I'll very much appreciate it if someone can clarify to me the difference between pulse disturbances and step disturbances,and their effect on the studied system as I don't have any automatic control background. I am trying to simulate a specific wastewater process and want to inspect how disturbances in the incoming flow could affect the simulated system Thank you.
Lucy,
Easy. Imagine a simple system consisting of a weight hanging from a spring. Abruptly adding a second weight would be a step disturbance. The system will eventually settle down at a new position.
An impulse would be to abruptly kick the weight. The impulse disturbance lasts only an instant and the system eventually settles down at its former position.
An interesting bit of mathematics is that an impulse is the derivative of a step. For a LINEAR system the response to an impulse is the derivative of the response to a step.
An impulse is a bit of a mathematical ideal in that it has a constant area with infinitesimal width and infinite height. In reality every impulse takes a certain amount of time. In computer simulation the impulse cannot be shorter than one cycle scan. Therefore its height is the finite value of magnitude / scan time. One can consider such an impulse as being a positive step function followed by a negative step function of equal size.
In your water treatment case it might be more realistic to use a positive ramp followed by a negative ramp as the disturbance. Note that a ramp is the integral of a step and the response to a ramp is the same as the integral of the response to a step.
Walter.
Thank you very much for the clarification.
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