R(s) H D(s) →→G₂OH(S) G(S) H(s) Q1) Consider the system given above with D(s) = answer the following questions. 9.4 (s+4

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R S H D S G Oh S G S H S Q1 Consider The System Given Above With D S Answer The Following Questions 9 4 S 4 1 (88.86 KiB) Viewed 43 times

R(s) H D(s) →→G₂OH(S) G(S) H(s) Q1) Consider the system given above with D(s) = answer the following questions. 9.4 (s+4.5) s(s+11.1) C(s) G(s) = 4, H(s) = 1 and a) Find the open-loop and the closed-loop transfer functions of the system when the sampling switches are closed and the ZOH block does not exist (in other words in the situation of continuous-time control system). Simulate the unit step response of the continuous closed-loop system in MATLAB/Simulink. Provide the screenshot of your block diagram in Simulink. Plot the output signals of the system. b) Find the bandwidth frequency of the continuous closed-loop system. Determine the sampling period (7) of the digital control system with respect to that frequency, which is appropriate for emulation design with Tustin Transformation. (You can find the bandwidth frequency via using a Matlab command.) c) Obtain the discrete transfer function D(z) of the controller employing Tustin Transformation with the T you determined in (b) above. d) Realize the digital controller D(z) in MATLAB/Simulink with standard programming and simulate the closed loop digital control system with this realized controller (Keep G(s) continuous in Simulink). Provide the screenshot of your block diagram in Simulink (I should be able to see the numeric gain values in your realization). Plot the control signal and the output signal of the system. 0.6 e-Tas Q2) Consider the system given above with G(s) = 0.35+1 H(S) = 1 where the time-delay is Ta = 20 ms and the sampling period is T = 20 ms. Then, answer the following questions. a) Draw the root locus plot for D (s) = K. b) Design a digital controller which makes the closed loop system steady state error zero to step inputs and the closed-loop system poles double on the real axis. c) Find the settling time and the overshoot of the digital control system with the controller you designed in (b). d) Simulate the response of the with your designed controller for unit step input in Simulink by constructing the block diagram. Provide its screenshot and the system response plot. Note: Q2 should be solved by hand instead of (d). You can verify your results by rlocus and sisotool commands in MATLAB.