This week, control theory and optimization...
Some minor inaccuracies in slides have been corrected in the online copies linked from the course materials page...[or will be as soon as I can get powerpoint with the right fonts:) - the key error is in the calculation of the steady state error of the proportional controller - for some reason, there's a subtraction of the two terms for U(s) where it should be +
(KUs + Rc) / (s(s+K)
I think {need to check this:) it kind of makes sense (if the completion rate increases, the admission rate should increase....)
then when we take the limit of s(U(s), as s->0, we'll get Us + Rc/K
so ess (error in steady state) is Us - (Us + Rc/K) which gives us -Rc/K
(i.e. the answer is right, but the system response wasn't...will check and correct soon...
again, to note, the chapter on control theory in Keshav's book is very clear if you want alternative source + some nice example problems.
Some minor inaccuracies in slides have been corrected in the online copies linked from the course materials page...[or will be as soon as I can get powerpoint with the right fonts:) - the key error is in the calculation of the steady state error of the proportional controller - for some reason, there's a subtraction of the two terms for U(s) where it should be +
(KUs + Rc) / (s(s+K)
I think {need to check this:) it kind of makes sense (if the completion rate increases, the admission rate should increase....)
then when we take the limit of s(U(s), as s->0, we'll get Us + Rc/K
so ess (error in steady state) is Us - (Us + Rc/K) which gives us -Rc/K
(i.e. the answer is right, but the system response wasn't...will check and correct soon...
again, to note, the chapter on control theory in Keshav's book is very clear if you want alternative source + some nice example problems.
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