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Address the items listed below and prepare a report with your answers using a word processor of your choice, such as Microsoft Word or Apple Pages, for example. Include the project title in your report, along with your name, and date of submission. Handwritten reports are not acceptable. Fill out the first page of this handout, and staple your report behind that page. Consider the standard feedback closed-loop configuration shown in the figure below, with transfer functions -Os (1) TS +1 K G(s) Ga(s) = K2 Gm (8) = Km and PI controller Gc(s) = K (1++) and where R' (s) is the set point, Y'(s) is the process output, U'(s) is the process input, Y. (s) is the measured output, D' (s) is a disturbance, and E'(s) = R' (s) - Y'(s) is the feedback error. The units of the Laplace variable s are sec-1 D'(s) GAS) R'(s)- KM E's). U's) GAS) G(S) OTY'(s) Y" (s) Gm(s) Figure 1: Closed-loop system with set-point signal R' (s), output Y'(s), input U'(s), disturbance D'(s), measurement Y(s), and feedback error E'(s). Create a MATLAB M-file that simulates the servo and regulation responses for the output signal y'(t) and input signal '(t), where t is the time variable. Servo tests are to be carried out with the following unit-step set-point signal r' (t) = = { i 0 1 t<0 t> 0 and regulation tests with the following unit-step disturbance signal d'(t) = t<0 t> 0
Problem 1. 1 Consider the case where the transfer-function parameters are fixed to the values K = 2,7 = 10,0 = 5, K2=1, Km = 1 Set the controller to P-only mode, and tune the controller (i.e, find a value of Kc) with the PI controller turned using: (a) The Ziegler-Nichols tuning method. (b) The Cohen-Coon tuning method. Document the values of the tuning parameters in a table in your report 2 Modify your MATLAB M-file to carry out the simulation of two servo-response tests respectively using: (a) The Ziegler-Nichols tuning method. (b) The Cohen-Coon tuning method. Create a graph consisting of 3 plots in one page, as follows: (a) The top plot should show the set point and each of the two output response tests, as a function of time. This plot should contain a legend, given that more than one signal is plotted as a function of time. (b) The middle plot should show each of the two input responses as a function of time. (c) The bottom plot should show the disturbance as a function of time. (d) The time axis in all graphs should be long enough so that the onset of steady-state can be observed. (e) You must use the MATLAB print command to generate a TIFF file for the graph. Include the TIFF-file graph in your report, and write a brief paragraph describing the nature of the responses observed (oscillatory or non-oscillatory, overshoot, decay ratio if oscillations are present, etc.). Discuss whether offset is eliminated. Discuss which controller tuning method is more aggressive. Include your MATLAB M-file in an Appendix of the report (note that the Appendix must placed at the end of the report, after the conclusion of your presentation of the results for the last problem in this project). Notes: • Use different line types for each of curve in a given plot. • Always include a legend when the plot has more than one curve. • The title of the top plot should read "COMPUTER ASSIGNMENT, Problem 1(b)", followed by your name, • Use the MATLAB commands subplot (131), subplot (132), subplot (133), grid, xlabel, ylabel, and legend. You may also find it useful to invoke the command axis to adjust the maximal and minimal values of your graph to better display the curves.
Problem 2. 1 Consider the case where the process parameters are again as in Problem 1: K=2,7 = 10,0 = 5, Kd = 1, Km=1 Set the controller to PI mode, and tune the controller (i.e, find a values of K and TI) for a servo test using: (a) The Ziegler-Nichols tuning method. (b) The Cohen-Coon tuning method. (c) The minimum ITAE criterion method. Document the values of the tuning parameters in a table in your report. 2 Modify your MATLAB M-file to carry out the simulation of three servo-response tests respectively using: (a) The Ziegler-Nichols tuning method (b) The Cohen-Coon tuning method. (c) The minimum ITAE criterion method. Create a graph consisting of 3 plots in one page, as follows: (a) The top plot should show the set point and each of the three output response tests, as a function of time. This plot should contain a legend, given that more than one signal is plotted as a function of time. (b) The middle plot should show each of the two input responses as a function of time. (c) The bottom plot should show the disturbance as a function of time. (d) The time axis in all graphs should be long enough so that the onset of steady-state can be observed. (e) You must use the MATLAB print command to generate a TIFF file for the graph. Include the TIFF-file graph in your report, and write a brief paragraph describing the nature of the responses observed (oscillatory or non-oscillatory, overshoot, decay ratio if oscillations are present, etc.). Discuss whether offset is eliminated. Discuss which controller tuning method is more aggressive. Include your MATLAB M-file in an appendix of the report. Notes: Use different line types for each of curve in a given plot. . Always include a legend when the plot has more than one curve. The title of the top plot should read "COMPUTER ASSIGNMENT, Problem 2(b)", followed by your name. Use the MATLAB commands subplot(131), subplot (132), subplot (133), grid, xlabel, ylabel, and legend. You may also find it useful to invoke the command axis to adjust the maximal and minimal values of your graph to better display the curves.