Dynamic model and input shaping control of a flexible link parallel manipulator considering the exact boundary conditions

Abstract

SUMMARYIn this paper, a rigid–flexible planar parallel manipulator (PPM) actuated by three linear ultrasonic motors for high-accuracy positioning is proposed. Based on the extended Hamilton's principle, a rigid–flexible dynamic model of the proposed PPM is developed utilizing exact boundary conditions. To derive an appropriate low-order dynamic model for the design of the controller, the assumed modes method is employed to discretize elastic motion. Then to investigate the interaction between the rigid and elastic motions, a proportional derivative feedback controller combined with a feed-forward-computed torque controller is developed to achieve motion tracking while attenuating the residual vibration. Then the controller is extended to incorporate an input shaper for the further suppression of residual vibration of flexible linkages. Computer simulations are presented as well as experimental results to verify the proposed dynamic model and controller. The input shaping method is verified to be effective in attenuating residual vibration in a highly coupled rigid–flexible PPM. The procedure employed for dynamic modeling and control analysis provides a valuable contribution into the vibration suppression of such a PPM.

Active Vibration Control and Coupled Vibration Analysis of a Parallel Manipulator with Multiple Flexible Links

“…where ( ) represents the generalized elastic motion coordinates of the th link and ( ) are shape functions matching pinned-free boundary conditions which were verified in our previous modal test experiments [12]. Then, the Lagrange multiplier equation which is used to integrate both rigid and elastic motions is given as…”

“…To suppress the residual vibration of a 3-DOF flexible planar parallel manipulator, Li et al [11] compared three different input shapers, namely, the zero-vibration (ZV) shaper, the zero-vibration-derivative (ZVD) shaper, and the extra insensitive (EI) shaper, in order to obtain better suppression results. In our previous work [12], a ZVD input shaper was incorporated with the motion controller to suppress the residual vibration of a 3-PRR parallel manipulator with three flexible links. However, due to the highly coupled dynamic characteristic of the 3-PRR rigidflexible manipulator, the ZVD input shaper can only suppress the unwanted vibration of the flexible links to some extent.…”

“…Hence, to investigate such coupled vibration phenomenon and achieve the vibration suppression of multiple flexible links is the goal of this research. In our previous researches [1,12,20], the active vibration suppression experiments are limited to only one flexible link and hence the control effects are restricted due to the coupled characteristic among the three flexible links. In this study, combined with input shaper and IMSC, active vibration control and coupled vibration features analysis of a parallel rigid-flexible manipulator with three flexible links are investigated both theoretically and experimentally.…”

Output Based Input Shaping for Optimal Control of Single Link Flexible Manipulator

“…It is designed using the signal output of the target system, thus in addition to being robust, the problems of parameter uncertainty are avoided. In addition, various types of input shaping techniques, zero vibration (ZV), zero vibration derivative (ZVD) and zero vibration derivative-derivative (ZVDD) to suppress residual vibrations and oscillations have been proposed in [2,[7][8][9][10]. PID control is very popular in the industry for feedback control [11].…”

Tracking Control and Vibration Reduction of Flexible Cable-Suspended Parallel Robots using a Robust Input Shaper

“…The controller was a combination of a VSC method for motion tracking of the end-e ector and a strain rate feedback control for suppressing the vibration of the elastic linkages. They also investigated the e ectiveness of combining a PD computed-torque control with the ZVD input shaper for suppressing the residual vibration of the mechanism [15].…”