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26 Introduction to Control Theory

EXAMPLE 2.2–2: Two-Platform System

Consider the MIMO mechanical system shown in Figure 2.2.2 which represents
a 2 platform system used to isolate experiments from external disturbances.
There are 2 inputs to the system given by u 2 which causes the ground to move
and u 1 which causes the platform m1 to move. The system also has 2 outputs,
namely the motion y 1 of platform m 1 and the motion y 2 of platform m 2 . The
experiments will be conducted on top of platform m 1 and therefore, one would
like to minimize the size of y 1 . The differential equations describing this system
are obtained using Newton’s second law:

A state-space formulation of this system can be obtained by choosing

Transfer Functions
Another equivalent representation of linear, time-invariant, continuous-time
systems is given by their transfer function, which relates the input of the
system u(t) to its output y(t) in the Laplace variable s or in the frequency
domain. It is important to note that the transfer function description has no

Copyright © 2004 by Marcel Dekker, Inc.