2 1. EXTRACTION OF UNCERTAIN MODEL OF DC-DC CONVERTERS
niques applied to DC-DC converters. Dynamics of a buck converter without uncertainty is
studied in the fourth section. Effect of changes in component values and operating conditions
on the converter dynamics is studied in the fifth section.
1.2 UNCERTAINTY MODELS
Modeling is the process of formulating a mathematical description of the system. A model, no
matter how detailed, is never a completely accurate representation of a real physical system. A
mathematical model is always just an approximation of the true, physical reality of the system
dynamics.
Uncertainty refers to the differences or errors between model and real systems and what-
ever methodology is used to present these errors will be called an uncertainty model. Successful
robust control-system design would depend on, to a certain extent, an appropriate description
of the perturbation considered.
1.2.1 PARAMETRIC UNCERTAINTY
Inaccurate description of component characteristics, torn-and-worn effects on plant compo-
nents, or shifting of operating points cause dynamic perturbations in many industrial control
systems. Such perturbations may be represented by variations of certain system parameters over
some possible value ranges. ey affect the low-frequency range performance and are called
“parametric uncertainties.”
Studying an example is quite helpful. Assume the simple RLC circuit shown in Fig. 1.1.
–
+
Vin
LR
C
Figure 1.1: Typical RLC circuit.
e transfer function between the capacitor voltage and the input voltage can be written
as:
v
c
.s/
v
in
.s/
D
1
LC
s
2
C
R
L
s C
1
LC
D
a
s
2
C bs C a
; (1.1)
where a D
1
LC
and b D
R
L
. R; L, and C can be written as R D R
0
C ı
R
, L D L
0
C ı
L
, and
C D C
0
C ı
C
. ı
R
, ı
L
, and ı
C
show the effect of aging, measurement error, replacement of the
components, etc.
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