1 Introduction.............................................................................................132 8.2 Reflector Shape Error Minimization.......................................................132 8.3 Far-Field Radiation Pattern Optimization...............................................138 9. CONCLUSIONS AND FUTURE WORK.........................................................160 BIBLIOGRAPHY .....................................................................................................163 x