Page 190 - Modern Control of DC-Based Power Systems

154 Modern Control of DC-Based Power Systems

The focus lies now on the calculation of the trajectory generation and
the optimal state feedback. For the decentralized model depicted in
Fig. 5.27 the state equations are given in (5.114):

x 2 x 1 I d
_ x 1 5 2 2
C f R L C f C f
(5.114)
dE x 2 R f x 1
_ x 2 5 2 2
L f L f L f
Where the states are x 1 5 V and x 2 5 I L .
The system can be written in matrix form, where d in (5.115) corre-
sponds to the duty cycle:

_ x 5 Ax 1 Bd 1 NI d
(5.115)
y 5 Cx
2 3
1 1
2
" # 6 7
V 6 R L C f C f 7
x 5 A 5 6 7
6 1 R f 7
I L
4 2 2 5
L f L f
(5.116)
h E i T

B 5 0 L f C 5 1 0
h 1 i T
N 5 2 C f 0
The nominal set-point of the system where V nom is equal to the refer-
ence bus voltage while the external disturbance is zero can be
determined:

0 5 Ax nom 1 Bd nom
(5.117)
V nom 5 Cx nom
The equilibrium point of the system is described by Eq. (5.117) as all
derivates are set to zero. The decentralized model does not take into
account the effects of the whole system; the disturbance has to be consid-
ered additionally when generating the set-point. This disturbance I d is
estimated and the actual set-point is adapted.

0 5 Ax e 1 Bd e 1 NI d
(5.118)
V nom 5 Nx e