Question: (a) When pumping or compression costs are high, incentive exists for controlling flows at minimum cost. Suggest approaches for controlling flow rates with low pressure drops across sensors and valves.

(b) Discuss the response of systems when the sensor, rather than the valve, fails to function properly. How can safety be ensured in such situations?

(c) Discuss a quick method for determining the maximum number of variables that can be controlled for a completed process design. Assume that a detailed process schematic (piping and instrumentation drawing) is available, but a detailed mathematical model is not.

(d) Discuss why controllability is analyzed with a linear model whereas the operating window is determined based on a nonlinear model.

(e) If a system is controllable and has a sufficient operating window, will all possible loop pairings provide stable dynamic performance (assuming proper constant tuning)?

(f) If the process dynamics are overdamped, would variable values between two steady states within the operating window remain within the window during the transient response?