To improve the shape accuracy of the antenna reflector, the mechanical modeling method and the shape control method for a reflector driven by the piezoelectric ceramic transducer (PZT) are studied. An integrated finite element model for the reflector structure and the PZT actuator is established. The influence coefficient matrix method is used to develop an optimization model for active shape control of the reflector with the objective of minimizing the mean square root error of the shape, and the optimal control laws of the actuator are solved by the least square method. An active shape control experimental system of the reflector is built, and the rotating paraboloid is taken as the target shape. Experimental results demonstrate that the shape accuracy of the reflector after active control is improved by nearly 50%, which are in good agreement with simulation results, and verifies the validity of the modeling method and feasibility of the control method.
SONG Xiangshuai
,
WANG Enmei
,
MU Ruinan
,
TAN Shujun
,
LAN Lan
. Active shape control of a reflector with PZT actuators assembled on ribs[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018
, 39(6)
: 221541
-221541
.
DOI: 10.7527/S1000-6893.2018.21541
[1] LANG M, BAIER H, ERNST T. Surface accuracy prediction and optimization of a high precision Q/V-band reflector:AIAA-2006-2216[R]. Reston, VA:AIAA, 2006.
[2] STEEVES J, PELLEGRINO S. Ultra-thin highly deformable composite mirrors:AIAA-2013-1523[R]. Reston, VA:AIAA, 2013.
[3] FANG H F, HUANG P M, ZHOU Y, et al. Analytical investigation of a high precision reflector:AIAA-2014-1508[R]. Reston, VA:AIAA, 2014.
[4] TANAKA H. Surface error estimation and correction of a space antenna based on antenna gain analyses[J]. Acta Astronautica, 2011, 68(7):1062-1069.
[5] SANTIAGO P J, BAIER H. Advances in deployable structures and surfaces for large apertures in space[J]. CEAS Space Journal, 2013, 5(3-4):89-115.
[6] CHEN P C, OLIVERSEN R J,ROMEO R C. Fabrication and testing of ultra-lightweight Gossamer-class composite mirrors[C]//Highly Innovative Space Telescope Concepts. Bellingham, WA:SPIE, 2002:339-347.
[7] EALEY M A, WELLMAN J A. Highly adaptive integrated meniscus primary mirrors[C]//UV/Optical/IR Space Telescopes:Innovative Technologies and Concepts.Bellingham, WA:SPIE, 2004:165-171.
[8] 黄志荣, 宋燕平. 型面可调整反射器结构与调整技术概述[J]. 空间电子技术, 2010, 7(3):84-89. HUANG Z R, SONG Y P. A review on the structure and adjustment technology of an adjustable reflector[J]. Space Electronic Technology, 2010, 7(3):84-89(in Chinese).
[9] CHOPRA I. Review of state of art of smart structures and integrated systems[J]. AIAA Journal, 2002, 40(11):2145-2187.
[10] SCHRÖCK J, MEURER T, KUGI A. Motion planning for piezo-actuated flexible structures:Modeling, design, and experiment[J]. IEEE Transactions on Control Systems Technology, 2012, 21(3):807-819.
[11] LAN L, JIANG S, ZHOU Y, et al. Geometry adaptive control of a composite reflector using PZT actuator[C]//Industrial and Commercial Applications of Smart Structures Technologies. Bellingham, WA:SPIE, 2015:943305.
[12] LAN L, JIANG S, ZHOU Y, et al. Shape control of a reflector based on generalized zernike functions:AIAA-2016-0704[R]. Reston, VA:AIAA, 2016.
[13] BRADFORD S C, AGNES G S, OHARA C M, et al. Piezocomposite actuator arrays for correcting and controlling wavefront error in reflectors:AIAA-2012-1743[R]. Reston, VA:AIAA, 2012.
[14] BADFORD S C, WILKIE W K, AGNES G S, et al. Controlling wavefront in lightweight reflector systems using piezocomposite actuator arrays:AIAA-2013-1525[R]. Reston, VA:AIAA, 2013.
[15] FANG H, PATTOM M, WANG K W, et al. Shape control of large membrane reflector with PVDF actuation:AIAA-2007-1842[R]. Reston, VA:AIAA, 2007.
[16] 曹玉岩, 王志, 周超, 等. 压电智能反射面静态形状控制与作动器位置优化[J]. 航空学报, 2015, 36(2):527-537. CAO Y Y, WANG Z, ZHOU C, et al. Static shape control of piezoelectric smart reflector and optimization of actuators' placement[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(2):527-537(in Chinese).
[17] ABUSAFIEH A A, FEDERICO D R, CONNELL S J, et al. Dimensional stability of CFRP composites for space-based reflectors[C]//Optomechanical Design and Engineering. Bellingham, WA:SPIE,2001:9-16.
[18] 董兴建, 孟光. 压电结构的热弹性比拟建模方法[J]. 应用力学学报, 2005, 22(3):346-350. DONG X J, MENG G. Thermal elastic analogy modeling method for piezoelectric structures[J]. Chinese Journal of Applied Mechanics, 2005, 22(3):346-350(in Chinese).
[19] 李敏, 陈伟民, 王明春, 等. 压电驱动的载荷比拟方法[J]. 中国科学(E辑:技术科学), 2009, 39(11):1810-1817. LI M, CHEN W M, WANG M C, et al. A load simulation method of piezoelectric actuator in FEM for smart structures[J]. Science in China (Series E:Technological Sciences), 2009, 39(11):1810-1817(in Chinese).
[20] ALLIK H, HUGHES T J R. Finite element method for piezoelectric vibration[J]. International Journal for Numerical Methods in Engineering, 1970, 2(2):151-157.
CJA