Gp4_Chapter 6 - EE2010 Systems and Control (Chapter 6) j j...

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EE2010 Systems and Control (Chapter 6) 6-1 Magnitude of a second-order system is Phase of a second order system is Bode diagram when 0 <  1 (Magnitude response) Quadratic factor,   1 2 ) ( ) ( 2 1 n n j j 2 2 10 2 2 2 ) 2 ( ) 1 ( log 20 ) 2 ( ) 1 ( 1 ) ( ) ( 2 1 1 2 2 2 2 n n n n n n j j 2 1 2 ) ( 1 ) ( 2 tan ) ( ) ( 2 1 1 n n n n j j
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EE2010 Systems and Control (Chapter 6) 6-2 When dB log 40 log 20 ) 2 ( ) 1 ( log 20 10 2 2 10 2 2 10 2 2 n n n n , n  High frequency asymptote is a straight line with a slope of 40 dB/decade. When Low frequency asymptote is the 0 dB line. dB 0 1 log 20 ) 2 ( ) 1 ( log 20 10 2 2 10 2 2 n n , n 
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EE2010 Systems and Control (Chapter 6) 6-3 Two asymptotes intersect at = n The approximate magnitude response (low and high frequency asymptotes) is independent of the value of When < , the magnitude response has a “resonant peak” whose size depends on the damping ratio, Resonance comes from Latin and means to “resound”, i.e., to sound out together with a loud sound. The output amplitude will be larger than the input amplitude when a system exhibits resonance Resonant frequency is the name given to the frequency which a system most likely to vibrate at, or equivalently, the stimulating frequency which gives the biggest response If < , the frequency response reaches a maximum value, M r , at the resonant frequency, r . 2 1 2 1
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EE2010 Systems and Control (Chapter 6) 6-4 Example of resonance: Radio tuner is a resonant circuit (also known as a series RLC circuit or a tuned circuit) Resonant magnitude and frequency formulae. Let Then from page 6-1, At the resonant frequency r , Substituting = r into G ( ju ), an expression for the resonant magnitude can be found . n u 2 2 2 ) 2 ( ) 1 ( 1 ) ( u u ju G 0 ) ( du ju G d 2 1 , 2 1 2 n r 2 1 , 1 2 1 ) ( ) ( 2 max r r j G j G M
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EE2010 Systems and Control (Chapter 6) 6-5 Bode diagram when 0 <  1 (Phase response) 2 1 2 ) ( 1 ) ( 2 tan ) ( ) ( 2 1 1 n n n n j j
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EE2010 Systems and Control (Chapter 6) 6-6 Polar plot: Polar plot lie in 3 rd and 4 th quadrant Real part > 0 only when < n Imaginary part always < 0 2 ) ( ) ( 2 1 1 n n j j       90
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This note was uploaded on 07/11/2011 for the course ECE 2010 taught by Professor Tankaychen during the Spring '11 term at National University of Singapore.

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Gp4_Chapter 6 - EE2010 Systems and Control (Chapter 6) j j...

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