Process Control and Instrumentation
In second order underdamped system,

Decay ratio = (overshoot)²
Decay ratio = overshoot
Overshoot increases for increasing damping co-efficient
Large damping co-efficient means smaller damping

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Process Control and Instrumentation
Suppose that the gain, time constant and dead time of a process with the following transfer function:Gc(s) = 10 exp( - 0.1s)/(0.5s + 1) are known with a possible error of ± 20% of their values. The largest permissible gain Kc of a proportional controller needs to be calculated below taking the values of process gain, time constant and dead time as

12, 0.4, 0.08
12, 0.6, 0.12
8, 0.6, 0.12
8, 0.6, 0.08

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