Jun Sérgio Ono Fonseca

This paper presents a topology optimization methodology of piezoelectric actuators in laminated composite structures. The Linear Quadratic Regulator (LQR) optimal control technique is used. The topology optimization is formulated to find the optimum localization of the Macro Fiber Composite (MFC), through of the maximization of the controllability index. Actuator location optimization results show that the technique implemented improves the structural vibration damping.

Este trabalho busca desenvolver uma metodologia de projeto ótimo para localização de material piezelétrico com efeito cisalhante para atenuar vibrações em estruturas tridimensionais. O objetivo é determinar a localização ótima de atuadores através do processo de otimização topológica. A localização dos atuadores é determinada por uma otimização que define onde o material deve ter propriedades piezelétricas; através da maximização da controlabilidade, medida por seu gramiano. Resultados preliminares mostram a eficácia do processo de otimização topológica quanto à localização dos atuadores na estrutura.

This work presents a new methodology for the parametric optimization of piezoelectric actuators installed in laminated composite structures, with the objective of controlling structural vibrations. Problem formulation is the optimum location of a Macro Fiber Composite (MFC) actuator patch by means the maximization of the controllability index. The control strategy is based on a Linear Quadratic Regulator (LQR) approach. For the structural analysis, the modeling of the interaction between the MFC and the structure is made taking into account the active material as one of the orthotropic laminate shell layers. The actuation itself is modeled as an initial strain arising from the application of an electric potential which deforms the rest of the structure. Thereby, modeling the electric field and the electromechanical coupling within the actuator is avoided because these effects are considered analytically. Numerical simulations show that the structural model presents good agreement with numerical and experimental results. Furthermore, the results show that optimizing the location of the actuator in the structure helps the control algorithm to reduce induced structural vibration.

This paper presents a control design for flexible manipulators using piezoelectric actuators bonded on nonprismatic links. The dynamic model of the manipulator is obtained in a closed form through the Lagrange equations. Each link is discretized using finite element modal formulation based on Euler‐Bernoulli beam theory. The control uses the motor torques and piezoelectric actuators for controlling vibrations. An optimization problem with genetic algorithm (GA) is formulated for the location and size of the piezoelectric actuator and sensor on the links. The natural frequencies and mode shapes are computed by the finite element method, and the irregular beam geometry is approximated by piecewise prismatic elements. The State‐Dependent Riccati Equation (SDRE) technique is used to derive a suboptimal controller for a robot control problem. A state‐dependent equation is solved at each new point obtained for the variables from the problem, along the trajectory to obtain a nonlinear feedback controller. Numerical tests verify the efficiency of the proposed optimization and control design.