Optimization of piezoelectric actuators for manipulators with flexible non-prismatic links

1. Abstract This work presents a tracking control model for a flexible robotic manipulator using motor torques and piezoelectric actuators. The dynamic model of the flexible manipulator is obtained in a closed form through the Lagrange Eq.s. The control uses the motor torques for the joints tracking control and also to reduce the low frequency vibration induced in the manipulator links. The stability of this control is guaranteed by the Lyapunov stability theory. Piezoelectric actuators and sensors are added for vibrations with frequencies beyond the reach of motor torque control. Robots' flexible links are built in complex geometries, which cannot be modeled by simple beam bending Eq.s. In this work we propose a methodology for accounting the complex geometry within the realm of the Euler-Bernoulli beam theory. The natural frequencies are calculated by the finite element method and the approximated eigenfunctions are interpolated by polynomials. Three mdes are used for the dynamics of the arm, while only two modes are used for the control. Additionally, this work introduces a formulation for simultaneous optimization of control and actuators and sensors through of dissipated energy maximization in the system by the control action with location and sizing optimization of piezoelectric actuators and sensors in the structures. Numerical experiments on Matlab/Simulink are used to verify the efficiency of the control model. 2. Keywords: Piezoelectric actuators, flexible links, tracking control, optimization, manipulators.