This paper deals with a method of optimizing the free coefficients
in the characteristic equation of a linear feedback control
system. The optimization is carried out by minimizing an index
of performance associated with the system's response to a given
test disturbance.
The index of performance is the integral of a quadratic function
of the system state variables. The structure of the index
rests upon a logical interpretation of the regulator nature of the
control problem. The index for an tr— order system contains n
I'll
weighting factors whose values are determined from an n-~- order
model system. This determination is such that the optimization
of a completely free system will yield the model system. A system
with fewer than n degrees of freedom in the state variable
feedbacks may be optimized with respect to the free feedback coefficients,
yielding a system whose dynamic response to a given
disturbance is, for this optimization scheme, a best approximation
to that of the model.
Examples are presented for illustration of the salient features
of the method. It is also shown by example that systems with
closed- loop zeros may be optimized by this method.
The author wishes to thank Dr. Harold A. Titus for his guidance
in this investigation.

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