##### Determine the numerical values of the time constant and of the gain of the process and comment on their values and units, particularly in relation to those obtained in.
EX40HC – Tutorial 3
Building basic dynamic simulations with SimulinkProblem
1. Consider Problem 1 of Tutorial 2 again, where we have a stirred tank heater with no inlet or outlet flow (see scheme below). The aim of the process is to heat the fluid in the tank until it reaches the desired temperature 𝑇𝑇 via heating that is provided by a coil, inside which steam condenses at a temperature 𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠. Assuming that the system is initially at steady-state determine the following:
a) Using the mathematical model already developed in Tutorial 2, verify that the dynamic response numerical values of the fluid temperature𝑇𝑇(𝑡𝑡) in relation to the steam temperature 𝑇𝑇𝑠𝑠𝑠𝑠(t) can be described by a first order lag process.
Determine the numerical values of the time constant and of the gain of the process and comment on their values and units. Assuming that at time 𝑡𝑡=0 the steam temperature increases by 10oC (step change) develop a Simulink model for this process and plot the time profile of the heater temperature versus time to verify the findings of Tutorial 2.
Determine the numerical values of the time constant and of the gain of the process and comment on their values and units, particularly in relation to those obtained in
a). Calculate the time necessary for the temperature in the vessel to increase by 9oC, if the steam temperature increases again via a step change of 10oC at time 𝑡𝑡=0, and verify your findings via an updated Simulink model. Provide an updated plot of the time profile of the heater temperature vs time and compare the response with that obtained in a). (Answers:𝜏𝜏𝑝𝑝=761𝑠𝑠, 𝐾𝐾𝑝𝑝=0.91°C°C, 𝑡𝑡=3505𝑠𝑠)