# Q. Consider the system of Figure 1. Let the digital controller be a variable gain K such that D(z)=

Q. Consider the system of Figure 1. Let the digital controller be a variable gain K such that D(z)= K .

(a) Determine the stability of the system for K=1.
(b) Sketch the Bode diagram and use this diagram to sketch the Nyquist diagram.
(c) Using MATLAB, plot the Bode diagram and Nyquist diagram and Compare with the results
in (b).
(d) If the system is stable, determine the gain and phase margins. If the system is unstable
find the value of K that gives a phase margin of 45°.
(e) From the Nyquist diagram, determine the value of K > 0 for which the system is
marginally stable.

0 for which the system is marginally stable.” src=”https://files.transtutors.com/cdn/qimg/19d569fab3644474aa8833219132e49c.jpg” aria-describedby=”gi4″> 2. Consider the system of Figure 1. Let the digital controller be a variable gain K such that D(z) K. Gp(s) R(s) E(s) C(s) T= 1s Figure 1 (a) Determine the stability of the system for K-1 (b) Sketch the Bode diagram and use this diagram to sketch the Nyquist diagram. (c) Using MATLAB, plot the Bode diagrahn and Nyquist diagram and Compare with the results in (b). (d) If the system is stable, determine the gain and phase margins. If the system is unstable find the value of K that gives a phase margin of 45°, (e) From the Nyquist diagram, determine the value of K> 0 for which the system is marginally stable.

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