Optimal placement of piezoelectric actuators using synthetic modal control force
YANG Yi-ling1, LOU Jun-qiang2, WEI Yan-ding1, FU Lei1, TIAN Geng1, ZHAO Xiao-wei1
1. Institute of Manufacturing Engineering, Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, Zhejiang University, Hangzhou 310027, China;2. College of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, China
This paper dealt with the optimal placement of actuators in smart flexible structures. Based on the analysis of dynamic equations and state space equations of flexible structures, the modal theory was adopted and the singular value decomposition of control matrices was employed. Then, a criterion of the maximum synthetic modal control force was proposed. The criterion involved the effect of reserved and residual modes to the modal control force. Meanwhile, modal weights were considered. Finally, a flexible beam with piezoelectric actuators/strain sensors was chosen as an example, theoretical calculations and the improved genetic algorithm were used for the optimal analysis. Thus, the optimal positions of piezoelectric actuators with maximum synthetic modal control force were found, and an experimental system was set up to verify the proposed method. The experimental results demonstrate that the system has a good synthetic modal control force and control effect by using the optimal placement result of actuators. The proposed evaluation criterion and optimal method is feasible.
YANG Yi-ling, LOU Jun-qiang, WEI Yan-ding, FU Lei, TIAN Geng, ZHAO Xiao-wei. Optimal placement of piezoelectric actuators using synthetic modal control force. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2015, 49(5): 841-847.
［1］ RAMOS F, FELIU V, PAYO I. Design of trajectories with physical constraints for very lightweight single link flexible arms ［J］. Journal of Vibration and Control, 2008, 14(8): 1091-1110．
［2］ 朱灯林, 吕蕊, 俞洁. 压电智能悬臂梁的压电片位置、尺寸及控制融合优化设计［J］. 机械工程学报, 2009,45(2): 262-267．
ZHU Deng-lin, LV Rui, YU Jie. Integrated optimal design of the PZT position, size and control of smart cantilever beam ［J］.Chinese Journal of Mechanical Engineering, 2009, 45(2): 262-267．
［3］ 魏燕定, 娄军强, 吕永桂, 等. 振动主动控制中性二次型最优控制问题研究［J］. 浙江大学学报：工学版,2009, 43(3): 420-424．
WEI Yan-ding, LOU Jun-qiang, LV Yong-gui, et al. Research on linear quadratic optimal control problem in active vibration control ［J］. Journal of Zhejiang University: Engineering Science, 2009, 43(3): 420-424．
［4］ HU Q L, MA G F. Vibration control of flexible spacecraft actuated by piezoceramics via variable structure strategy ［J］. Journal of Harbin Institute of Technology, 2007, 14(5): 604-608．
［5］ DUTTA R, GANGULI R, MANI V. Swarm intelligence algorithms for integrated optimization of piezoelectric actuator and sensor placement and feedback gains ［J］. Smart Materials & Structures,2011, 20(10501810): 114．
［6］ GURSES K, BUCKHAM B J, PARK E J. Vibration control of a single-link flexible manipulator using an array of fiber optic curvature sensors and PZT actuators ［J］. Mechatronics, 2009, 19(2): 167-177．
［7］ 钱锋, 王建国, 汪权, 等. 基于模态应变能分布的压电致动器/传感器位置优化遗传算法［J］. 振动与冲击, 2013,32(11): 161-166．
QIAN Feng, WANG Jian-guo, WANG Quan, et al. Optimal placement of piezoelectric actuator/sensor using genetic algorithm based on modal strain energy distribution［J］. Journal of Vibration and Shock, 2013, 32(11):161-166．
［8］ LINDBERG R E, LONGMAN R W. On the number and placement of actuators for independent model space control ［J］. Journal of Guidance, Control, and Dynamics, 1984, 7(2): 215-221．
［9］ AMBROSIO P,RESTA F, RIPAMONTI F. An H2 norm approach for the actuator and sensor placement in vibration control of a smart structure ［J］. Smart Materials and Structures, 2012, 21(12): 125016．
［10］ 邱志成. 挠性板振动抑制的敏感器与驱动器优化配置［J］. 宇航学报, 2002,23(4): 30-36．
QIU Zhi-cheng. Optimal placement of sensors and actuators for flexible plate of vibration suppression［J］. Journal of Astronautics, 2002, 23(4): 30-36．
［11］ BRUANT I, PROSLIER L. Optimal location of actuators and sensors in active vibration control ［J］. Journal of Intelligent Material Systems and Structures, 2005, 16(3): 197-206．
［12］ NESTOROVIC T, TRAJKOV M. Optimal actuator and sensor placement based on balanced reduced models ［J］. Mechanical Systems and Signal Processing, 2013, 36(2): 271-289．
［13］ SUN D, MILLS J K, SHAN J, et al. A PZT actuator control of a single-link flexible manipulator based on linear velocity feedback and actuator placement ［J］. Mechatronics, 2004, 14(4): 381-401．
［14］ WANG Q, WANG C M. A controllability index for optimal design of piezoelectric actuators in vibration control of beam structures ［J］. Journal of Sound and Vibration, 2001, 242(3): 507-518．
［15］ BIGLAR M, MIRDAMADI H R, DANESH M. Optimal locations and orientations of piezoelectric transducers on cylindrical shell based on gramians of contributed and undesired Rayleigh-Ritz modes using genetic algorithm ［J］. Journal of Sound and Vibration, 2014, 333(5): 1224-1244．
［16］ SRINIVAS M, PATNAIK L M. Adaptive probabilities of crossover and mutation in genetic algorithms ［J］. Systems, Man and Cybernetics, 1994, 24(4): 656-667．
