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Consider cascade control as shown below: with G v = 5 s + 1 ; G p 1 = 4 ( 4 s + 1

Consider cascade control as shown below: with
Gv=5s+1;Gp1=4(4s+1)(2s+1)
Gp2=1;Gd2=1;Gm1=0.05
Gm2=0.2;Gd1=13s+1
Derive the closed-loop transfer functions for Y1D1 and Y1Dz as a function of Kc1 and Kc2
Examine the effect of Kc2 on the critical gain of Kc1 by varying Kc2 from 1 to 20. Do a comparative analysis on what values of Kc2 do the benefits of cascade control seem to be less important?
Suppose a unit step change in secondary disturbance variable D2 occurred, calculate the resulting offset assuming Kc2=4
Suppose if instead of a proportional controller, PI controller is used in Gc1 with I1=5 mins, calculate the ultimate controller gain. Provide your analysis on whether the offset with a unit step change in D2 be avoided with PI controller
I need appropriate results please
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