Page 206 - Modern Control of DC-Based Power Systems

170 Modern Control of DC-Based Power Systems

Therefore, the equilibrium point of z 1 ; z 2 Þ 5 0 is globally stable.
ð
With (5.156) the tracking problem is also solved as for t-N; x 1 -y ref .It
should be mentioned this is not restricted only to the quadratic CLF and
may in certain conditions render better results as certain nonlinearities are
not canceled out [62].

5.5.3 Application to MVDC System Backstepping With
Virtual Disturbance
The controller which is synthesized here is based on similar principles to
the controller presented in Section 5.4.2. It uses also the virtual distur-
bance current as a decoupling approach. This simplifies the Backstepping
approach, as now only a linear system must be controlled but requires the
design of a linear Kalman filter for the estimation of the disturbance.
Fig. 5.41 depicts the overall control scheme. The design is composed of
two independent blocks. The Kalman filter receives only the bus voltage
measurement and estimates the inductor current and disturbance current
which are fed to the controller.
The design of the controller is carried out in two steps:
1. The Backstepping procedure is applied including the estimated distur-
bance current as if it was already known.
2. The design of the Kalman filter is performed afterwards.
The circuit which is presented in Fig. 5.42, leads to the following sys-
tem description with the following two states, x 1 5 V and x 2 5 I L .:

x 2 x 1 I d
_ x 1 5 2 2
C f R L C f C f
(5.157)
dE x 2 R f x 1
_ x 2 5 2 2
L f L f L f

V bus Augmented Estimates: Backstepping
kalman filter ^ ^ ^
V bus L d
;I ; I

Measurement Plant: Control signal
generators and loads

Figure 5.41 Structure of Backstepping controller with a Kalman filter for disturbance
estimation.