A process consisting of two CSTR's in series is reasonably well modeled by the following transfer...

 

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A process consisting of two CSTR's in series is reasonably well modeled by the following transfer function model: y(s) = 1.5 (12s + 1)(5s + 1) ¹(s) The time constants are in minutes, and the valve and sensor dynamics may be considered negligible. a) Show that under proportional feedback control in continuous time, the closed loop system is always stable, for all values of proportional controller gain K. positive. b) Under digital proportional feedback control, incorporating a ZOH, find the range of Ke values for which the closed-loop system will remain stable if the sample time T= 1 min. Use Simulink to check your result. c) Repeat part (b) for 7= 5 min. d) Comment on the effect of sampling time on the range of K, values required for closed loop stability. A process consisting of two CSTR's in series is reasonably well modeled by the following transfer function model: y(s) = 1.5 (12s + 1)(5s + 1) ¹(s) The time constants are in minutes, and the valve and sensor dynamics may be considered negligible. a) Show that under proportional feedback control in continuous time, the closed loop system is always stable, for all values of proportional controller gain K. positive. b) Under digital proportional feedback control, incorporating a ZOH, find the range of Ke values for which the closed-loop system will remain stable if the sample time T= 1 min. Use Simulink to check your result. c) Repeat part (b) for 7= 5 min. d) Comment on the effect of sampling time on the range of K, values required for closed loop stability.