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corresponding only to the modes present in the reference and disturbance
signals. From the results derived here, it is obvious that this type of
approach may not be adequate. In fact, tracking error will always occur
when modes which are required to be present in the input for tracking
are not incorporated into the dynamics of the internal model system.
Hence, our idea is to incorporate enough modes into the internal model
system's dynamics to insure that the tracking error is indeed small.
These modes, if sinusoidal, could actually be sinusoids at frequencies
which are harmonics or subharmonics of the frequencies found in the
reference and disturbance signals.
Once the formulation for the internal model system was complete,
the controller design was given. In this design, state feedback was
used and the internal model system was incorporated into the feedback
loop. It was shown that a necessary condition for a solution to the
servomechanism problem (for arbitrary K^) was observability of the
internal model system's state through its feedback gain matrix. This
was a key requirement which has not been postulated for the linear
servomechamism problem, but was needed here due to the different
approach used in solving the nonlinear servomechansim problem. Later it
was indicated that the observability condition would also be required
for stability of the closed-loop system. Consequently, it is enough to
consider only the stability problem since the observability condition is
satisfied automatically whenever stability is achieved.
The stability requirement for the nonlinear servomechanism problem
was imposed upon a dynamic system which modeled the difference between
the actual state trajectory and the desired state trajectory of the
closed-loop system. Thus, the dynamical model was referred to as the