# Exact definition of overshoot

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).

• Unfortunately like many engineering terms it is somewhat dependant on context and convention. In a control systems context it is easier to think of signals scaled to unity, it is generally more useful to state the relative overshoot than absolute. Whether you define transform to unity and overshoot relative to unity or percentage overshoot is up to whatever is more convenient for the data being compared but otherwise mathematically interconvertible – crasic Jul 13 '15 at 9:51
• @crasic What is the convention for overshoot apart from % overshoot. The way I have used overshoot is by scaling ss to unity but I have not explicitly stated that ss is scaled to unity. Is that okay? I need a reference because I have to mention this in a paper and I just don't want to say I just invented a measure. I wish to convey that these are some standard metrics used for control systems. – WYSIWYG Jul 13 '15 at 9:56
• Check this books.google.co.in/… – Umar Jul 13 '15 at 10:06
• I refer to the actual difference between steady state value and the peak as overshoot. – Umar Jul 13 '15 at 10:14
• @Umar - but regarding the 'steady state value' are you considering actual steady state or the expected steady state? – docscience Jul 16 '15 at 20:12

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.

When you mention an example where steady state is unity, that is normalized. Typically we are only interested in the percent overshoot, so unity makes it easy to scale. I.e. If a system has 10% overshoot on a system that's steady state is unity, the max peak is 1.10.

Your definition is identical to the control systems approach. Overshoot is simply the difference between the max peak and the steady state value. If a system has a quick response, it will typically have a larger overshoot value. If a system has a slow response, typically the overshoot is very small.

This image has a good breakdown of a response. You can see that the overshoot is simply the difference between the max and steady state value.

Hope this helps. If you have any other questions, please shoot them my way.

Good luck! - Josh

## EDIT

This is a page out of the book I use:

• I agree that % overshoot is more useful but I do not want percentages in my plots. What I am doubtful about is whether overshoot is defined as the max peak or the difference between max and steady state. Can you also provide me with a well known reference (I need to cite a reference). – WYSIWYG Jul 13 '15 at 9:53
• If we aren't talking about % overshoot, it is quite unuseful to talk about it as a max value or a diff between steady state and max. In both cases you would need the steady state value to make sense of it. – Josh Jobin Jul 13 '15 at 10:14
• I studied from "Modern Control Systems" by Richard C. Dorf & Robert H. Bishop. They always talk about overshoot as a percentage. So it is probably best to think percentage when you hear someone say "overshoot" – Josh Jobin Jul 13 '15 at 10:16
• I added a page out of my book that might be more clear. – Josh Jobin Jul 13 '15 at 10:20
• You could use per-unit overshoot, which is a more useful measure than percent – Chu Jul 13 '15 at 10:46

You should review the references cited in some of the answers given here, but regarding what you should use - I suggest you define your own. There are IEEE, ASME Standards, but as far as I'm aware no one defines a 'standard' way to define overshoot. You should define it as you see fit - for what works best in your situation.

When the step response is expressed as a non-dimensionalized equation, the definition of maximum percentage overshoot becomes easy. For some second-order systems, the original equation itself is a non-dimensionalized equation (when it has wn^2 in the numerator) and the steady-state value will be unity for a unit step response. That is not generally true for all second-order systems depending on the numerator. Therefore, we must ensure that the given step response equation is converted into a non-dimensionalized equation by dividing by an appropriate value of constant that would give unity steady-state value.