In a perfectly stirred chemical reactor the following reactions occur:
Compound A is fed into the reactor inlet stream at constant concentration. Compound B is the desired product and its concentration is measured at the outlet of the reactor. For normal operation of the reactor, was derived by the following transfer function, which relates the concentration of compound B, CB, with the dilution rate (ratio between the input rate and the volume of liquid in the reactor, Q / V):
The concentration has units of mol / liter and the dilution rate has units min.
We intend to implement a system for monitoring the concentration of compound B by manipulating the flow rate of the incoming stream. The valve that operates the flow meter inlet and the outlet concentration can be assumed to have very fast dynamic response. To facilitate the design of the control system, we will also assume that your earnings are unitary.
With the controller in operation, it is intended that this effectively respond to changes of 0.1 mol / liter in the amount established in the concentration of compound B. The performance criteria previously defined for this system are:
- Stabilization time of 5 minutes.
- Ratio of superelevation less than 1/10
- Ratio of decay less than 1/4.
a) Using Simulink to simulate the behavior of the system, tune the controller using the method of continuous oscillation, using the Ziegler-Nichols relations for P, PI and PID control and relations of Tyreus-Luyben for PI and PID control. Describe the procedure used in tuning and display intermediate results and diagrams relevant blocks. Compare and discuss the results obtained with the different relationships and driver settings. Select suitable parameters for the operation of the controller.
b) Verify that the gain threshold identified above is in accordance with the criteria laid down by Routh.
c)Verify that the persistent deviation observed previously for operation with proportional control is consistent with the theoretically predicted.
d)Would it be appropriate to tune this system using the process reaction curve method? Justify.
e) Assume that in reality the concentration meter has a dynamic response of the first order with transport delay, and the time constant delay of 0.5 minutes and 0.06 minutes. Check how this fact affects the response of the control system whose parameters selected in a). Explain the behavioral changes observed. Without using a method of tuning, tune the parameters of PID controller in order to obtain an adequate response. Briefly illustrate the procedure and explain the reasons for their choices.