More and more today, an increasing number of applications of the manipulators demand the capability of larger workspace, more accurate positioning, faster motion, lower power consumption, and great payload. Inevitable flexibility of these manipulators induce bad performance such as a residual vibrations. However the exact model and appropriate control algorithm concerned with the physical meaning of the system properties such as the pole and the zero of the flexible manipulator can improve the performance of the flexible manipulator. The physical meaning of the pole has been explained in numerous researches. but the physical explanation of the zero is relatively insufficient. Therefore the physical interpretation of the zeros is an important issue for the control of a flexible manipulator. This paper present the physical interpretation of the real axis zero of the flexible manipulator and suggest some applications of this real axis zero.
To obtain the transfer function of the 1 link flexible manipulator without approximations, the exact solution of Euler-Bernoulli beam equation is solved including boundary conditions. It is well kwon that the non-collocation of the sensor and the actuator causes the real axis symmetry zero in flexible manipulator. Furthermore, the value of the real zero is not depend on the boundary condition elements of the joint and the linear boundary condition elements of the end point but can be changed by the rotational boundary condition element of the end point. The meaning of the real axis zero is physically explained in terms of the stored energy, the time delay, and the resistant forces in the end point, respectively. For the expansion to the multi-link flexible manipulator, Passive 2 link flexible manipulator is modeled exactly and the zero behavior is presented. Finally it is proposed the stop motion algorithm for the flexible manipulator. The physical meaning of the zero is applied to this algorithm, and the performance is more improved than the conventional PD control in stop motion.