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To obtain a desirable step response of a closed-loop system, we know that the poles of the s-domain closed-loop transfer function T(s) should be at s = -1.2 + j1.6.

find the z-domain poles of the equivalent discrete-time closed-loop transfer function, we will require a sampling frequency of equal to or more than 20 rad/s or3.183 Hz. What is the condition based on which this limit is derived? Give a brief explanațion to support your answer b) Based on the range specified in Question 1a), choose your own sampling frequency, and write it down clearly in your answer script. Based on this value of sampling frequency, find the z-domain poles of the equivalent discrete-time closed-loop transfer function. Express your answer in the form of z, = a t jb. c) A plant is regulated using a digital control system as shown in Figure 1 where the sampling frequency is based on that you have chosen in Question 1b) and discrete-time transfer function for D/A converter + plant is given by G_{d}(z)=\frac{z+0.5}{z-p} where P has a value determined in Preamble. Determine K(z) so that the closed-loop system transfer function has a DC gain of 1,its poles are ęqual to those determined in Question 1b), and it has no zero. Write your final answer in the form K(z) \frac{b_{0}+b_{1} z^{-1}+b_{2} z^{-2}+\cdots}{1+c_{1} z^{-1}+c_{2} z^{-2}+c_{3} z^{-3}+\cdots}

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