Information Technology Reference
In-Depth Information
is obtained from the reduced-order model with dimension n, denoted as
J
n
(
i
+1).
Then we can define difference over the whole working time Z, as follows:
(
J
n
(
i
+1)
J
n
(
i
))
2
/J
n
(
i
)
Z
−
1
ΔJ
n
=
−
(6)
i
=1
This criterion is to ensure a smooth command profile of the output variables.
The structure selection criterion aims to find the optimal structure which mini-
mizes the sum of quadratic partial variances of the evaporator pressure and the
superheat of evaporator. With different controller dimension n, different
ΔJ
n
can be computed. The n-order control structure with minimum
ΔJ
n
should be
chose as the optimized control structure.
Thus, the structure selection criterion algorithm performs the following steps:
Step 1: The overall system model is reduced first from 12th-order to a par-
ticular low order model using singular perturbation method, and then further
reduced in descending order from that reduced-order model to 2nd-order model;
Step 2: Giving same random various inputs to the full-order model and the
reduced-order models, respectively;
Step 3: Compute the criterion J between the reduced-order models and the
full-order model as described in (5) at each sampling time;
Step 4: Calculate the differences
ΔJ
n
of the reduced-order models expressed
as (6) over the whole simulation time;
Step 5: Compare the values of
ΔJ
n
and choose the model which minimums
ΔJ
n
as the optimized control structure.
4 Experiment Results
4.1 Simulation Results of the Control Structure Selection
To verify that the control structure selection can choose optimized control struc-
ture effectively, a comparison study has been carried out. The model has been
firstly linearised around a steady state operating point indicated in Table 1.
Then with the singular perturbation method, the system model is reduced to
4th-order model while which is still complicated to control, therefore, according
to the step 1 of structure selection criterion, the model is further reduced to
3rd-order and 2nd-order model, and the
ΔJ
n
among the 4th-order, 3rd-order
and 2nd-order control structures are compared.
Through the simulation, the structure selection criterion is calculated shown
in Table 2 which indicates that the 3rd-order control structure has the minimum
structure selection criterion. According to the structure selection criterion in
(5)-(6), the 3rd-order control structure is thus finally chosen for optimal control
model structure, convenient to the controller design of the refrigeration cycle
system.
Search WWH ::
Custom Search