Question number 1 thanks Hand in the problems below .the work you submit must be

Question

Question number 1 thanks

Hand in the problems below .the work you submit must be your own and on paper (stapled) .electronic submission are not accepted .show all work used to arrive at an answer .Box the answers. Text refers to the 7 th edition of Thomas and Rosa. A PI controller (Proportional - integral controller )" is a feedback controller which drives the plant to be controlled with a weighted sum of the error (difference between the output and desire set-point ) and the integral of that value " (from ) such that v0(t) = vs(t) +K o v s (x) dx where K is a constant and vs is the error signal. Draw this circuit on your solutions and show the applications of KVL, KCL and element constraints that are used to show that the PI output above is achieved by the circuit . Also, determine the value of K for this circuit. Assume that both vo and vs are equal to 0 at t=0. In this circu, R1 = 200 Ohm, R2 =300 Ohm, and R3 =50 Ohm, also, Vs1 =5 V and Vs2 =10 V. The switch is in upper position . The capacitor value is 1 muF. Which if any of the following variables in the above circuit are state variables? [ic vc iR1 VR 2]?

Explanation / Answer

apply KCL :: current through 20 k ohm reisitor = current through capacitor  

   Vs(t)/20   = i

    Vs(t)/20   = C*dVc/dt  

    Vc = integration[ Vs*dt]/(20*c)

now    apply KvL ::; V(s) = vo(t) - Vc(t)

                                Vo(t) = Vs -Vc(t)

                                       = Vs(t) - integration[ Vs*dt]/(20*c)

                                   

hence   k =1/(20*c) =500

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