PWARX Model Identification Based on Clustering Approach - Complex System Modelling and Control Through Intelligent Soft Computations - page 176

For the Chiu clustering algorithm, we have only one synthesis parameter:
n q ¼ 17.

The number of submodels s depends on the initial parameters chosen. With the
parameters described above, we obtain s =6.
The parameter vectors are presented in Tables 3 and 4 .
Figures 3 and 4 illustrate the outputs and the relative error signals of the two
proposed methods.
In Table 5 , the FIT is computed for the identi

cation and the validation with the
two proposed methods. The obtained results are very satisfactory and show that the
performances of the two methods are close.

5.4 Identi cation Results of a PH Neutralisation Process

5.4.1 Process Description

The is used to describe the reaction result between an acid and a

base in which the properties of H þ and OH that characterized the acid and base
will be destroyed or neutralized. In fact, the ions H þ and OH will be combined to
form the water molecule H 2 O. The resulting solution produced by the reaction is

neutralization

' '

Table 3 Estimated parameter vectors with the Chiu ' s method
Parameters vector Estimated values with Chiu

h

T

1 : 0996 0 : 6338 1 : 0259 0 : 8247 0 : 0762 ½

1

T

h 2

0 : 7769 1 : 0611 1 : 0016 0 : 8446 2 : 2539 ½

h 3

T

½

0 : 5066 0 : 9219 0 : 9781 0 : 7686 0 : 1886

h 4

T

½

0 : 6576 0 : 4256 0 : 9388 0 : 8097 1 : 4943

h 5

T

½

0 : 3013 0 : 5044 1 : 0644 0 : 6904 1 : 7459

h 6

T

½

0 : 8306 0 : 5365 1 : 0030 0 : 7557 2 : 7559

Table 4 Estimated parameter vectors with the DBSCAN method
Parameters vector Estimated values with DBSCAN

T

h 1

0 : 5134 0 : 4871 1 : 0377 0 : 8082 0 : 0187 ½

h 2

T

½

0 : 5974 0 : 3021 0 : 8905 0 : 7355 2 : 1231

h 3

T

½

0 : 7044 0 : 0158 1 : 0153 0 : 8255 0 : 1468

h 4

T

½

0 : 6958 0 : 6557 1 : 0714 0 : 7435 1 : 5669

h 5

T

0 : 3111 0 : 0277 0 : 9738 0 : 7616 0 : 3855 ½

h

T

0 : 6177 0 : 3720 0 : 9606 0 : 7291 1 : 2358

½

6