Peak overshoot ratio

Problem 6.11 gives some very useful relationships between these parameters (damping coefTicient and time constant) and the shape of the response curve. There is a simple relationship between the peak overshoot ratio and the damping coefficient. Then the time constant can be calculated from the rise time and the damping coefficient. Refer to Prob. 6.11 for the definitions of these terms. 

As shown in Fig. 14.1, the steadystate gain and deadtime are obtained in the same way as with a first-order model. The damping coefficient can be calculated from the peak overshoot ratio, POR (see Prob. 6.11), using Eq. (14.3). 

Figure 9,7 Common performance criteria for PID tuning techniques. The peak overshoot is the ratio A/B, C/A is the decay ratio, and T is the period of oscillation.

Note that OS and DR are functions of only. For a second-order system, the decay ratio is constant for each successive pair of peaks. Figure 5.11 illustrates the dependence of overshoot and decay ratio on damping coefficient. 

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