G. Foutsitzi

Design and robust optimal control of smart beams with application on vibrations suppression

This paper presents the design of a vibration control mechanism for a beam with bonded piezoelectric sensors and actuators and an application of the arising smart structure for vibrations suppression. The mechanical modeling of the structure and the subsequent finite element approximation are based on Hamiltons principle and classical engineering theory for bending of beams in connection with simplified modeling of piezoelectric sensors and actuators. Two control schemes LQR and H2 are considered. The latter robust controller takes into account uncertainties of the dynamical system and moreover incompleteness of the measured information, it therefore leads to applicable design of smart structures. The numerical simulation shows that sufficient vibration suppression can be achieved by means of the proposed general methods.

Robust H/sub 2/ vibration control of beams with piezoelectric sensors and actuators

This paper studies vibration control of a beam with bonded piezoelectric sensors and actuators. Basic equations for piezoelectric sensors and actuators are presented. The equation of motion for the beam structure is derived by using the Hamiltons principle. A robust H/sub 2/ controller is designed. The numerical simulation shows that the vibration can be significantly suppressed by the proposed controller.

Fine tuning of a fuzzy controller for vibration suppression of smart plates using genetic algorithms

Piezoelectric sensors and actuators are used for vibration control and suppression of a smart composite plate. In the present paper, the vibration suppression of smart structures using intelligent control strategy is considered. A smart plate described by Mindlin plate theory is used in the finite element modeling of laminates with piezoelectric layers. The control is based on a set of fuzzy rules that combine the membership functions of the system variables by using fuzzy inference techniques. A genetic algorithm is used in order to optimize the parameters of the fuzzy controller. The numerical results indicate that the problem statement is successful and the proposed method is very efficient. In addition, the results obtained are very satisfactory compared to previous investigations of our team. All implementations are built and tested within MATLAB environment.

A Multi-layer Piezocomposite Model and Application on Controlled Smart Structures

In smart structural applications, multi-layered piezocomposite plates are very common for the study of active control applications. In this paper a finite element formulation is presented to model the static and dynamic response of laminated composite plates containing integrated piezoelectric sensors and actuators subjected to electrical and mechanical loadings. The formulation is based on a third order shear deformation theory and Hamilton’s principle. A nine-noded \(C^0\) plate element is implemented for the analysis. The element was developed to include stiffness and the electromechanical coupling of the piezoelectric sensor/actuator layers. The electric potential is assumed to vary linearly through the thickness for each piezoelectric sublayer. The model is validated by comparing with existing results documented in the literature. A displacement and optimal LQR control algorithm is used for the active control of the static deflection and of the dynamic response of the plates with surface bonded piezoelectric sensors and actuators layers or patches. The main aspects of the application of the present model are discussed through a set of numerical examples.

OPTIMAL CONTROL TUNNING IN SMART STRUCTURES WITH DELAMINATIONS

Abstract. An efficient strategy for calculation of delaminations in composite beams and intelligent structures is used in order to quantify structural uncertainties within a finite element model of a piezocomposite (multilayered plate theory). Furthermore the dynamical system is connected with robust and neurofuzzy control. The problem of positioning of actuators and sensors has been investigated. Model based simulations of increasing complexity illustrate some of the attractive features of the strategy in terms of accuracy as well as computational cost. This shows the possibility of using such strategies for the development of smart structural and systems.

Optimization of Design Parameters for Active Control of Smart Piezoelectric Structures

The objective of this work is to design an optimal controller for plate structures to control their response under the influence of external excitation. The finite element method based on the Mindlin–Reissner plate theory has been extended to incorporate the piezoelectric effects. A genetic algorithm is applied to find the optimal placement of piezoelectric actuators and input voltages for static shape control. The objective function is the error in transverse displacements between the desired and the achieved shape.In addition, the optimal placement of actuators and sensors for vibration control of laminated plates is studied. The objective taken into consideration is the controllability index, which is the singular value decomposition of a control matrix as can be found at the bibliography. The index measures the input energy required to achieve the desired structural control using piezoelectric actuators.Finally, the linear quadratic regulator (LQR) closed loop control is applied to study the control effectiveness. A comparison is made between the optimal locations of piezoactuators obtained through controllability index and a nonoptimal case.

ROBUST CONTROL OF SMART STRUCTURES WITH OPTIMALLY PLACED ACTUATORS AND SENSORS

The objective of this work is to design robust controller for smart structures to control its response under the influence of external excitation. An accurate model for the analysis of smart composite beams with surface bonded piezoelectric sensors and actuators patches is considered. Optimal placement of five piezoelectric sensor/actuator pairs are found, by exhaustively examining all possible configurations in order to suppress the first six modes of vibration. The LQR performance index is used as objective function to locate the sensor/actuator pairs. Vibration reduction for the cantilever beam with piezoelectric patches bonded in the optimal location was investigated to attenuate the first six modes of vibration using a Hinfinity scheme. After modeling multiplicative uncertainty, the augmented uncertain plant is obtained; an optimal robust controller is designed using Hinfinity. A robust controller is designed based on the augmented plant composed of the nominal model and it’s accompanied uncertain. Robust and nominal performances of designed controllers are achieved for perturbed plants and results were compared.