Part $1$: Dynamic Modeling

A jacketed stirred tank is used to cool a process by causing cooling water to flow

trhough the jackes as shown in Figure $1.$ The process input variable is the flow of cooling water

$f_c(t),$ The inlet temperature of the process stream $T_i(t)$ is considered as a disturbance variable.

The output of interest is the outlet temperature of the process and the water $T(t),T_c(t),$

Figure $1$ Jacketed process

Part $2$: Process Identification

Experimental data of the process is provided within the Project$\_7.$m file.

$1-$ Use data to derive a reasonable model between $T(s)$ and $F_c(s).$ Compare results obtained

from dynamic model and explain the difference in results.

$2-$ Use Smith's method as well as nonlinear regression based on MATLAB to identify a model

$3-$ Provide a comparison of the model parameters and the sum of squared errors for each model

$4-$ Plot the step responses of fitted models with the original data.

$5-$ Conclude

Part $3$: Controller Design & Tuning

In what follows, use the identified FOPTD model from Part $2.$ For each question,

compare the designed controllers for unit step changes in the set point and disturbances.

Consider the plot of results in a single graph, for a clear comparative analysis.

$1-$ Based on Direct Synthesis Method calculate PID controller settings for the process, for

three different values of ${}_c$ of your choice.

$2-$ Using the Internal Model Control method, design a PI and PID controller for three different

values of ${}_c.$

$3-$ Design a PI and PID controller using ITAE, AMIGO and Z$-$N methods.

$4-$ Compare the performance of the controllers developed previously

$5-$ Conclude