## How to calculate maximum overshoot?

## 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.

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## RE: How to calculate maximum overshoot?

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## RE: How to calculate maximum overshoot?

Are you ready for the future?

## RE: How to calculate maximum overshoot?

TTFN

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## RE: How to calculate maximum overshoot?

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?

compesator λ * (s+α) / (s+β), then what I can say for λ,α,β ?

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## RE: How to calculate maximum overshoot?