Design of feedback controllers

IV.4 Design of feedback controllers 
The controller design problem is associated with three logical questions in series: 
•  What type of controller should be used for a given process – P, PI or PID ? 
•  What should be the best values of controller parameters – 
•  What performance criterion should be used for answering above two questions? 
Various performance criteria are available for the above purpose, both simple criteria and complex criteria. Following subsections give an account for the same. 
IV.4.1 Simple Performance Criteria 
The simple performance criteria are based on some characteristic features of closed loop response such as overshoot, rise time, settling time, decay ratio, frequency of oscillation of transient etc . Designer may choose one or more of such criteria in order to arrive at a set of controller parameters. Unfortunately, controller design based on multiple performance criteria often yields conflicting response characteristics. For an example, smaller value of gain reduces overshoot but at the cost of increase in settling time. The control engineers must use their experience and subjectively balance these conflicting characteristics. From all these criteria stated above, decay ratio has been the most popular. It has been seen that one-fourth decay ratio is a reasonable trade-off between rise time and settling time. 
IV.4.1.1 Example of one-fourth decay ratio 
Let us consider that a first order system is controlled by a PI controller, with . Then the closed loop response is given as 

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