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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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).