Handout 1: Bode plot rules reminder Eric Feron Feb 4, 2004 General: Bode plot is to plot magnitudes using logarithm scale, phases using log scales. Indeed: G(jω) = s 1 s 2 = r 1 e jθ 1 r 2 e jθ 2 = s 3 r 3 e jθ 3 Thus |G(jω) =| Then log 10 |G(jω) =.| Recall log 10 Ae jφ = In decibels: G| db =| ? Bode plots of systems ? The range over which system behavior can be plotted is ? Bode plots can be determined ? Compensation can jωτ 1 + 1 Example: KG(jω) = (jω) 2 (jωτ a + 1) 1 Phase(KG(jω))= log |KG(jω) =| in Decibels, |KG(jω) db | = 2 Basic terms for transfer functions: 1. K(jω) n Bode plot for n = 0, 1, ?1, ?2 3 2. (jωτ + 1) ±1 4 ? ? ( jω 3. ) 2 + 2ζ jω + 1 ±1 ω n ω n 5 2000(s + 0.5) Example: G(s) = s(s + 10)(s + 50) Write transfer function in standard form Bode plot 6 0.01(s 2 + 0.01s + 1) Example: G(s) = s 2 ((s/2) 2 + 0.02(s/2) + 1) Bode plot 7