# INFT 940 -- Design Project #1

## Robust Analysis of Vibration Control System

INFT 940, Spring 1997,
Assigned 2/27/97, Due 4/3/97

- At the bottom of this web page are shown the equations for a system to control mechanical
vibration. The complete open-loop system is the series combination of those transfer functions.
The quantities which are uncertain are the spring constant (
*k*), damper
constant (*d*), and the outer mass (*m1*). The uncertainty in these
variables will be considered individually. The nominal value for each of these
variables is denoted by the subscript 0 (e.g., *k0*). Variations in the
variables will be with respect to those nominal values. Therefore, the range of
values for a variable will have the form

- The table below shows the range of variations in the three variables. Three
sets of variation are shown for each of the three variables. The nine experiments
are treated individually. The variables which are not being perturbed are held
constant at their nominal values. For each experiment, the closed-loop
characteristic equation will be considered an interval polynomial.

Table of parameter values

- For each of the experiments, perform a robustness analysis of the closed-loop
system under the assumption of the characteristic equation being an interval
polynomial. Kharitonov plots must be used to graphically support your analysis.
Other methods, such as the Frequency Sweeping Function, discussed in Chapter 6,
may also be used.

- For variations in
*k* and *d*, perform a root locus analysis and
see if these results agree with those from the Kharitonov analysis.

- Document your analysis in a typed report. Plots should be included to
illustrate your discussion and conclusions.

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