The liquid level in a drum boiler used in the utilities section of a research laboratory complex is controlled by the feedwater flowrate as indicated in Figure P15.3. An approximate transfer function model representing this process is given by: y(s)=s(5s+1)0.1(12s)u(s) where, in terms of deviation variabies, y is the drum level (in inches) and u is the feedwater flowrate (in lb/hr ), time is in minutes. Figure P15.3. It is known that there are no significant sensor dynamics, but that the valve dynamics are represented by: gv(s)=(0.8s+1)1.2 (a) Design a proportional controller for this process by generating an appropriate Bode diagram and using the Bode stability criterion in conjunction with a gain margin of 1.7. Redesign the proportional controller using a phase margin of 30, Which controller is more conservative? (b) Using a control system simulation package, implement the two controllers obtained in (a) and obtain a simulation of the closed-loop system response to a step change of 5 inches in the drum level set-point. Plot both the y and u response in each case. Briefly evaluate the performance of each controller