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U of M College of Engineering Control Seminar Series Sponsored by Ford Motor Company, General Motors, and Whirlpool |
Algebraic Methods for Solving Nonlinear Systems
Problems
Professor John Chiasson
Department of Electrical and Computer Engineering
The University of Tennessee
Knoxville, TN 37996
In this presentation, it is shown
how some nonlinear systems problems can be solved completely using (nonlinear)
algebraic techniques. As a first example, parameter identification is
considered. Standard least-squares identification works very well when the
system model (differential equation) is linear in the unknown parameters and
all of the state variables are measured. However, in many physical problems,
not all of the state variables are available for measurements. Such systems can
be made linear in the parameters, but are then overparameterized. It is shown
for a class of nonlinear systems that the identification problem can be
formulated as a nonlinear least-squares identification problem that is not overparameterized.
Further, for this class of problems in which the nonlinearities are rational
functions of the parameters, it is shown how the global minimum solution can be
found in a finite number of steps using elimination theory (resultants) from
Algebraic Geometry. The methodology is illustrated on an induction motor.
As a second example, the problem of nonlinear observers is
considered. In particular, the estimation of the speed of an induction motor
based only on measurements of the stator currents (two of the five state
variables) and stator voltages (inputs) is addressed. It is shown how both a
purely algebraic speed estimator and a differential equation speed estimator
can be developed and the possiblity of combining them for achieving desired system
properties.
3:30 – 4:30 p.m.