Please assist with this questions with details on how to do it. Thank you. 1. Construct the Bode Plot for a system whose transfer function is given byG(s) =1000s(s+10) (s+50)Determine the gain cross over frequency, the phase cross over frequency, the Gainmargin and phase margin of the system from your plot.Determine the stability based on values of phase cross over frequency and gaincross over frequency.Determine stability based on the gain margin and phase margin of the system.

The open loop transfer function of the system is given as Gs=1000ss+10s+50,Now convert the transfer…

Answered: 1. Construct the Bode Plot for a system…

Introductory Circuit Analysis (13th Edition)

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ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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Please assist with this questions with details on how to do it. Thank you.

1. Construct the Bode Plot for a system whose transfer function is given by
G(s) =
1000
s(s+10) (s+50)
Determine the gain cross over frequency, the phase cross over frequency, the Gain
margin and phase margin of the system from your plot.
Determine the stability based on values of phase cross over frequency and gain
cross over frequency.
Determine stability based on the gain margin and phase margin of the system.

Expert Solution

Step 1

The open loop transfer function of the system is given as

$G (s) = \frac{1000}{s (s + 10) (s + 50)}, Now convert the transfer function in frequency domain by put s = jω, we get G (jω) = \frac{1000}{jω (jω + 10) (jω + 50)}, Here corner frequency is ω_{p 1} = 10 rad . / \sec, ω_{p 2} = 50 rad . / \sec, DC gain K will K = \frac{1000}{10 \times 50} = 2, K_{dB} = 6 Now the gain at ω = 0.1 rad . / \sec will M_{ω} = K_{dB} - 20 logω M_{ω = 0.1} = 6 - 20 \log 0.1 M_{ω = 0.1} = 26 db Magnitude response of transfer function will, |G (jω)| = \frac{1000}{ω \sqrt{ω^{2} + 100} \sqrt{ω^{2} + 2500}}, Phase response of the transfer function, ϕ = - 90 ° - \tan^{- 1} (\frac{ω}{10}) - \tan^{- 1} (\frac{ω}{50}),$

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