MANJUNATH and BANDYOPADHYAY: DESIGN OF MULTIVARIABLE POF CONTROLLER I.J. of SIMULATION Vol. 7 No. 9 ISSN 1473-804x online, 1473-8031 print 49 DESIGN OF MULTIVARIABLE POF CONTROLLER FOR SMART COMPOSITE BEAM USING EMBEDDED SHEAR SENSORS AND ACTUATORS T.C. MANJUNATH, B. BANDYOPADHYAY Interdisciplinary Programme in Systems & Control Engineering, 101 B, ACRE Building, Indian Institute of Technlogy Bombay, Powai, Mumbai - 400076, Maharashtra, India. Email : tcmanju@sc.iitb.ac.in ; bijnan@ee.iitb.ac.in URL : http://www.sc.iitb.ac.in/~tcmanju ; http://www.sc.iitb.ac.in/~bijnan Phone : +91 22 25767884 ; +91 22 25767889 ; Fax : +91 22 25720057 Abstract: In this paper, the modelling and design of a multivariable controller for a smart thick composite cantilever beam with embedded shear sensors and actuators is investigated. The first 3 dominant vibratory modes are retained in the modelling of the composite beam. The beam is divided into 8 finite elements and shear piezoelectric patches are embedded into the master structure. These shear piezoelectric patches serve as sensors and actuators at 2 finite element locations to obtain a multivariable system with 2 inputs and 2 outputs. The beam is subjected to an external disturbance at the free end. The vibrations are damped out quickly when the POF controller is put in a feedback loop with the beam. The effect of placing the non-collocated sensor / actuator pairs at 2 finite element locations in between the two beam layers is observed and the conclusions are drawn. The closed loop responses with the output feedback gain were found to be satisfactory. Shear and axial displacements, neglected in the classical Euler-Bernoulli beam theory are considered in this research to produce an accurate beam model. Keywords : Smart structure, Timoshenko, POF, FEM, State space model, vibration control, LMI. 1. INTRODUCTION Smart materials and smart structures, often called as the intelligent structures, form a new rapidly growing interdisciplinary technology in the modern day world embracing the fields of materials, structures, sensors and actuators, information and signal processing, electronics and control [Gandhi and Thompson, 1992]. A smart structure incorporates distributed actuators and sensors and has the data processing and power conditioning capabilities. Also, it has the capability to respond to a changing external environment (such as loads and shape changes) as well as to a changing internal environment (such as damage or failure). Smart structures involve the synergism of intelligent materials with embedded or surface mounted sensors whose information is collected, processed and controlled by a sophisticated controller, which controls the actuator to perform the corrective action. Recent advances in smart structure technology provide [Chopra, 2002] a means for integrating sensors and actuators into the structure and make them self-adapting, self-controlling, and intelligent in various types of mechanical, flexible and rigid engineering structures. These include aerospace applications, civil engineering applications, robotics, bio-technology, MEMS and NEMS. The need for such intelligent structures called smart structures [Culshaw, 1992] arises because of their high performance in numerous structural applications. Such intelligent structures incorporate smart materials called actuators and sensors (based on Piezoelectrics, MR Fluids, Piezo-ceramics, ER Fluids, SMA, PVDF, Optical fibres, etc.) that are embedded into the structure. They have structural functionality with highly integrated control logic, signal conditioning, and power amplification electronics. These materials can be used to generate a secondary vibrational response in a mechanical system. This secondary response has the potential to reduce the overall response of the system by the destructive interference with the original response of the system, caused by the primary source of vibration [Herman, 1994]. Piezoelectric materials [Rao and Sunar, 1994] are used in our research work as embedded shear sensors and actuators to suppress the structural vibrations. Considerable interest is focused on the modelling, control and implementation of smart structures using the Euler-Bernoulli beam theory and the Timoshenko beam theory with integrated piezoelectric layers in the recent past. The assumption made in the Euler Bernoulli beam theory is that plane cross sections of the beam remain plane and normal to the neutral axis after deformation.