The transfer functions for the components of a system are gi

The transfer functions for the components of a system are given as follows: G_v(S) = 6.4/7.1s + 1 G_p(s) = 0.58e^-5s/84.3s + 1 G_M(s) = 1/1.1s + 1 Find the optimal parameters for a PI controller that minimized ISE for a step change in set point Find the optimal parameters for a PI controller that minimized ITAE for a step change in set point Find the optimal parameters for a PI controller that minimized IAE for a step change in set point Hand in a copy of your VISSIM program and the step response output using the optimal parameters for each controller design.

Solution

a) Gv(s) = 6.4/(1+7.1s)

alpha = 6.4/7.1 = 0.9

PI controller , Kp = 0.8 Ki = 1.2

b) Gm(S) = 1/1.1s + 1

alpha = 1/1.1 = 0.91