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Tabl e 1.
The steady state operating conditions for the model linearization
State variables
Units
Value
Condensing pressure
kPa
933
Evaporating pressure
kPa
342
◦
C
Air temperature at the condenser inlet
29
◦
C
Air temperature at the evaporator inlet
23
Air mass flow rate through the condenser
kg/s
0.45
Air mass flow rate through the evaporator
kg/s
0.19
Compressor speed
rpm
1100
EEV Opening
%
11.8
Tabl e 2.
The Structure Selection Criterion
Control structure
2I2O
3I3O
4I4O
Selection
40.3048
14.3525
15.3394
4.2 Experimental Results of the MPC Controllers
In this section, MIMO predictive controllers are designed and the control per-
formances are compared with the conclusion drawn from the optimized control
structure chosen in the previous section.
MPC is a control algorithm which computes a sequence of control inputs based
on an explicit prediction of outputs within some future horizon. The application
of MPC in HVAC systems can be found in the research of Xu[9] and Matthew S.
Elliott[10]. In order to define how well the predicted process tracks the set-point,
an objective function
J
(
k
)forthepredictivecontrol needs to be optimized as
follows:
minJ
(
k
)=
J
y
(
k
)+
J
Δu
(
k
)
(7)
n
y
P
j
=1
{
2
J
y
(
k
)=
q
j
[
ω
j
(
k
+
i
|
k
)
−
y
j
(
k
+
i
|
k
)]
}
(8)
i
=1
M−
1
n
mv
j
=1
{
2
J
Δu
(
k
)=
λ
j
Δu
j
(
k
+
i
|
k
)
}
(9)
i
=0
(8) computes the weighted sum of squared deviations for the deviation of the
outputs from the setpoints. (9) computes the weighted sum of squared deviations
for incremental manipulated variables. Where k is the current sampling interval,
k
+
i
is the future sampling interval, P is the prediction horizon,
n
y
is the number
of plant outputs,
q
j
and
λ
j
are the weight of output and input j,
ω
j
(
k
+
i
)isthe
desired output at instant
k
+
i
,
y
j
(
k
+
i
) is the actual output at instant
k
+
i
,M
is the control horizon,
n
mv
is the number of the inputs.
Three MPC controllers have been designed based on three different control
structures and the performances of them have been compared in terms of refer-
ence tracking and disturbance rejection. To verify the robustness of controllers,
the changing ambient temperature as the disturbance is added as Figure 2.
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