Maximally Robust Input Preconditioning for Residual Vibration Suppression Using Low-Pass FIR Digital Filters

Abstract

A method for suppressing residual vibrations in flexible systems is presented and experimentally demonstrated. The proposed method is based on the preconditioning of the inputs to the system using low-pass Finite Impulse Response (FIR) digital filters. Provided that the cutoff frequency of FIR filters is selected lower than the lowest expected natural frequency of the system and their stop-band is maximized, we show that these filters can be designed to exhibit maximally robust behavior with respect to changes of the system natural frequencies. To perform the proper design of FIR filters for robust vibration suppression, this paper introduces a series of dimensionless performance indexes and the Delay-Error-Order (DEO) curves that represent graphically the delay time introduced by the filter as a function of the remaining residual vibrations, and the filter order. Several classes of FIR filters such as: a) Parks-McClellan; b) Window-based methods (using Chebyshev window); and c) Constrained Least Squares method, are shown to present maximally robust behavior, almost identical to the theoretically predicted. Parallel, they demonstrate excellent vibration suppression while they introduce the minimum possible delay. Further advantages offered by the proposed method, is that no modeling of the flexible system is required, the method can be used in a variety of systems exhibiting vibrations, it is independent of the guidance function and it is simple to implement in practical applications. The results are experimentally verified on a flexible aluminum beam with a significantly varying mass, attached to the end-effector of a robot manipulator. The beam is rotated, using one joint of the manipulator, from an initial to a final position. It is shown that the preconditioned inputs to the flexible system induce very little amount of residual vibrations compared to the inputs with no preconditioning.

General motion planning method for manipulators with no impact

“…The motion planning of the manipulator in the Cartesian space satisfies (2). In which, S(t) denotes the curve coordinate in the Cartesian space.…”

“…Singer et al [1], Economou et al [2], Baumgart et al [3], Cole et al [4]- [6] research the problem of suppressing the residual vibration of the flexible links of manipulators, with the input shaping or low-pass filtering method respectively. Luo [7], Ohta et al [8], Seki et al [9] use the method of strain feedback to control the vibration of the flexible links.…”

Disturbance Filtering and Identification on the Naval Postgraduate School 3-Axis Spacecraft Simulator

“…Ref. [13][14][15]. Comparisons between Input Shaping and conventional filtering methods have shown Input Shaping to be more successful in some studies, and conventional filtering to be more successful in other studies, as a result of improved filter tuning 16,17 .…”

A Command Generation Method of Point-to-Point Control for Suppressing Residual Vibration

“…The parameter r can be determined analytically. By substituting (10) into the left side of (6) and using the productto-sum identity of the trigonometrical function, the parameter r is obtained so that left side of (6) becomes zero. …”

“…It is known that when controlling a vibration system by PI or PID controls (the most frequent control method in the industry), there is a trade-off relation between vibration suppression performance and response performance. To solve this problem, many have researched the command for positioning from the viewpoint of suppressing residual vibration [1]- [10].…”