For the series reactors in Figure Q8.15, the outlet concentration is controlled at 0.414 mole/m3 by adjusting the inlet concentration with a proportional only feedback controller. At the initial base case operation, the valve is (a) Determine whether the reactors are stable without feedback control. (b) Determine the closed-loop transfer function for a set point response. (c) By analyzing the denominator of the transfer function (the characteristic polynomial), determine the stability of the feedback system for controller gain, Kc, values of (i) 0.0, (ii) 121, (iii) 605, and (iv) 2420 (in % valve opening/mole/m3). (d) By analyzing the total closed-loop transfer function, determine the steady-state offset for a set point change with controller gain, Kc, values of (i) 0.0, (ii) 121, (iii) 605, and (iv) 2420 (in %valve opening/mole/m3). (e) Without simulating, sketch the general shape of the dynamic response for a set point step change for each of the cases in (c) and (d) above.
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