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vovangra [49]
1 year ago
13

Sketch the asymptotes of the Bode plot magnitude and phase for the open-loop transfer ()=100(S+1)/((S+10)(S+100)) Use MATLAB to

verify your solution.
Engineering
1 answer:
Salsk061 [2.6K]1 year ago
6 0

The asymptotes of the open loop transfer are:

  • Horizontal: y = 0
  • Vertical: x = -10 and x = -100

<h3>How to plot the asymptotes?</h3>

The open loop transfer function is given as:

f(s) = 100(s + 1)/((s + 10)(s + 100))

Set the numerator of the function to 0.

So, we have:

f(s) = 0/((s + 10)(s + 100))

Evaluate

f(s) = 0

This means that, the vertical asymptote is y = 0

Set the denominator of the function to 0.

(s + 10)(s + 100)  0

Split

s + 10 = 0 and s + 100 = 0

Solve for s

s = -10 and s = -100

This means that, the horizontal asymptotes are s = -10 and s = -100

See attachment for the graph of the asymptotes

Read more about asymptotes at:

brainly.com/question/4084552

#SPJ1

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Use Routh's stability criterion to determine how many roots with positive real parts the following equations have:
Pavlova-9 [17]

Answer:

a) no roots not in LHP

b) 2 roots not in LHP

c) 2 roots not in the LHP

d) 2 roots not in the LHP

e) 2 roots not in LHP

Explanation:

a) s^4 + 8s^3 + 32s^2 + 80s + 100 = 0\\\\s^4:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:32\:\:\:\:\:\:100\\s^3:\:\:\:8\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:80\\s^2:\:\:\:22\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:100\\s^1:\:\:\:80-\frac{800}{22} =43.6\\s^0:\:\:\:100

No roots not in the LHP

b) s^5 + 10s^4 + 30s^3 + 80s^2+344s + 480 =0 \\\\s^5:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:30\:\:\:\:\:\:344\\s^4:\:\:\:10\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:80\:\:\:\:\:\:480\\s^3:\:\:\:22\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:296\\s^2:\:\:\:-545\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:480\\s^1:\:\:\:490\\s^0:\:\:\:480

2 roots not in the LHP

c) s^4 + 2s^3 + 7s^2 -2s + 8 = 0 \\\\s^4:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:7\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:8\\s^3:\:\:\:2\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:-2\\s^2:\:\:\:8\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:8\\s^1:\:\:\:-4\\s^0:\:\:\:8

There are roots in the RHP (not all coefficients are greater than 0).

2 roots not in the LHP

d) s^4 + 2s^3 + 7s^2 -2s + 8 = 0 \\\\s^3:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:20\\s^2:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:78\\s^1:\:\:\:-58\\s^0:\:\:\:78

There are two sign changes in the first column of the Routh array.

2 roots not in the LHP

e) s^4 + 2s^3 + 7s^2 -2s + 8 = 0 \\\\s^4:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:25\\s^3:\:\:\:4\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:12\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: new \:\:row \\s^2:\:\:\:3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:25\\s^1:\:\:\:12-\frac{100}{3}=-21.3 \\s^0:\:\:\:25

2 roots not in LHP

check:

 a (s) = 0  ⇒

 s^2 = -3 \limits^+_- 4j = 5e^{j(\pi \limits^+_- 0.92)}\\\\s = \sqrt5 e^{j( \frac{\pi}{2} \limits^+_-  0.46)+n\pi j},\:\:\:\:\: n= 0, 1\\

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When your complex reaction time is compromised by alcohol, an impaired person's ability to respond to emergency or unanticipated
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Answer:

decreased

Explanation:

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Opinion: Choose a side and defend it in four to five sentences. Given the choice between a vehicle that runs on gasoline or one
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Answer:

my opinion would be electric

Explanation:

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There are four spheres of earth. These include __________, _________, ________ and _________. They are important because when th
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Answer:

"lithosphere" , "hydrosphere" , "biosphere" , "atmosphere"

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The connection is made using a bolt and nut and two washers. If the allowable bearing stress of the washers on the boards is (sb
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Answer:

P = 0.490 kip

Explanation:

given data

allowable bearing stress = 2 ksi

allowable tensile stress = 18 ksi

diameter = 0.31 in

outer diameter = 0.75 in

inner diameter (hole) = 0.50 in

solution

we find here cross section area of shank that is express as

Area = \frac{\pi }{4} \times d^2      ..................1

area = \frac{\pi }{4} \times 0.31^2

area  = 0.0754 in²  

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\sigma = \frac{P}{A}     ...................2

P = \sigma \times A  

P = 18 × 10³ × 0.0754

P = 1357.2 = 1.357 kip

and

now find here area of washer is

Area = \frac{\pi }{4} \times (d^2-d1^2)     .......................3

put here value

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P = 2 × 10³ × 0.245

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