Problem 3 Consider the single CSTR 1st order reaction below fitted with a feedback controller. For an anticipated CA setpoint (SP) change - step change - in the PL (Proportional-Integral) controller, determine the range of controller gain (1) Kc given t; = 1 min, and (2) integral time t, given Kc = 2 (%open)/(mol Cao/m), that will provide a stable control of the output variable CA. Shown below are the transfer functions for the dynamics of valve opening MV on Cao: Gy(s)=Cao(s)/MV(s); and the process dynamics Go(s)=Ca(s)/CAo(s). Time is in minutes. AC S CAO CA A-pure reactant S-pure solvent A B ra = -KCA Gp(s) 0.41667 1.667s+1 [(mol Ca/m)/(mol Cao/m3)] Gy(s) = 1, [(mol Cao/m*)/(%open)] / S+1