Control Systems Engineering
Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
Question
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Chapter 8, Problem 37P

a.

To determine

The location of the closed-loop dominant poles if the system is operating with 15% discount.

b.

To determine

The value of the gain, K.

c.

To determine

The closed-loop poles.

d.

To determine

The accuracy of the second-order approximation.

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Which of the following sequences converge and which diverge? 20) an = 21) a = n! 106 1/(Inn) 3n+1 " 22) a = 3n-1 1/n x" 23) a = , x>0 2n+1 3" x 6" 24) an 25) a, = tanh(n) = 2" xn! n² 1 26) a = sin 2n-1 n 27) a = tan(n) 1 28) a = 1 3 ++ (Inn) 200 2" 29) an n 30) =n-√√n²-n 1"1 31) a == dx nix
Which of the following sequences converge and which diverge? n+1 6) a = 1- 2n (-1)+1 7) a = 2n-1 2n 8) an = n+1 1 9) a = sin + 2 n sin n 10) a = n 11) an = 12) a = 13) an 14) an 15) an 16) an n 2" In(n+1) = 81/n n n =(1+7)" = = 10n 3 n 1/n 17) an = In n 1/n n' 18) a =√4"n

Chapter 8 Solutions

Control Systems Engineering

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