Answer Happy

PART C ONLY
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(s) = $2 + 2s + 2 Using this transfer function, show that the poles are at approximately s = -1 + j and s = -1-j? (3 marks) 1 OSCH SC 000 80 020 SC9ooos SEO . 8 1 T 5 2.00 225 2.50 2.75 3.25 3.50 3.75 4.00 3.00 Time (s) Time (s) Pole locations Pole 1: -1.001 +0.993; Pole 2: -1,001 -0.993 Zoom and pan @ @ A Reset 100% Zoom and pan @ @ Pole locations Pole 1: -1.001 +0.993 Pole 2: -1,001 -0.993 Reset 400% (a) A unit step response of a second-order process, (b) zoomed in on the Figure 2 overshoot c. It is decided that the process in Figure 2 will be controlled using a PD controller with a derivative gain, KD' of 0.5, so that the transfer function of the PD controller is: C(s) = Kp(1 + 0.58) Using the combined transfer function of the forward path, C(s)G(s), use the root-locus software to plot the root locus with the value of Kp going from a minimum gain of 0 to a maximum of 50. Include a screenshot of your root-locus plot as your answer.