Adopting pade approximation for first order plus dead time models for blending process

Abstract

Dead-time is common to real time processes and occurs when the process variable doesn’t acknowledge to any changes in the set point. Existence of dead time in the systems poses a challenge to control and stabilize, especially in a control feedback loop. Padé approximation provides a determinate approximation of the dead time in the continuous process systems, which can be utilized in the further simulations of equivalent First Order plus Dead Time Models. However, the standard Padé approximation with the same numerator- denominator derivative power, exhibits a jolt at time t=0. This gives an inaccurate approximation of the dead time. To avoid this phenomenon, increasing orders of Padé approximation is applied. In the following manuscript, equivalent First Order plus Dead-Time models of two blending systems of orders four and seven are analysed for the same. As the orders of the Padé approximation increases, the accuracy of the response also increases. The oscillations are increased on a much smaller scale rather than having one big dip in the negative region (as observed in the first few orders of Padé approximation), and the approximation tries to synchronize with the desired response curve in the positive region. All the simulations are done in MATLAB.