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Linear quadratic optimal control systems can be designed in the
time domain and in the frequency domain. In the time domain
approach, the optimization is based on the solution of an LQR
problem; while in the frequency domain approach, the problem
becomes Wiener''s least square (WLS) procedure. These two
procedures are developed with different system structure and
system description. Till 1970, the return difference equality
is derived by MacFarlane, the optimal design between the time
domain approach and the frequency domain approach is proved to
be equivalent for a regulating problem. The main purpose of
this paper is to continue this work, A complete discussion
between the time domain and the frequency domain approach of
optimal system is made in this paper. Input signal equality is
derived in this paper first. To- gether with the return
difference equality, the equivalence between the time domain
and frequency domain approach of model following system is
derived. Next, we derive the feedforward disturbance equality,
and the equivalent problem is extended to the model following
system with output disturbance. The same problem for the
frequcncy shaped system is discussed, and the relation between
the weighting filter and the weighting function is found. In
order to extend this idea to multivari- able systems, we
introduce a generalized system description. With the
generalized system description the equivalent problem of MIMO
system is discussed. Moreover, a time domain approach to Wiener
filter design is proposed. Finally, this concept is applied to
the two degree of freedom LQR design, and the optimal QFT or
EDA design procedure is generated. Examples are given in every
cases.
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