lecture38 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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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, well 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 polezero plots are provided. Match them their bode plots given in the next page. PoleZero Map 1 (one pole at zero) PoleZero 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 PoleZero Map 3 (one pole at 1) PoleZero 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 PoleZero Map 5 (two poles at 1 j3) PoleZero 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 PoleZero Map 7 (one pole at 1, one zero at 1.2) PoleZero 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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