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A process is subjected to a unit step change in input and responds in the way shown in Figure 1. Fit a first order plus dead-time model to this process and find the values of the model parameters.

A process is subjected to a unit step change in input and responds in the way shown in Figure 1. Fit a first order plus dead-time model to this process and find the values of the model parameters.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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2. The idea was not to overcomplicate (after all, we are reading numbers from a graph) the analysis but to find parameter values that make sense in terms of fitting the curve given in the question. T = t90-t30 In(7) ; ta = t90 − − ln(10) My (very rough) estimates are: t30 ≈ 30s t90≈ 50s T≈ 0.5 * (50 – 30) ≈ 10s ta≈ 1.2 × 30 – 0.2 × 50 ≈ 26s Note that this short-cut method of fitting the FOPDT model is based on forcing agreement with the process data where it reaches 30% and 90% of its ultimate value.
Transcribed Image Text:2. The idea was not to overcomplicate (after all, we are reading numbers from a graph) the analysis but to find parameter values that make sense in terms of fitting the curve given in the question. T = t90-t30 In(7) ; ta = t90 − − ln(10) My (very rough) estimates are: t30 ≈ 30s t90≈ 50s T≈ 0.5 * (50 – 30) ≈ 10s ta≈ 1.2 × 30 – 0.2 × 50 ≈ 26s Note that this short-cut method of fitting the FOPDT model is based on forcing agreement with the process data where it reaches 30% and 90% of its ultimate value.
2. A process is subjected to a unit step change in input and responds in the way shown in Figure 1. Fit a first order plus dead-time model to this process and find the values of the model parameters. Figure Q2 15.0 14.8 14.6 14.4 14.2 14.0 13.8- 13.6 13.4 13.2 13.0- 12.8 12.6 12.4- 12.2 12.0 0 I 10 1 20 30 40 50 Time (sec) 60 70 80 Figure 1: Model response to a step change. 90 100
Transcribed Image Text:2. A process is subjected to a unit step change in input and responds in the way shown in Figure 1. Fit a first order plus dead-time model to this process and find the values of the model parameters. Figure Q2 15.0 14.8 14.6 14.4 14.2 14.0 13.8- 13.6 13.4 13.2 13.0- 12.8 12.6 12.4- 12.2 12.0 0 I 10 1 20 30 40 50 Time (sec) 60 70 80 Figure 1: Model response to a step change. 90 100
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