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Control Approaches for Parallel Source Converter Systems 191
T should be high for good command tracking at low frequencies, but
be low for high frequencies since we are not interested in tracking noise
from the reference command. Ideally, we would prefer low values for S
to eliminate the impact of disturbance. There is a conflict at higher fre-
quencies that both S and T are required to be low. This is not possible
due to the complementarity nature of S and T as evident from
Eq. (5.224). To resolve this conflict, it is ideal to have S with high pass
characteristics and T with low pass characteristics. The transfer function
from noise source to the control input is known as the noise sensitivity
transfer function RðjωÞ. R is required to have low pass characteristics,
since the noise generally belongs to the higher side of the spectrum.
Hence a low pass R would imply that the control input would not be
sensitive to measurement noise. The expressions of the three key transfer
functions are shown in (5.225).
21
SjωðÞ 5 ½I1GK
21
TjωðÞ 5 GK½I1GK 5 I 2 S (5.225)
21
RjωðÞ 5 K½I1GK 5 KS
5.7.4.1 Generalized Plant Modeling
In the weighted sensitivity approach, some crucial control signals of inter-
est are augmented with dynamic weighting functions. In the previous sec-
tion, the three sensitivity transfer functions were introduced. These
sensitivity functions can be modified by choosing appropriate weighting
functions. The explanation of how modifying each weighting function
would modify its respective characteristic function is explained in the
next section. In this section, the modeling of generalized plant or in other
words the augmented plant is briefed. The weighting functions W e , W T ,
and W u are frequency-dependent weightings of error signal v, plant out-
put y, and the control input u. The augmented or generalized plant P
consists of the actual plant G and the three weighting functions. It can be
seen from Fig. 5.54, that the input for P are the reference command w
and u and the outputs are z 1 , z 2 , z 3 , and v. By using the MIMO rule,
one can write the transfer functions from each output to input. The
transfer function of the augmented plant P(s) represents the mapping from
the exogenous inputs (w,u) to the exogenous outputs (z 1 , z 2 , z 3 , v) and it
is given by Eq. (5.226).
