CHAPTER EIGHT
CONCLUSIONS AND OPEN PROBLEMS
A control scheme has been developed which solves the servomechanism
problem for nonlinear systems satisfying assumptions (A.l) and (A.2).
Existence of a solution is guaranteed by (A.l) and (A.2) requires the
state and input (which occur during tracking) to satisfy a linear
differential equation.
It has been argued that when (A.2) does not hold it is still
possible to design a satisfactory controller. For example, when the
reference and disturbance signals are periodic then the state and input
signals must be periodic if tracking is to occur (assuming an autonomous
system). Therefore, since many systems attenuate high frequency
signals, a truncated Fourier series expansion of the true input and
state is likely to be a reasonable approximation from which to base the
design. The state and input resulting from such an approximation do
satisfy a linear differential equation. The above argument has also
been verified using simulations of a 2-link robotic manipulator.
Tracking will be local if only local stability of the system NCT
can be shown (see the definitions given in Chapter Two). Furthermore,
when the feedback giving local stability is obtained using a lineariza
tion of the closed-loop system about the origin; tracking will occur for
only small reference and disturbance signals. In many cases it is not
necessary to have tracking for large disturbance signals, since by
nature, disturbance signals are frequently small. Also, it is likely
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