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Unformatted text preview: MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.004 Dynamics and Control II Fall 2007 Lecture 38 Overview of the frequency response and Bode plots In this lecture, we’ll practice on the topic of frequency response and Bode plots. Se- lect at least one partner, and work out the problems together. Call on the instructor(s) for help. 1 1. Consider the following eight distinct systems whose pole–zero plots are provided. Match them their bode plots given in the next page. Pole−Zero Map 1 (one pole at zero) Pole−Zero Map 2 (double poles at zero) 2 2 1.5 1.5 1 1 Imaginary Axis Imaginary Axis Imaginary Axis Imaginary Axis Imaginary Axis Imaginary Axis Imaginary Axis Imaginary Axis 0.5 0.5 0 0 −0.5 −0.5 −1 −1 −1.5 −1.5 −2 −2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 1 Real Axis 2 Real Axis Pole−Zero Map 3 (one pole at −1) Pole−Zero Map 4 (two poles at −1 and −2) 2 2 1.5 1 1.5 1 0.5 0.5 0 0 −0.5 −0.5 −1 −1 −1.5 −1.5 −2 −2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 Real Axis 4 Real Axis Pole−Zero Map 5 (two poles at −1 ± j3) Pole−Zero Map 6 (one pole at −1, one zero at 1.2) 2 3 4 1.5 2 1 1 0.5 0 0 −1 −0.5 −2 −1 −3 −1.5 −4 −2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 5 Real Axis 6 Real Axis Pole−Zero Map 7 (one pole at −1, one zero at −1.2) Pole−Zero Map 7 (one pole at −1, one zero at zero) 2 2 1.5 1 1.5 1 0.5 0.5 0 0 −0.5 −0.5 −1 −1 −1.5 −1.5 −2 −2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 7 Real Axis 8 Real Axis 2 Bode plots: Bode Plot Bode Plot 5 10 0 −5 −10 −15 −20 0 Magnitude (dB) Phase (deg) Magnitude (dB) Magnitude (dB) 5 0 −5 −10 180 135 90 45 −45 −90 Phase (deg) Magnitude (dB) Phase (deg) Magnitude (dB) Phase (deg) −135 0 −180 −1 1 0 1 10 10 10 10 10 a Frequency (rad/sec) (rad/sec) b Frequency (rad/sec) (rad/sec) Bode Plot Bode Plot 10 0 −10 −20 −30 −10 −20 −30 −40 −40 0 0 −90 −180 −270 Phase (deg) Phase (deg) −30 −60 −360 −90 10 0 10 1 10 −2 10 −1 10 0 10 1 10 2 c Frequency (rad/sec) (rad/sec) d Frequency (rad/sec) (rad/sec) Bode Plot Bode Plot 10 0 −10 −20 −30 −40 Magnitude (dB) Phase (deg) Magnitude (dB) 5 0 −5 −10 −50 90 0 Phase (deg) 60 30 −30 −60 −90 0 −2 −1 0 1 2 −1 0 1 10 10 10 10 10 10 10 10 e Frequency (rad/sec) (rad/sec) f Frequency (rad/sec) (rad/sec) Bode Plot Bode Plot 0 −20 −40 −60 −80 Magnitude (dB) −20 −40 −60 −80 −100 0 −45 −90 −135 −45 −90 −135 −180 −180 10 10 10 10 10 10 10 10 −1 1 2 −1 1 2 g Frequency (rad/sec) (rad/sec) h Frequency (rad/sec) (rad/sec) 3 2. Nise chapter 10, problem 25 (page 679)....
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lecture38 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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