Hello, I had a question about control systems. In the following question why is
ID: 2293926 • Letter: H
Question
Hello, I had a question about control systems.
In the following question why is that one portion of the laplace transform considered the natural response and the second portion is considered the forced response?
In the second page how does Y(s) become 2/3, Its multiplied by s which goes to 0 and would multiply the whole thing by 0 no? Also conceptually what is Yss compared to Ess ?
I know its a bit blurry but on the second page in the first line it is taking the lim of sY(s) as s goes to 0.
Matwral and Fonedes posce (0)=1 natural cent nl s 3 ?? 3. conitant So record pause stopExplanation / Answer
In your solution, forced response is output due to input only i.e. unit step and natural response is just because of initial values. Complete output will be sum of both the responses.
No Y(s) has not become 2/3, Yss will be 2/3 its steady state output value in complete reponse there is s in forced response which will cancel there after by putting s=0 we will get 2/3. Conceptually Ess is steady state error which is given by lims=0 sE(s) where E(s)=R(s)-Y(s) and Yss is steady state value of output response.
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