PSI - Issue 33

Nassima Naboulsi et al. / Procedia Structural Integrity 33 (2021) 989–995 Nassima Naboulsi et al. / Structural Integrity Procedia 00 (2019) 000–000

992

4

2.2. Identification system Since the transfer function of the heating collar is unknown in our case, there is a classical method for system identification which consists in obtaining a mathematical representation of the real system based on the response curve. However, the heating system is a linear system with an aperiodic index response, so we used Broïda's method to assimilate the transfer function of the system to first order affected by a pure delay from the experimental index response. The Broïda model is represented by a first order function as shown in (3).

1 p Ke Tp   

( )

H p



(3)

With The key parameters K is the Static gain, τ is the delay and T is the time constant. The ideal transfer function of a process is practically impossible to determine. It is then necessary to use a model as representative as possible of this process. To identify a process, it is necessary to find, from experimental data, the parameters that characterize this model. For this reason, we made an experiment, as shown in Fig. 3, of measurement of the temperature of the heating collar with a multimeter as a function of time supplied by a stabilized voltage of 220V. Then we presented these results by a curve of the real system showing the variations of the temperature every 30s until the maximum temperature of 370°C in the Fig. 5. Then from the Table 1 of the parameters of the model.

Table 1. Model parameters. Parameters

Values

� � � � � ��� � � ����

� � (E = 220V) � � ��� � � � � �

1,68

0,028 min 2,79 min

The resulting transfer function of the Broïda model is then of the form (4).

0,028 1, 68 e 

p

( )

H p



(4)

1 2,97 

p

Fig. 3. Experiment to measure the temperature as a function of time.