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
I am trying to simulate a specific wastewater process and want to
inspect how disturbances in the incoming flow could affect the
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
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.
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