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that the reference will be known in advance so that the controller can
be designed accordingly. For instance, the feedback law can be chosen
to give stability relative to a nominal trajectory as was discussed in
Chapter Five.
There are several aspects of the approach taken here which deserve
investigation. Some of these are:
(1) Analyze the situation which occurs when the internal model
system's poles are not placed at the correct locations. For
example, what is the consequence of placing poles at j2 when they
are actually needed at j2.1.
(2) Find a way to bound the tracking error when (A.2) is not satis
fied. Also show the relationship between the error bound and the
number of terms taken from a Fourier series expansion of the true
state and input.
(3) Develop a feedback law which either gives global stability or
increases the region of stability for the system NCT. Since the
resulting feedback may be nonlinear, further conditions are likely
to be imposed for a solution to the servomechanism problem. One
scheme which warrants investigation is the use of prestabilizing
nonlinear feedback on the plant.
(4) Investigate the effect of the proposed scheme on the transient
behavior of the system. Although it is true that the steady-state
error can be improved with this scheme, the use of an internal
model system of large dimension may degrade transient performance.