Module 15 Bode Diagram (3 hours Plot the bode diagram of a complex system Write the transfer function of system through the Bode diagram
Module 15 Bode Diagram (3 hours) • Plot the Bode diagram of a complex system • Write the transfer function of system through the Bode diagram
Bode diagram are the third method (root locus and nyquist Methods are the other two), used to design a stable closed-loop system. Bode diagrams are similar to the nyquist diagrams, in the sense that we plot the phase and magnitude of the open- loop Ta, but this time against the frequency In comparison with the nyquist diagrams, the bode diagrams contain additional information about the system in the frequency data. Knowing the Bode diagram one can construct the corresponding nyquist diagram, but the reverse is not possible Consider the closed-loop system described below 只 G H
Bode diagram are the third method (root locus and Nyquist Methods are the other two), used to design a stable closed-loop system. Bode diagrams are similar to the Nyquist diagrams, in the sense that we plot the phase and magnitude of the open-loop TF, but this time against the frequency. In comparison with the Nyquist diagrams, the Bode diagrams contain additional information about the system in the frequency data. Knowing the Bode diagram one can construct the corresponding Nyquist diagram, but the reverse is not possible. Consider the closed-loop system described below: R C G H
Elementary Bode Diagrams We will first learn how to plot Bode Diagrams of simple(elementary) TFs and then learn how to combine them In general an open loop tF will have the following form G(SH(S) X∏I+厘T+(25/0)s+1l0) (1+s)(1+(250)8+s/0) +slk We will first sketch each of the elementary TFs: 1, 2, 3, 4, 5 and 6
15.1 The Definition of Bode Diagram (Bode图的定义) Ma Magnitude(201gGH(jo) db--decibel (dB) Mdb=201g M 20lgGH(jO) 10 100 (g o) ● ● ● ∠GH(o) 10 @(g o) ● 90° l80
15.1 The Definition of Bode Diagram (Bode 图的定义) (lg) Magnitude (20lg GH( j) (lg) GH( j) db−−decibel 20lg ( ) 20lg GH j Mdb M = = Mdb (dB) 0.1 1 10 100 0.1 1 10 100 −90 −180
15.2 Bode Diagram of Simple system Case 1: GH()-1 →M o=-tan( ar) 1+Isls=jo 1+ jar 1+a-T Mm=20g0M=20-|g+o72) 0> T (break point) Ma=20-0g(+0)=0 dB=20 lg(+1)==MB/M=20-wr) g=tan(0)=0 20 logT-20 o q=-tan(l)=-45 g=-tan(o∞)=-90 3dB log o 20dB/ decade 10T T log o -90
15.2 Bode Diagram of Simple system
C ase 2 GH(S) → 90 S s=jo MdB=20log,o M=-20n log a de n×20dB/ decade log o logo n×90
Case 3: GH(s)=K db (dB) 201g K Muh=201g K 100 o(g o) p=0° ● 100 o(g o) 90° 180
(lg) (lg) Mdb (dB) 0.1 1 10 100 0.1 1 10 100 −90 −180 20lg K Case 3: GH(s) = K = = 0 20lg Mdb K
C ase GH()=1+3=1+107→M=+o72;g=n(mr) MaB=20logo M=20-logl1+@ T2 2 0<< @=-(break point) Ma=202g(7) 2 g=tan(0)=0 o=tan (1 )=45 =+20 logT+20l0g o g=tan(∞) 20dB/decade 3dB 107
Case 5: GH(S 1+s+ 02)442 s=j0 Mur=20 log p=-tan-1a 2 >0台>>1 =20l og 0+0 M≈20log =20(-) +43 q=-tan(0)=0 M=20 lo =-20log25=20(-)og =20(-+k4 (log @-log a, )=-40(log a-log a 1)+45 g=-tan(∞)=-90 q=-tan(-0)=-180
Case 5(cont 5<1 6dB 5 og 40dB/ decade 0=0 O=100 10g o