Background

# Background - ME421LAB5BACKGROUND Whatarethey...

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ME 421 L AB 5 ‐ B ACKGROUND Standard form of Transfer funcbons Review of Bode Diagrams ‐ What are they? ‐ Creabng from data ‐ Gekng system informabon from them 1

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T RANSFER F UNCTION S TANDARD F ORMS First order Second order Dynamic QuanBBes K: Gain τ : Bme constant ζ : damping coeﬃcient ω n : natural frequency 2 G ( s ) = K τ s + 1 G ( s ) = K 1 ω n 2 s 2 + 2 ζ n s + 1
B ODE D IAGRAMS Top: |G dB (i ω )| X‐axis (Log scale) ω in rad Y‐axis (Linear scale) Plot 20log(|G(i ω )|) Bo\om X‐axis the same Y‐axis phase ( φ ) in degrees MatLab 3 >> bode(G) 1 decade

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E XPERIMENTAL B ODE D IAGRAMS Needed: |G( ω i)|, φ ( ω ) Collect sinusoidal output for a sinusoidal input at various frequencies Calculate |G| dB , φ Pick frequencies based on knowledge of system 4 G dB = 20log Out In φ = 360 T L T T=Period T L =Time lag
E XAMPLE 5 ω (rad/sec) In max Out max T L (sec) 1.5 2 0.0205 -0.04 4 2 0.0235 -0.05 20 2 0.0063 -0.144 70 2 0.0004 -0.044 From the data shown in the following table plot the bode diagram of the system.

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Background - ME421LAB5BACKGROUND Whatarethey...

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