CHAPTER FOUR
FEEDBACK CONTROL
In this chapter various concepts related to selecting the feedback
gains for the servomechanism problem are discussed. The beginning of
the chapter deals primarily with the nonlinear servomechanism problem
while some results for the linear servomechanism problem are given in
later sections.
Since it is often difficult to show global stability in nonlinear
systems, here the emphasis is placed on achieving only local
stability. Conditions are given showing when it is possible to obtain a
time-invariant feedback control law which stabilizes the system NCT.
These conditions apply mainly to the case when the reference and
disturbance signals are small. An example is provided to demonstrate
the method.
Also discussed in this chapter is the interpretation of using
optimal control techniques in the selection of the feedback gains for
the linear servomechanism problem. The optimal control approach can be
applied to the nonlinear servomechanism problem when the linearized
equations are used; however, the interpretation is less precise.
Stabilization Using the Linearized Equation
To solve the tracking and disturbance rejection problem it is
necessary to have asymptotic stability of the system NCT. Furthermore,
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