First-Order Response to an Input Step-Change Disturbance

1 First-Order Response to an Input Step-Change Disturbance 

The simplest response of a linear system, is described mathematically by the following standard form of first-order differential equation 

For the step change condition, shown in Fig. 2.2, the initial conditions are given by y = 0, when t = 0. The solution to the differential equation, with the above boundary conditions, is given by 

Hence the value of the equation time constant, x, is simply determined as the time at which the response achieves sixty three per cent of its eventual steady-state value, when following a step change disturbance to the system. 

Liquid flows through a tank of constant volume V, with volumetric flow rate F and feed concentration Cq as shown in Fig. 2.3. 

Chemical Engineering Dynamics An Introduction to Modelling and Computer Simulation, Third Edition J. Ingham, I.J. Dunn, E. Heinzle, J. E. Prenosil, J.B. Snape 

Copyright 2007 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim ISBN 978-3-527-31678-6 

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