Answer Happy

PART B ONLY
This question asks you to analyse a second-order step response and design a controller using the root-locus method. You are advised to use no more than 500 words in your answer to this question. Figure 2 shows a unit step response of a second order process. It shows that there is a small overshoot and then the output settles at 1. At the bottom of the figure it shows the values of the pole location which are approximately at s= -1 + j and s=-1-j. a. Using the step response software, by trial and error, find the values for the damping ratio and the natural frequency that produces this response; (Hint: See Figure 2.5 on page 18 of Book 2). Make sure you include a screenshot of your step response. (3 marks) b. By substituting the values for the damping ratio, natural frequency and gain into the standard form of the second-order transfer function, the transfer function for this system is found to be: 2 G (8) $2 + 2s + 2 Using this transfer function, show that the poles are at approximately s = -1 + j and s = -1-j? (3 marks) 1.379 은 1.125 1.250 1.000 Gain 0.875 . OSZO 290 000 SZE ! 2 3 1 5 6 200 225 2.50 2.75 3.25 3.50 3.75 4.00 3.00 Time (s) Time (s) Zoom and pan Pole locations Pole 1: -1.001 +0.993 Pole 2: -1.001 -0.993; Pole locations Pole 1: -1.001 +0.993; Pole 2: -1,001 -0.993; Reset 100% Zoom and pan Q Reset <-- 400%