Page 226 - Modern Control of DC-Based Power Systems

190 Modern Control of DC-Based Power Systems

Min :F l ðP; KÞ: (5.221)
K 2
Both H 2 and LQG paradigm do not have guaranteed stability margins
as far as robustness is concerned [72,73]. The LQG control is only a spe-
cial case of H 2 control, where the noise is uncorrelated white noise with
zero mean.

5.7.3.2 H N Optimal Control Problem
Minimizing the infinity norm the transfer function T zw parametrized by
the controller K, leads to the H N optimal controller.

Þ: (5.222)
Min :F l P; Kð N
K
The H N is designed with pessimistic approach as it tries to minimize
the worst-case disturbance on the system. The H N control guarantees
robust stability margins. The infinity norm satisfies multiplicative property
and hence can be used to represent unstructured uncertainty. This is not
possible with H 2 norm.
:AsðÞBðsÞ: # :AsðÞ: :BðsÞ: (5.223)
N N N
When the plant has low margins, bandwidth due to presence of RHP
zero, [74] proposes design of pre- and postcompensator to condition the
plant and then design of a weighting function to apply a mixed sensitivity
approach for control design.

5.7.4 Weighted Sensitivity H N Control

In this section, the H N weighted sensitivity control is explained. In this
approach, dynamic weighting functions, which are basically filters, are
used to modify the loop shape of the plant in the desired manner. We are
considering the output feedback structure, where only the output quan-
tity is measured and used for negative feedback, the full information of
the plant, which is the state measurements, are not required. The sensitiv-
ity transfer function SðjωÞ is the transfer function from the disturbance d
to the output y, similarly the complementarity sensitivity function TjωðÞ
represents the command tracking transfer function from the reference w
to output y. The sum of S and T add up to unity for all frequencies as
given in Eq. (5.224)

SjωðÞ 1 TjωðÞ 5 I (5.224)