# Calculate the steady-state error.

A robot is programmed to have a prescribed action. Consider a robot tool that is to follow a saw tooth path, as shown in the attachment. The transfer function of the plant is G(s)=(50(s+1))/(s(s+6)(s+9)) for the closed-loop system shown in the attachment. Calculate the steady state-error

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#### Solution Preview

First we have to find the laplace transform of the input function. It is a periodic function with T=20. Then it is enough to find the laplace transform of its main harmonic and call it F(s) and the laplace transform of the input will become:

F(s)/(1-exp(-20s))

But first we have to find the function of the main period in time domain. According to the given diagram the function ...

#### Solution Summary

First we have to find the Laplace transform of the input function. It is a periodic function with T=20. Then it is enough to find the laplace transform of its main harmonic and call it F(s) and the laplace transform of the input will become: F(s)/(1-exp(-20s)). Using the final value theorem we get: ess= lim sE(s).