Study of system parameters and control design for a flexible manipulator using piezoelectric transducers

In this paper, a nonlinear control scheme is presented to achieve small tracking errors in a flexible manipulator with two degrees of freedom. A secondary actuation mechanism using piezoelectric materials is added to the system for suppressing residual vibrations at the end point of the flexible link. A small piece of piezo-ceramic is also used, as a sensor, in order to obtain the modal states of the system. The effects of changing physical parameters such as relative thickness of the piezo-ceramic with respect to the flexible link, the optimum location and the length of the actuator are studied based on the singular value decomposition of the controllability Grammian of the system. A partial feedback linearization technique based on output redefinition is utilized to obtain an appropriate control output for each joint and the piezoelectric actuator. A model for friction is obtained and included in the control law. Experimental results show that applying the suggested control scheme results in smooth and precise motion of the flexible manipulator without exciting unwanted vibration modes. Comparisons are made when a linear control scheme is used for the tracking problem.