(IV.67)

Using the above expressions,

The optimal values for and are calculated by minimizing as follows,

(IV.68)

and

(IV.69)

There are two equations (IV.68-69) and two unknowns . It is however left for the reader as an exercise to solve these equations and calculate the designed value of controller parameters. In a similar fashion, the controller parameters can also be designed by optimizing IAE and ITAE.

Use of simple criteria for controller design such as one-fourth decay ratio, minimum settling time or minimum overshoot are easy to use, however, they seldom produce multiple solutions and hence additional criteria are needed to break the multiplicity. Time integral performance criteria such as ISE, IAE or ITAE are most effective, however, they are heavily dependent on mathematical models. Real time application of such techniques is cumbersome. Use of semi-emperical techniques, on the other hand, is effective yet easy to use. Process Reaction Curve Method , developed by Cohen and Coon, is one of such empirical tuning methods for feedback controllers.