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lecture4

# lecture4 - MAE 171A Dynamic Systems Control Lecture 4...

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MAE 171A: Dynamic Systems Control Lecture 4: Dynamical System Properties step response and design specifications Goele Pipeleers

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Recall from Lecture 3 . . . System Poles and Impulse Response first-order system: G ( s ) = σ s + σ pole: p = - σ , and time constant τ = 1 impulse response: g ( t ) = σe - σt = 1 τ e - t/τ second-order system: G ( s ) = ω 2 n s 2 + 2 ξω n s + ω 2 n poles: p i = - ξω n |{z} σ ± i p 1 - ξ 2 ω n | {z } ω impulse response: g ( t ) = σ 2 + ω 2 ω e - σt sin( ωt ) ℑ{ p } ℜ{ p } ω σ ω n arcsin ξ 1
Overview Impulse Responses ℑ{ p } ℜ{ p } 2

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In This Lecture system poles and step response step response design specifications first controller designs 3
System Poles and Step Response First-order System G ( s ) = σ s + σ = 1 τs + 1 step response: Y ( s ) = σ s + σ 1 s = 1 s - 1 s + σ L - 1 --→ y ( t ) = 1 - e - t/τ t τ 1 y 1 - e - 1 4

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Second-order System G ( s ) = ω 2 n s 2 + 2 ξω n s + ω 2 n = σ 2 + ω 2 ( s + σ ) 2 + ω 2 step response: Y ( s ) = σ 2 + ω 2 ( s + σ ) 2 + ω 2 1 s = 1 s - s + 2 σ ( s + σ ) 2 + ω 2 L - 1 --→ y ( t ) = 1 - e - σt cos( ωt ) + σ
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lecture4 - MAE 171A Dynamic Systems Control Lecture 4...

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