17-09-2012, 05:27 PM
SETTLING-TIME IMPROVEMENTS IN POSITIONING MACHINES SUBJECT TO NONLINEAR FRICTION USING ADAPTIVE IMPULSE CONTROL
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ABSTRACT
A new method of adaptive impulse control is developed to precisely and quickly
control the position of machine components subject to friction. Friction dominates the
forces aecting ne positioning dynamics. Friction can depend on payload, velocity,
step size, path, initial position, temperature, and other variables. Control problems
such as steady-state error and limit cycles often arise when applying conventional
control techniques to the position control problem. Studies in the last few decades
have shown that impulsive control can produce repeatable displacements as small as
10 nm without limit cycles or steady-state error in machines subject to dry sliding
friction. These displacements are achieved through the application of short duration,
high intensity pulses.
The relationship between pulse duration and displacement is seldom a simple
function. The most dependable practical methods for control are self-tuning; they
learn from online experience by adapting an internal control parameter until precise
position control is achieved. To date, the best known adaptive pulse control methods
adapt a single control parameter. While eective, the single parameter methods suer
from sub-optimal settling times and poor parameter convergence.
Introduction
This dissertation presents a new method for controlling the position of machines
subject to nonlinear friction. By developing control methods that more accurately
compensate for nonlinear machine dynamics, performance can be improved while
maintaining precise control. Specically, mean settling time can be improved for
many tolerances and displacements. This dissertation describes the development,
implementation, and testing of a new multi-point adaptive impulse control method.
Motivation
For millennia, man's quest to organize his environment has required him to move
objects from place to place. Machines used in such work have progressively been
rened to meet higher demands on precision and speed. Objects, both large and
small, need to be moved quickly and precisely to support a high standard of living.
Computer control over the last several decades has been introduced to help meet
the demand. Computers have been instrumental in measuring and analyzing the
forces that aect motion. Often, nonlinear friction poses one of the greatest challenges
to ne position control. Improvements are still needed in computer control if demands
for precise position control are to be met with ever greater accuracy, eciency, and
speed.
The Challenge
Friction poses a challenge to precise control. In fact, according to prominent tribology
researchers, \friction is the nemesis of precise control" [25]. Friction often dominates
the forces aecting system dynamics during the small moves that must occur during
ne position adjustments. Friction can depend not only on the mass of the payload,
but also on velocity, step size, path, initial position, and temperature.
New tools for measuring and analyzing friction have become available during the
last few decades. Computer analysis and laser interferometry have been instrumental
in gaining new insights into the repeatability of friction at low speeds and through
short distances. Several new friction models have been developed as a result of these
studies. Many of the recently developed models greatly improve the delity and
range of prediction. Because several physical mechanisms combine to create the
friction forces, the new models often have higher degrees of complexity. Despite the
complexity, however, friction has been found to be more repeatable and predictable
than previously expected [2].
Survey of Friction Models for Nonlinear Friction
The earliest documented friction model is Leonardo Da Vinci's work, circa 1519. He
modeled friction force as proportional to normal load, always opposing motion, and
independent of contact area [14]. Coulomb further developed Da Vinci's work in 1785.
Coulomb reported the friction characteristic shown in Figure 3 [12].
Note, the change from F(v = 0