Using the Cohen and Coon tuning method, develop initial controller settings for a PI controller applied to a temperature control loop on a water$-$cooled CSTR that operate under regulatory control. Based on these initial controller settings, determine the characteristic equation. By observing the process operation, it has been determined that the process gain is approximately $1F-h\frac{r}{l}b.$ The response time of the process has been estimated to be $1$ minutes, and the amount of deadtime in the process is $0\mathrm{.}5$ minute.