Assignment 5 Solutions 2009

System will not show oscillatory behavior as it does

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Unformatted text preview: Root­Locus for PI controller for t I = 1 (the dot at k c = -1.2 ). Figure 11: Root­Locus for PI controller for t I = 0.2 (the dot at k c = -1.2 ) Figure 12: Root­Locus for PI controller for t I = 1 (the dot at k c = -20 ). The fo llowing can be concluded: · The system is always stable for any value o f the controller parameters both for P and PI controllers as long as the controller gain is negat ive (reverse action) · The addit io n of integral act ion increases the order of the system and introduces a pole at the origin · For P­controller the po les are always real while for PI controller, they may beco me complex for certain co mbinat ion of the controller parameters To apply the ZN method, we need to incorporate a small delay; otherwise, the system will not show oscillatory behavior as it does not have a crossover frequency. Adding a delay o f 0.1, the modified Root­Locus plot shown in Figure 13 is obtained. We can now observe the changes in the locus due to the incorporation o f the delay. There is now a regio n in the Root­Locus, which crosses the imaginary axis, thus, indicat ing a region o f unstable operation. The ult imate gain is k cu = -7.5 , with a period of oscillat ion according to Figure 14 (showing the t ime response for gain k c = -7.5 ) with Pu = 0.65 . Consequent ly, the ZN settings can be obtained fro m Table 12.3 they are k cu = -3.375 and t I = 0.54 . Figure 15 illustrates the closed­loop response for a set­ point change using the tuning parameters. Figure 13: k c = -7.5 (P controller) with addit ion o f a time delay of 0.1. Figure 14: k c = -7.5 (P controller) with addit ion o f a time delay of 0.1. Figure 14: Closed­Loop response with PI using ZN settings ( k cu = -3.375 and t I = 0.54 ). 3. For the heat­exchanger system in C­Station, we would like to implement a feedback control system using a PID controller by contr...
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This note was uploaded on 01/12/2014 for the course CHE 4198 taught by Professor Hjortso,m during the Fall '08 term at LSU.

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