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Control Approaches for Parallel Source Converter Systems 145

R fn L fn I Ln

d ·E n C fn
n
I = P /V
V C eq R L CPL CPL
R fm L fm I Lm

d ·E m C fm
m

Figure 5.22 Decoupled Shipboard Power System.

results may be applied to nonlinear systems. An optimal control is
designed for a nonlinear system with the assumption that the system will
start in a defined initial state. For each state there exists an optimal con-
trol. If the system starts in a slightly different initial state, then a first
approximation to the difference between the two optimal controls may
normally be derived, if desired, by solving a linear optimal control prob-
lem. This holds independently of the criterion for optimality for the non-
linear system [39 41]. This difference between the different operating
points is precompensated in this research work with the set-point trajec-
tory generator.
In Sections 5.4.1.1 and 5.4.1.2 the theoretical framework of this con-
cept is presented. The reader who is familiar with these concepts may
jump straight to Section 5.4.2 where the application of the decentralized
LQG on the MVDC system is presented, while in Section 5.4.3 a cen-
tralized formulation of this control concept is shown.

5.4.1 Procedure of Observer-Based Control
5.4.1.1 Linear Quadratic Regulator
Linear optimal control is a special sort of optimal control. The plant that
is controlled is assumed linear, and the controller, the device that gener-
ates the optimal control, is constrained to be linear. Linear controllers are
achieved by working with quadratic performance indices. These are qua-
dratic in the control and regulation/tracking error variables. Such meth-
ods that achieve linear optimal control are termed Linear Quadratic (LQ)
methods [33,41].
The LQ controller, also called Riccati controller, is a state controller
for a linear dynamic system whose feedback matrix is determined by the