Polar Plot Analysis of Transfer Functions: First and Second Order Systems, Study notes of Automatic Controls

Download Polar Plot Analysis of Transfer Functions: First and Second Order Systems and more Study notes Automatic Controls in PDF only on Docsity! 16.06 Lecture 27 Polar Plots November 6, 2003 Today’s Topics: 1. First order system polar plot 2. Second order system polar plots 3. Other examples docsity.com Recall from last time that if the system G(s) receives a steady sinusoidal input of amplitude A, so then the steady state output will be a sinusoid of magnitude A ˜ M(Z ) with its phase shifted by I(Z ) where Now let’s pause for a bit and think about some interpretations of G( jZ ). 2 docsity.com Example-first order system As Z goes from zero to plus infinity G( jZ ) traces a contour in the complex plane 5 docsity.com Example: second order system 6 docsity.com Some typical second order system polar plots for k G( s) 2 rl 2 s  2GZ s Z n n Critical damping (G 1)- Medium damping (G 0.7) 7 docsity.com A differentiator (zero at the origin) 10 docsity.com docsity.com