This work presents a tracking control model for a flexible nonprismatic link robotic manipulator using simultaneously motor torques and piezoelectric actuators. The dynamic model of the flexible manipulator is obtained in a closed form through the Lagrange equations. 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 controlling vibrations with frequencies beyond the reach of motor torque control. The naturals frequencies are calculated by the finite element method, and the approximated eigenfunctions are interpolated by polynomials. Three eigenfunctions are used for the dynamics of the arm, while only two are used for the control. Numerical experiments on Matlab/Simulink are used to verify the efficiency of the control model. Copyright © 2009 M. Schellmann and V. Jungnickel.
Bottega, V., Molter, A., Fonseca, J. S. O., & Pergher, R. (2009). Vibration control of manipulators with flexible nonprismatic links using piezoelectric actuators and sensors. Mathematical Problems in Engineering, 2009. https://doi.org/10.1155/2009/727385