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Observation of a Typical Open Loop Dynamic Responses of Second Order Systems

Dynamic Responses
In vibration and control, we always deal with the following three types of the dynamic responses from a system due to the step input to that system. These responses are: over damped, critically damped, and under damped signals.

  • Overdamped - where the damping ratio is higher than the expected or optimum. As the name suggests, 'damped' means to stabilize or settle down a signal, and over-damped is in the same perspective that the signal is sized or filtered overly to reach a desired value. In the following response curves, the yellow colored signal represents an overdamped response.
  • Underdamped - where the damping ratio is below the desired limit. Again, from its title, 'under' defines that the signal is not sufficiently filtered or processed to reach the optimum or desired level. The light blue colored signal in the following response curve shows the underdamped signal response. We see that the signal has couple of overshoots and undershoots until it settles down to the desired value.
  • Critically Damped - This is the response that we desire to achieve, which means that the system response to the step input should have a shape that is shown by the pink colored signal in the following response curve.

SIMULINK Representation
The following block diagram represents the generation of three types of responses using three SIMULINK transfer function blocks.

Open-Loop Dynamic Responses

Response Curves

Response Curves
#OverDamped   #UnderDamped   #CriticallyDamped   #DynamicResponse

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