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3. (3 points) Consider the level control loop shown below. f(t), gpm 10 ht) fl), som The controller is proportional and the gain is expressed in %C0/%TO. At steady state, the controller signal is 50% CO. This corresponds to a steady state height of h = 6 ft, which is also the setpoint. The output of the controller is expressed in %TO. It has a span of 0 to 20 ft. Assume that the valve fails closed for this process. At time t=0, the flowrate increases from its steady state operation conditions of f, = f. = 150 gpm to fi=170 gpm and comes to a new steady state height of 8 ft. At this new steady state, the output of the controller is 60% CO. a. Determine the gain of the level transmitter, Km in %TO/ft. b. Determine the gain of the transfer function H(t)/Fi'(t). c. Determine the error at the new steady state in ft and %CO. d. What is the correct sign of Kc? Determine the gain of the controller. (Hint: This is not a closed loop response problem. Use definitions from transmitter and controller transfer functions here)