Closed-Loop Behavior of a Feedback-Controlled Flexible Arm: A Comparative Study

Abstract

The dynamics of mechanical systems with distributed flexi bility are described by infinite-dimensional mathematical models. In order to design afinite-dimensional controller, a finite-dimensional model of the system is needed. The con trol problem of a flexible beam is a typical example. The general practice in obtaining a finite-dimensional model is to use modal approximation for distributed flexibility, retain a finite number of modes, and truncate the rest. In this approx imation, the appropriate selection of the mode shape func tions and the number of modes is not clearly known. Mostly standard pinned-free and clamped-free mode shapes are used for the flexible beam model, retaining only two or three modes and truncating the rest. The actual system, on the other hand, is infinite-dimensional, and the modes describing its flexible behavior under feedback control would be neither pinned-free nor clamped-free boundary condition modes. Rather, the mode shapes themselves are a function of the feedback control. The infinite-dimensional transcendental transfer functions for a flexible beam are formulated without any modal ap proximation. Finite-dimensional transfer functions with different shapes and numbers of modes are formulated. The closed-loop performance predictions of different models under the same colocated and noncolocated controllers, which attempt to achieve high closed-loop bandwidth, are compared. Results are surprisingly consistent in all cases; the predictions of clamped-free mode shape models are much more accurate than the predictions of the pinned-free mode shape models.

A Torque Cancelling System for Quick-Motion Robots

“…Moreover, the elastic vibration that occurs in the links becomes a serious issue for the control. Therefore, much effort has been made to model and describe robot dynamics with elastic links and to control them (Cetinkunt & Yu, 1991;Tzes & Yurkovich, 1991;Hui et al, 2002;Subudhi & Morris, 2002;Theodore & Ghosal, 2003;Wang & Mills, 2005;Feliu et al, 2006). In contrast, we decided to develop a solution scheme of kinematics using the finite element approach combined with the parallel solution scheme to handle analysed models comprehensively in a single calculation process (Isobe & Kato, 2008).…”

Modeling of a One Flexible Link Manipulator

“…Examples of interpolation functions are Hermite cubics (Chen & Menq, 1990), cubic splines (Cho et al, 1991;Saad et al, 2006) and cubic B-splines (Saad et al, 2006). In the literature, most of the comparison studies that have been done are for clamped versus pinned mode shapes (Barbieri & Ozguner, 1988;Cetinkunt & Yu, 1991;Hastings and Book, 1987). The general conclusion is that for a slewing beam, clamped modes are more appropriate than pinned modes.…”

Stability Analysis for Digital PD Control of Flexible Systems

“…In another investigation, PD control is proven to guarantee stability for flexible robot arms (3) . Collocated and non-collocated PD controls for flexible arms are investigated (4) . Here, it is shown that the first control mechanism stabilizes the arm whereas the other does not if the system damping is not included.…”