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% % % % define the loop transfer function of a PID (s^2Kd + sKp +Ki)/s in cascade with a 2nd order plant 1/(s+a)(s+b) % GH(s) % The characteristic
The objective of this project is to utilize root contours as a way to select a set of admissible parameters {KP, KI, KD} based on a damping ratio and settling time criteria. Here we will use the “same type of criterion” as in Matlab Exercise 3 to define the region of the s-plane with admissible parameters.20 < P.O < 252 <= Ts <= 1.0 secsettling band is < 5% (use #TC=3)1) Make sure that you can get the m-file to run, and experiment with the values of the gains defining the black asterisks, and the ranges of the gains. You do not need to turn anything in for this part2) Add overlays showing the admissible regions to the plot that shows all contours (the last one plotted in the code). Show with the provided gains.3) Try to find a few (more than 2 less than 5) sets of parameters that meet the specifications. These should have significantly differentvalues of {KP, KI, KD}.4) Verify the results by drawing the block diagram and finding C(s)/R(s) for the closed loop system and then use Matlab to plot the step response. Hint try using the function step(num,den, time). You may need the Matlab controls toolbox, older versions of student Matlab have this built in, otherwise be creative…Matlab code is attached.Any help would be greatly appreciated. Thank you.
