Page 160 - Modern Control of DC-Based Power Systems

124 Modern Control of DC-Based Power Systems

system based on the MVDC shipboard power system is presented in
Section 5.2.2 for highlighting the actual implementation steps.

5.2.1 Procedure of Synergetic Control
Synergetic control was developed by Kolesnikov and his coworkers [12]; it is
a state-space approach based on dynamic control of the interaction of energy
and information within the system [15]. The authors of [19] often refer to
this approach as the stabilization and control via system restriction and mani-
fold invariance. The major idea behind this concept is to restrict the motion
or trajectories of the system to a manifold or hyperplane. This includes forc-
ing the system onto the manifold when it is not on the manifold already.
The control problem addressed in this work is voltage stability (i.e., damping
any voltage oscillation and transient behavior that may arise due to distur-
bances in the system). The synergetic controller forces the system to take the
characteristics of the manifold. Therefore, the manifold has to be constructed
in such a way that the closed-loop system behavior is stable.
The design approach consists of two major steps: the construction of a
stable manifold or hyperplane and the synthesis or design of a controller
such that the trajectories of the system are forced onto, and subsequently
remain on, the manifold. The objective of the controller is responsible
that the manifold is invariant and attractive.
The technique of synergetic control is similar to that of SMC in the
way the manifold is being constructed [20,21]. The difference lies in the
fact of how the system is forced to reach the manifold. In the case of syn-
ergetic control, the system is caused to reach the manifold in an exponen-
tial manner and therefore not showing a chattering effect which appears
in SMC due to the fact that the system is forced to reach the manifold in
a finite period of time which introduces some form of discontinuities in
the control action and creates chattering on the manifold [22].
The synergetic control design procedure follows the Analytical Design
of Aggregated Regulators (ADAR) method. The steps involved in the
control design can summarized according to [17]. Assume the system to
be controlled can be described by a set of nonlinear equation of the form:
(5.36)
ð
_ x 5 fx; uÞ
where x and u are the system state variable vector and the input vector
respectively.