Please Solve Just Question 6 And 7 1 (59.58 KiB) Viewed 43 times
T R(s) C(s) D(s) H(s) K 10 ,H(s) = 1 and answer Consider the system given above with D(s) = ½‚G(s) = the following questions. (s+2) (s+4) 1) 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 when K=0.5. Plot the control and output signals of the system. 2) What should the sampling period of the digital control system for K=1 be at most considering the primary strip in which the continuous closed-loop poles in s-domain should lie? 3) Find the discrete-time transfer function where K is remained as a parameter. C(Z) R(z) 4) Find the interval for K where the closed-loop discrete-time system is stable via employing Jury test. 5) Find the steady state errors (ess) for K=1 when (i) the unit step input, (ii) the unit ramp input and (iii) unit parabolic input is applied. T GZOH(S) G(S)
6) Find the approximate settling time and the overshoot of the system output for K=1 and T=2 s. = 0.5 T z Z-1 7) Consider the digital controller transfer function as D(z) and simulate the unit step response of the digital control system in MATLAB/Simulink for the sampling period values T= 0.5, T=1, T=2, T=3, T=4 s. (Keep G(s) continuous in Simulink.) a. Plot the output of the system for those simulations with different sampling periods, together with the continuous output you obtained in Question 1. b. Plot the discrete-time control signal of the system for those simulations with different sampling periods, together with the continuous control signal you obtained in Question 1. c. Find the sampling period value which makes the system marginally stable from the interval you found in Question 4. Simulate the unit step response of the system for this sampling period value and plot it. Note 1: Solve the Ques. 1-6 by hand. You can verify your results for Qs. 1-3 by Matlab commands. Also, you can verify your answers for Qs. 4, 5 and 6 via the simulations in Q7.
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