Process Control and Instrumentation
A typical example of a physical system with under damped characteristic is a

Spring loaded diaphragm valve
CSTR with first order reaction
U-tube manometer
Thermocouple kept immersed in a liquid filled thermowell

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Process Control and Instrumentation
In a closed loop system, the process to be controlled is an integrating process with transfer function l/2s. The controller proposed to be used in an integral controller with transfer function 1/T₁s. When a step change in set point is applied to such a closed loop system, the controlled variable will exhibit

Undamped response
Overdamped response
Unstable response
Underdamped response

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