Control of Deposited Zinc in Hot Dip Gal

Figure 8.46. Scheme of the hot dip galvanizing process at Sollac - Florange





air air
Steel strip ^zinc
Figure 8.47. Details of the hot dip galvanizing process

The pressure in the air knives is regulated through a pressure loop, which can be approximated by a first-order system. The delay of the process will depend linearly on the steel strip speed. Therefore, for describing the relationship between the

Practical Aspects of Digital Control 367

variations of pressure and the variations of the deposited mass, one can consider a continuous time dynamic model of the form

s
_H(s) _1sT ; _V

where L is the distance between the air knives and the transducers and V is the strip speed.

When discretizing this model, the major difficulty comes from the variable time delay. In order to obtain a controller with a fixed number of parameters, the delay of the discrete-time model should remain constant. Therefore, the sampling period is tied to the strip speed (it is an “open loop adaptation”) in order to get a discrete time model of constant complexity, using the formula

^L 
T_s ^V _d ^; d integer

where d is the discrete-time delay (integer) and is an additional small time-delay due to implementation.

The corresponding linearized discrete-time model, which has been identified around various operating points, has the form

with d = 7. The fractional delay (which corresponds to the presence of an additional term b₂q^-2) is negligible because of the way the sampling period T_S is selected and this was confirmed by the model identification procedure. However, the parameters of the model, given above, will depend on the distance D and on the speed V.