Do I start by multiplying 18/s+3 * 1/s+3 = 18/(s+3)^(2)?
Then is it (18/(s+3)^(2))/(1+(18/(s+3)^(2)*4)) = 18 / ((s + 3)^2 * (72 / (s + 3)^2 + 1))?
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1 Answer
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The most left part in the 2nd line is still correct - however, the most right part is wrong. After multiplying both - numerator and denominator - with (s+3)² the whole expression reduces to
18/[(s+3)² + 72].
But note that this expression is the transfer function of the small inner loop only.
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\$\begingroup\$ Do I then multiply that by the Gain of 50? \$\endgroup\$ Commented Apr 8 at 13:55
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\$\begingroup\$ Is \$\dfrac{900}{s^2+6s+81}\$ the correct answer? \$\endgroup\$ Commented Apr 8 at 14:06
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\$\begingroup\$ @ NonComposMentis No - I don`t think so (the last numer (81) is not correct.) \$\endgroup\$– LvWCommented Apr 8 at 14:48
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\$\begingroup\$ @NonComposMentis No. It's \$\frac{900}{s^2\,+\,6s\,+\,981}\$:
ratsimp(solve(Eq(((vin-vout)*50-4*vout)*18/(s+3)*1/(s+3),vout),vout)[0]/vin)\$\endgroup\$ Commented Apr 8 at 14:49 -
\$\begingroup\$ @ periblepsis Instead of 972 I arrive at (972+9).....ahh I see, you have corrected the constant term. \$\endgroup\$– LvWCommented Apr 8 at 14:51
18/(s+3)^(2)becomes \$\dfrac{18}{(s+3)^2}\$ by using this:\$\dfrac{18}{(s+3)^2}\$<-- you ought to show your steps too because of the poor/difficult format of your final formula and, the lack of steps make it tricky to follow what you did. \$\endgroup\$