I am a computational biologist and am working on some aspects of control theory in biological systems. Since control theory concepts are not well known among biologists, I need a good standard reference for certain terms. I was thinking of citing a control theory textbook. Now I have a doubt regarding the definition of overshoot.
The book — Modern Control Engineering by Ogata defines maximum overshoot as:
The maximum overshoot is the maximum peak value of the response curve
measured from unity. If the final steady-state value of the response differs from unity, then it is common to use the maximum percent overshoot.
It does not say what maximum overshoot is, when the final steady state is not unity. In my analysis, at present, I am defining overshoot as the max value above the tolerance zone normalized by the steady state value. I am not sure if this fits the above definition (steady state being scaled to unity, however I do not report the steady state anywhere).
When I google overshoot I see images that have labelled overshoot differently which is either of these two:
- The dynamic maximum
- The difference between the maximum and the steady state.
Can someone please let me know what is the correct definition of overshoot (not percentage overshoot)? I need a good citable reference (a book or a review).
Best Answer
WYSIWIG - as you need to cite a reference:
G.F. Franklin, J.D. Powell and A. Enami-Naeini: Feedback Control of Dynamic Systems, Prentice Hall, 4th edition:
(Quote)
The requirements for a step response are expressed in terms of the standard quantities illustrated in Fig. 3.27:
...
3.) The overshoot Mp is the maximum amount the system overshoots its final value divided by its final value (and often expressed as percentage).
EDIT/UPDATE:
Karl Johan Astroem, Richard M. Murray (Princeton University Press)
"Feedback Systems":
Quote: The overshoot Mp is the percentage of the final value by which the signal initially rises above the final value. This usually assumes that future values of the signal do not overshoot the final value by more than this initial transient, otherwise the term can be ambiguous.