Question

1. A unity feedback system has open-loop transfer function given by an 100 G(s)s2)(s +4) a. Use analytical techniques (i.e. without using any plots) to estimate the closed-loop: i. Resonant frequency, w (8 marks) ii. Resonance peak, Mp (in decibels) (2 marks) i. Phase at w = 3rad/s (2 marks) b. Obtain a table for the response of the open-loop transfer function for a set S of frequency values, where S {1.5,3,5,7, 10, 15, 20} rad/s (8 marks) Hence draw the magnitude versus phase plot of the open-loop transfer func- tion on the Nichols chart provided C. (4 marks) d. Use your Nichols plot to: i. Estimate the closed-loop resonant frequency, w,, and resonance peak Mp (in decibels). (4 marks) i. Find the phase of the closed-loop system at w 3rad/s (2 marks) e. Explain what the constant M and N circles of the Nichols chart represent (3 marks)

Answer 1

Given Ppen loep transfer function s On comye carcleridie eruatim wih s lon da cfny e of and erder oe 2fwn § = 3 w -2 ( EN as fi Resonant peak P GiS) = +dan wt4 roD tan tautw phase angle of dan 3 phasesar2 w3 radre - 93-79 REDMI NOTE 5 PRO