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The FOPDT model parameters are used to calculate the tuning parameters.
In this work a real implementation of a Sliding Mode Controller based on a FOPDT model of the system [13] is established.
Based on the actual system, the relationship between the thickness and the roll gap can be approximated as a FOPDT model [29]
The FOPDT models (2) and (4) of the process and disturbance transfer functions are employed in the feedforward controller design:
As an estimated model of the process, the following FOPDT transfer function can be considered:
Combining (6) and (8), the following first order plus time delay (FOPDT) model can be obtained:
Thus, an additional advantage in using the FOPDT approximation is that empirical design correlations can be used.
The FOPDT assumption was also justified from the typical delayed exponential response to steps obtained for all variables with the Aspen Plus dynamic simulator of the distillation column.
Generally, the interactions in most industrial models [12] can be effectively represented by a FOPDT model of the following form:
The SOPDT transfer functions that have been obtained from the open loop response and the respective FOPDT models are shown in the table 2.