09-10Chapter 7_2 Bode plots

# 09-10Chapter 7_2 Bode plots - Bode plots(Logarithmic plots...

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Bode plots (Logarithmic plots ) Principle of Automatic Control CHAPTER 7 requency Response (P244 Ch 8) By Hui Hui Wang Wang Frequency Response (P.244, Ch.8) 浙江大学控制科学与工程学系

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Bode plots (Logarithmic plots ) Outline of Chapter 7 9 Introduction 9 Bode Plots (Logarithmic plots) 9 Direct Polar Plots 9 Nyquist’s Stability Criterion 9 Phase Margin and Gain Margin and Their elation to Stability Relation to Stability 9 ……… 2 Wintersweet
Bode plots (Logarithmic plots ) Frequency Response qy p 2. Bode plots (Logarithmic plots ) The use of semilog paper eliminates the need to take logarithms of very many numbers and also expands the low-frequency rang, which is of primary importance. The advantages of logarithmic plot are following 1) The mathematical operations of multiplication and division re transformed to addition and subtraction; are transformed to addition and subtraction; 2) The work of obtaining the transfer function(fall into several categories) is largely graphical instead of analytical. Preliminary design ------using the straight-line asymptotic approximations to obtain approximate performance characteristics pecified design ---- rrecting the straight ne curves for greater Specified design- ------correcting the straight-line curves for greater accuracy. ogarithmic plots olar plots enough data 3 Logarithmic plots polar plots

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Bode plots (Logarithmic plots ) Frequency Response qy p 2. Bode plots (Logarithmic plots ) Basic definition of logarithmic terms: Logarithm: The logarithm of a complex number is itself a complex number. The abbreviation “log” is used to indicate the logarithm to the base 10 g g g ) ( ) ( ω φ j j ) ( 434 . 0 ) ( log log ) ( log ) ( log j j G e j G e j G + = + = Decibel (dB): the unit of the logarithm of the agnitude It is omitted in rest of this book magnitude 4
Bode plots (Logarithmic plots ) Frequency Response qy p 2. Bode plots (Logarithmic plots ) Log magnitude. The logarithm of the magnitude of a transfer function G(j ω ) ( 幅频特性 ) expressed in decibels is dB j G ) ( log 20 ω The quantity is called the log magnitude , abbreviate Lm . Thus dB j G j LmG ) ( log 20 ) ( ω= Since the transfer function is a function of frequency, the Lm is also a function of frequency. Octave ( 倍频 ). An octave is a frequency band from f 1 to f 2 ,where f 2 /f 1 =2 . For example: the frequency band from 1 to 2 Hz is 1 octave inwidth, and the frequency band from 17.4 to 34.8 Hz is also 1 octave in width. 5

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Bode plots (Logarithmic plots ) Frequency Response qy p 2. Bode plots (Logarithmic plots ) Decade( 十倍频 ). There is an increase of 1 decade from f 1 to f 2 when f 2 /f 1 =10 .Thefrequencybandfrom1to10Hzorfrom2 .5to25Hzis1 ecade idth decade in width. 1 2 8 10 20 80100 ω decades he B alues f me mmon umbers re iven 49 able The dB values of some common numbers are given in P.249 Table 8.1.
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09-10Chapter 7_2 Bode plots - Bode plots(Logarithmic plots...

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