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1. Using SIMULINK, create the following control system block diagram [F(s) 4e Gd (3s+1) 10 &e-4 Ge C1(s) c's(s) F(s) (10s+1 G, (4s+1) G, a. Using any appropriate method, tune PI controller for this loop. Show the response of your control system to unit increase in setpoint. Show the response of your control system to a 2 unit increase in the disturbance. Comment on the behavior. b. Design and implement feedforward control system in your SIMULINK diagram for the system that can help reject the disturbance. Assume you have fast and properly calibrated sensor that can measure the disturbance FA' Show how well your control system responds now with the feedforward control system in place to the same unit increase in FA' like in Part A Comment on the behavior. c. It turns out that the time delay in the process is not units as originally thought, but is 6 time units In this case, test to see your feedforward controller still functions well to the unit increase in FA' If does not perform well, can you redesign/retune better feedforward controller that can realized? 2. Let's look at this same system again. 4e Ga (3s+1) 10 8e G. C,(s) c(s) [2s+1 Fg(s) (10s+1) Gp (4s+1) G. a. Design and implement Smith Predictor control structure for this system SIMULINK. b. Tune PI controller for this new Smith Predictor structure using any appropriate tuning method. Comment on the tuning that possible for this PI controller as compared to the original PI controller the simple feedback. You may for example want to determine the ultimate gain for the original feedback loop and for the new Smith Predictor structure c. Show how your Smith Predictor structure with your tuned PI controller responds to 2 unit increase in setpoint Show the response of your new system to unit increase in the disturbance. Comment on the behavior d. Investigate and comment on how much of process time delay error you can tolerate in your Smith Predictor process model before the control system performance worse than your simple feedback controlsystem e. Investigate and comment on how much of process time constant error you can tolerate in your Smith Predictor process model before the control system performance worse than your simple feedback control system. 3. You are in charge of pharmaceutical production process in which toxic trace impurity must be controlled to not exceed 50ppm or your product can harm people. As result, your company policy is that no product with an impurity concentration higher than 30 ppm allowed to be sold. Your current target for the impurity concentration in your process has been set at 25ppm as result. Given the data in the IMPURITY MEASUREMENT DATA, which represents 10 measurements taken every hour for 12 hours of the concentration of the trace impurity in the pharmaceutical product stream while the process deemed to be good control, answer the following questions a. Your manager tells you to implement standard +/- 3o control limits or a Shewart Chart to monitor this impurity concentration and alert operators to potential problems Given the data, what would be your Upper Control Limit (UCL) and Lower Control Limit (LCL) for the average impurity concentration from each measurement set? b. you choose these +/ 3a limits for your Shewart Chart (x) control chart. what the probability of making Type Error (recall Type Error is rejecting the null hypothesis in statistical test when iti in fact true. i.e. here calling the process out of control because data point exceeds +/- 3o limits when the process is still centered with its average impurity concentration the target)? c. you choose these +/- 3o limits for your Shewart Chart (x) control chart. what the probability of making Type Error (recall Type Error is accepting the null hypothesis in statistical test when it i in fact false i.e here calling the process in control when in fact the average impurity concentration has deviated from the target)? In determining the Type 2 Error rate, you have decide how large of shift in the mean important. Here ,it would be important the average impurity had shifted to 30ppm, i.e. the maximum concentration allowed by company policy. d. What should you set as the UCL and LCL on an Control Chart for this process as well that can be used to determine faults with the measurements and other issues well? 4. In addition to single measurement set tests like Shewart Chart, many SPC applications use some version of Pattern Tests as well. In the case of your company, they decide to implement the Western Electric Rules but they want to know what their Type Error rate will be with this new rule set versus standard Shewart Chart (x) control chart analysis. Answer the following questions a. What the Type error rate for each of the rules in the Western Electric Rules set? b. What the total Type error rate for the full combination of Western Electric Rules?

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