CONTROL IMPROVEMENT OF UNDER-DAMPED SYSTEMS BY INPUT SHAPING

https://www.ariel.ac.il/sites/conf/mmt/mmt-2014/service%20files/papers/3-1-10.pdf

1.1 Background and Motivation

Vibrations exist all around us. Many examples of such systems range from the
positioning of disk drives head, spinning of a computer's hard drive to the motion of a
car as it travels over a series of bumps, vibration of the tip of a manufacturing robotic
arm, flexible manipulators, container cranes and large space structures.
Vibrations are a part of everyday life.
It is a serious problem in mechanical systems that are required to perform precise
motion in the presence of structural flexibility.
Many common engineering problems involve getting rid of or reducing the levels
of vibration.
In most cases, the residual vibration at the end of a move is the most detrimental
and the extent of the residual vibration limits the performance of the system. The
effective use of such systems can only be achieved when such vibration can be
properly handled. As a result, there is active research interest in finding methods that
will eliminate vibration for a variety of mechanical and structural systems.
It is possible to reduce vibration by adding stiffness to the system, but that often
adds cost and slows down the operation speed. A better solution is to intelligently
choose a control strategy that minimizes residual vibration, yet still moves quickly.

1.2 Problem Statement
The control of flexible or lightly damped systems is an immense field of research.
There are a variety of reasons why mechanical systems are designed and built to be
flexible. For example, many mechanical systems need to be lightweight. Lightweight
systems can be moved faster and/or with less energy than heavier mechanical
systems. Unfortunately, making a mechanical system lightweight usually means that it
will also be flexible. And, if speed is a primary goal, then vibration control will be a
necessity. Lightly damped systems moving at high accelerations and velocities will,
generally vibrate. This vibration can cause a variety of problems including positioning
errors, slow overall move times (if vibration must naturally damp out), and system
damage.
The three primary methods for limiting vibrations on lightly damped, mechanical
systems are to intelligently choose motion commands, to utilize some form of
feedback control or to move so slowly that the flexible dynamics are not excited.
Given that moving slowly is undesirable for many reasons and feedback control
sometimes impossible to perform in a system, this research seeks to study the
command generation method.
Command generation is a technique that specifically designs unique reference
commands for a given system. The unique reference command is chosen based on its
ability to drive the system according to a set of performance constraints. One example
of command generation is the use of S-curves to drive flexible systems.
Command shaping generation method is a similar process by which a desired
reference command is modified so as to improve the performance of a given system.
For instance, the reference command might be altered so as to reduce the residual
vibration which typically would result from an unmodified reference command. One
example of command shaping is the use of low-pass filters.
Depending on the application, some of these command shaping techniques will be
more useful than others. Many command shaping techniques have little robustness to
modeling errors. In addition, many are not applicable in real time, requiring precomputation
of command functions.

1.3 Objective and Project Overview
This project attempts to analyze a lightly damped system and to specify a reference
control signal that will drive the system from an initial position into a target position,
with minimal vibrations or without vibration at all.
The project experimental setup is pendulum system. It is simple and imitates
lightly damped systems that will continue to oscillate long after the desired move has
ended.
As a whole, this project considers only both analyzing plant and input command
need to reduce vibrations.
Simulation is done using MATLAB to obtain the output response and desired
shaped command. The control for the system is realized in real time using LabView.