美国麻省理工大学：《航空系统的估计与控制》教学资源（讲义，英文版）Handout 1：Bode plot rules reminder

Handout 1: Bode plot rules reminder Eric fer Feb4,2004 General: Bode plot is to plot magnitudes using logarithm scale, phases using log scales. Indeed Gw $1s2 Ller2e302 Ths|G(元u)= Then logo GGu)l= Recall og10 Aeio In decibels: IGldb Bode plots of systems The range over which system behavior can be plotted is Bode plots can be determined Compensation can Example: KG(w) 1∞7+1 Gjw)2(jwTa+1

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) = s1s2 = r1ejθ1 r2ejθ2 = s3 r3ejθ3 Thus |G(jω) =| Then log10 |G(jω) =. | Recall log10 Aejφ = 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 jωτ1 + 1 Example: KG(jω) = (jω)2(jωτa + 1) 1

Phase(kG(u)) KGW) in Decibels, KGGwabl 2

Phase(KG(jω))= log |KG(jω) =| in Decibels, |KG(jω)db| = 2

Basic terms for transfer functions 1.K(ju)2 Bode plot for n=0, 1,-1,-2 3

Basic terms for transfer functions: 1. K(jω)n Bode plot for n = 0, 1, −1, −2 3

2.(jur+1)+1

2. (jωτ + 1)±1 4

士1 5

� � ( jω 3. ) 2 + 2ζ jω + 1 ±1 ωn ωn 5

xample: G(s 2000(+0.5) s(s+10(s+50) Write transfer function in standard form Bode plot

2000(s + 0.5) Example: G(s) = s(s + 10)(s + 50) Write transfer function in standard form Bode plot 6

0.01(s2+0.01s+1) Example:G(s)=2(/2)2+0.02(s/2)+1 Bode plot 7

0.01(s2 + 0.01s + 1) Example: G(s) = s2((s/2)2 + 0.02(s/2) + 1) Bode plot 7