Question: Sketch the root locus diagram for the loops of Problem. Use the first-order Padt approximation to the dead time when necessary.
Problem: Steam Flow Control Loop. A process heater requires 3500 lb/h of steam to heat a process fluid. A control valve and linear flow transmitter are installed to control the flow of the steam. The conditions are as follows: Control valve upstream conditions are 45 psig, superheated 50°F; downstream pressure is 20 psig; critical flow factor is 0.8. A linear valve sized for 100% overcapacity is proposed. The flow transmitter is sized to measure a maximum flow of 5000 lb/h, and its output is linear with flow; that is, it has a built-in square root extractor. Draw the block diagram for the flow control loop, showing all transfer functions, and write the closed-loop transfer function. Use a proportional-integral (PI) feedback controller with the integral time set equal to the time constant of the control valve. Find the time constant of the loop for Kc = 0.5 %CO/%TO.