×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Are you an
Engineering professional?
Join Eng-Tips Forums!
• Talk With Other Members
• Be Notified Of Responses
• Keyword Search
Favorite Forums
• Automated Signatures
• Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

#### Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

# How to calculate maximum overshoot?2

## How to calculate maximum overshoot?

(OP)
Hello all. I have the open loop transfer function G(s) = (5s+2) / [s(s-2)]. How to calculate the maximum overshoot of the closed loop system when I have a unit step input? How many overshoots exist? Only the maximum one? Thank you.

Are you ready for the future?

### RE: How to calculate maximum overshoot?

(OP)
For my mind. We cannot use the formula exp[(-ζ/(1-ζ^2)^0.5)π] ?

Are you ready for the future?

### RE: How to calculate maximum overshoot?

The numbers involved are so simple I can't help but feel I'm doing someone's homework, but it's such an easy problem that I haven't wasted much time on it.

Why bother with formula short-cuts? There might be some esoteric formula that gives the answer in this specific case, but it's very easy just to find the exact solution and see for yourself the result. Given they're asking about multiple overshoots and G(s) has a zero, I wouldn't bother with zeta and damping factor and specific formulae. Here:

G(s) = (5s+2) / [s(s-2)]
T(s) = (5s+2) / [s(s-2) + 5s+2] (closed loop)
= (5s+2) / [(s+2)(s+1)] (factor the quadratic on the denominator)
Y(s) = (5s+2) / [s(s+2)(s+1)] (step response)
= 1/s + 3/(s+1) - 4/(s+2) (partial fraction decomposition)
y(t) = 1 + 3e^(-t) - 4e^(-2t) (inverse laplace)

Plot it. One overshoot. Find maximum by differentiating w.r.t. t and setting =0:

y'(t) = -3e^(-t) + 8e^(-2t)
y'(t) = 0 => 8e^(-2t) = 3e^(-t)
=> e^(-t) = 3/8
=> t = ln(8/3)

So max value is y(ln(8/3)) = 1 + 3*(3/8) - 4*(3/8)^2 = 25/16

Any errors are deliberately placed to prevent casual copying.

### RE: How to calculate maximum overshoot?

(OP)
Thank you for answers. And if I want to reduce the maximum overshoot 20% with a
compesator λ * (s+α) / (s+β), then what I can say for λ,α,β ?

Are you ready for the future?

### RE: How to calculate maximum overshoot?

Sorry mate, you've exhausted the work I'll do for you. Perhaps have a go yourself and let us know where you get stuck. I think you'll have a hard time convincing people it's "for my mind" though.

#### Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

#### Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

#### Resources

White Paper - Effects of AIA Quick Guide to UL 489 or UL 1077
The function of a circuit breaker is to provide overload (thermal) and short-circuit (magnetic) protection to a circuit and its downstream components. A circuit breaker functions like an airbag in a car, protecting circuit components and people by tripping the circuit to interrupt the current flow if it detects a fault condition in the control system. Download Now
White Paper - Guide to Integrate Large-Format Additive
As with any new technology, getting into large-format 3D printing begins with investigation. The first question may be a simple one: what does “large-format” mean? For 3D printers, “large” is a relative term. Many extrusion-based (FFF) 3D printers are referred to as desktop machines, because they fit on table space. Some of these have very respectable build volumes – but when it comes to “large-format,” the machines will need their own dedicated floor space. Large-format 3D printers have significant build volumes and are most often found in professional settings, like manufacturing facilities and R&D centers. Download Now

Close Box

# Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

• Talk To Other Members
• Notification Of Responses To Questions
• Favorite Forums One Click Access
• Keyword Search Of All Posts, And More...

Register now while it's still free!