timeDomain - Time-domain specifications and the...

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Unformatted text preview: Time-domain specifications and the corresponding pole locations (second-order systems) ECSE 404 (Control Systems) Consider the transfer function H (s) = The poles p1,2 = −σ ± jωd of H (s) are related to the coefficients of a(s) according to the following diagram: θ = sin−1 ζ Im(s) 2 ωn b(s) . =2 2 a(s) s + 2ζωn s + ωn ωn Re(s) σ ωd Let tr be the rise time, then tr ≈ 1.8 . ωn 1 Let Mp be the overshoot, then Mp = e − √ πζ 1− ζ 2 , which is depicted in the following figure: 100 90 80 70 60 Mp (%) 50 40 30 20 10 0 0 0.1 0.2 0.3 0.4 0.5 ζ 0.6 0.7 0.8 0.9 1 Let ts be the settling time, then ts = 4.6 4.6 . = σ ζωn 2 ...
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timeDomain - Time-domain specifications and the...

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