Consider a process with transfer function( )p K G s s = and let1v mG G= = . a) (10 points) Find the conditions for the parameters of a PI controller that ensure that the closed loop system is stable. b) (10 points) Show that (assuming that the conditions found in a) above are met) implementing a PI controller will result in an oscillatory closed loop behavior if4c IKK . c) (20 points) Show that the amplitude of the oscillations of the closed system to a unit change in setpoint DECREASES ascK increases. This is contrary to the tuning guidelines regarding the selection of controller parameters that we discussed in the past (e.g., figure 8.17 SEMD). Please explain