P7.2.5** Consider the actuator, process and sensor models for the DO process (Figure P7.2.5) presented in Example 3.9: Actuator: For = (Far)spec k_a=0.25+0.001(Fair 500) Process: dCo, =k_a(Co, -C,,)-K., H.mart dt dCow --(Co-Co,-) Sensor: dt Co, - concentration of O2 in the reaction broth (initially 1.1x10* g-moles/1) . Co, - saturated concentration of O2 in the broth (2.20x104 g-moles/l) lo () () O Cogs - the measurement of the O2 concentration in the broth (initially 1.1x10* g-moles/1) Fair - the volumetric flow rate of air to the bio-reactor (500 cfm) Ko, -cellular uptake of Oz (1.98 g-moles 02/g-cells) kya - the overall liquid phase mass transfer coefficient for transport from the bubble surface to the bulk broth (initially Air . Variable Speed Air Compressor 0.25 s) T - broth temperature (35C) Figure P7.2.5 Schematic of a DO controller applied to a batch bio-reactor. t-time (s) V - the volume of broth in the bio-reactor (1000 1) x- constant cell concentration in the bio-reactor (0.25 g/1) Umax - maximum specific growth rate (5.56x10^s!) Is - the time constant of the DO sensor (30 s) Using the characteristic equation and the Routh stability criterion, determine the stability limits for the controller gain for a PI controller with a reset time equal to 30 s. 072** Sonsider the actuator, process and sensor models for the level in a tank process (Figure P7.2.5) presented in