Page 148 - Modern Control of DC-Based Power Systems

112 Modern Control of DC-Based Power Systems

control technique has found successful application in the stabilization of
Constant Power Loads (CPLs) in [3 5]. In this control the nonlinear part
of the controlled system is compensated and it is possible to design a
closed-loop control on a linear control system. Strictly speaking this
technique is based on the concept of exact linearization [6] and refers to
the input output linearization. In Section 5.1.1 the theoretical frame-
work of this concept is presented; readers familiar with the theory can
jump straight to Section 5.1.2 where this concept is applied to the
MVDC ISPs.

5.1.1 Procedure of Linearizing State Feedback
The theory of exact linearization can be explained while considering a
nonlinear system described by (5.1):
_ xtðÞ 5 axðÞ 1 bxðÞu
(5.1)
y 5 cðxÞ
Those are systems which are nonlinear in x but linear in u.Those
systems are called input linear systems or control-affine systems.
The assumption of a linear acting control variable u is not a big restric-
tion, as many technical systems are linear in u or the manipulated
variable [6].
Now the question whether a state feedback control exists, is posed:
u 52 rxðÞ 1 vxðÞw (5.2)

And a change of variables [1], which will render the resulting system
linear.
(5.3)
z 5 TðxÞ
The system has the order of n 5 dim(x). The consideration of multi-
ple input multiple output (MIMO) systems is possible without great
effort and in a similar manner as in the single input single output
(SISO) case; this is presented to the reader in detail in [1,7 9].Here,
just the SISO systems are considered with the aim to present the main
idea of the method. When performing an exact linearization two differ-
ent exact linearizations are possible, depending on the goals of the con-
trol design:
• Input-to-State Linearization
• Input output Linearization.