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superheated region. It can be formulated by a fifth order non-linear model.
Z
e
(
x
e
,u
e
)
· x
e
=
f
e
(
x
e
,u
e
)
(4)
where the state variables are length of two phase flow
L
e
1
; refrigerant pressure
P
e
; refrigerant outlet enthalpy
h
eo
; the wall temperatures in the saturated and
the superheated region,
T
ew
1
and
T
ew
2
, respectively; the input variables are mass
flow rate of the inlet and outlet, ˙
m
ei
and ˙
m
eo
, refrigerant inlet enthalpy
h
ei
,air
temperature
T
ea
and air mass flow rate ˙
m
ea
, respectively.
The composite model of whole vapor compression refrigerant cycle can be
obtained by appropriately combining the component models according to the
relations between the variables.
3 Dynamic Modeling and Model Linearization
For the purposes of high control accuracy and simple calculation, the optimized
control structure needs to be chosen for advancing towards further studies. A
structure selection criterion, which is used to evaluate the performance of differ-
ent control structures and choose the optimal simplify model, is proposed in the
following section.
Firstly, a twelfth-order linear state-space model obtained from the model lin-
earization considering the steady-state point of operation. After designing a con-
tinuous process at steady state for given operating conditions, control structure
selection is an important part of process control. A popular control structure se-
lection method is the singular perturbation model reduction method[8] by which
the model is decoupled into two parts: the fast one and the slow one. This algo-
rithm can to some extent simplify the model, but it does not show whether it is
the optimized control structure for controller design.
In this section the evaporator pressure and the superheat of evaporator are
chose in the proposed criterion for controller design of this system. The overall
system model is firstly reduced from 12th-order to reduced-order models using
singular perturbation method, and then giving random varying inputs to the
full-order model and the same varying inputs to the reduced-order models, then
the structure selection criterion is defined as follows:
J
(
i
)=(
P
e
(
i
)
P
e
(
i
))
2
+(
T
e
−
sh
(
i
)
T
e
−
sh
(
i
))
2
i
=1
,...,Z
−
−
(5)
where
P
e
and
T
e
−
sh
are separately the values of the evaporator pressure and
the superheat of evaporator computed by the full-order model,
P
e
and
T
e
−
sh
are
separately the values of the evaporator pressure and the superheat of evaporator
computed by the reduced-order model. Z is the whole simulation time. This
criterion evaluates the deviations between the full-order model and the reduced-
order model in each sample point i.
Denote the cost value J in (5) of the reduced-order model with dimension n
as
J
n
, the value of
J
n
at time i is obtained from the reduced-order model with
dimension n, and denote it as
J
n
(
i
). Similar to
J
n
(
i
), the value of
J
n
at time
i
+1
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