Question No.1 (CLO-2, PLO-3) Consider the system of two tanks in series shown in Figure, where the volume of the liquid in each tank (V1 and V2) is constant. The volumetric flowrate of the feed stream is F (constant) and its temperature is T0(t) and varies significantly (disturbance). A heating coil has been installed in the first tank to control the temperature of its liquid content by adjusting the amount of heat exchanged between the heating medium and the liquid in the tank is Q(t) (manipulated variable). The model equations for the tanks are given by: The heating rate Q is the manipulated input, the inlet temperature T0 is the disturbance input, the outlet temperature T2 is the controlled output, and V1, V2, F, ρ, cp are constant parameters. Suppose that manipulation of the heating rate Q can be accomplished very quickly and that both temperatures T1 and T2 can be measured on-line with very fast sensors. We would like to build a cascade control system with T2 as the primary output and T1 as secondary output. (a) Draw the block diagram of a cascade control system, where the inner (secondary) loop regulates T1 and the outer (primary) loop regulates T2. (b) Build a model-based PI controller for the inner loop and a model-based PID controller with filter for the outer loop