ece580 lecture 15

ece580 lecture 15 - Nov. 1, 2011 Feedback Control Systems...

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Unformatted text preview: Nov. 1, 2011 Feedback Control Systems (I) Douglas Looze 1 Lecture 15 ECE 580 Feedback Control Systems (I) MIE 444 Automatic Controls Doug Looze Nov. 1, 2011 Feedback Control Systems (I) Douglas Looze 2 Announce Nov. 1, 2011 Feedback Control Systems (I) Douglas Looze 3 Last Time Example Sketching Nyquist diagrams Determining margins from Nyquist plot Relation of step response measures to gain/phase margins Nov. 1, 2011 Feedback Control Systems (I) Douglas Looze 4 Today Frequency response Definition View (Bode plots) Interpretation Construction Reading FPE 6.1 Nov. 1, 2011 Feedback Control Systems (I) Douglas Looze 5 Frequency Response System response (output) to cos t (input) cos t ( 29 y t ( 29 g t Write input as real part of exponential cos Re j t t e = Response Re j t e ( 29 y t ( 29 g t j t e ( 29 y t ( 29 g t ( 29 ( 29 Re y t y t = Nov. 1, 2011 Feedback Control Systems (I) Douglas Looze 6 Frequency response from convolution ( 29 ( 29 j y t g t e d - =- t =- d d = - = - = = = - ( 29 ( 29 j t g e d -- = ( 29 j t j e g e d -- = ( 29 j t e G j = Fourier transform of g ( t ) Frequency response Nov. 1, 2011 Feedback Control Systems (I) Douglas Looze 7 Viewing Frequency Response Frequency response at a given frequency is a complex number Two functions of frequency Real part Re[ G ( j )] Imaginary part Im[ G ( j )] Must view both simultaneously ( 29 ( 29 ( 29 Re Im G j G j j G j = + Equivalent (polar) form ( 29 ( 29 ( 29 j G j G j G j e = R Nov. 1, 2011 Feedback Control Systems (I) Douglas Looze 8 Bode plots Two plots of features of the same frequency response ( 29 ( 29 s j G s G j = = Magnitude (amplitude) bode plot ( 29 log vs. log G j Phase bode plot ( 29 vs. log G j R ( 29 ( 29 j G j G j e = R Nov. 1, 2011 Feedback Control Systems (I) Douglas Looze 9 10-3 10-2 10-1 10 10 1 10 2 Magnitude (abs) Bode Diagram Frequency (rad/sec) 10-1 10 10 1 10 2-360-315-270-225-180-135 Phase (deg) ( 29 ( 29 ( 29 ( 29 2 2 2000 1 5 4 404 s L s s s s s + = + + + Note: Unwrap phase Automatic in Matlab bode (L) Nov. 1, 2011 Feedback Control Systems (I) Douglas Looze 10 Nichols chart Nyquist diagram ( 29 ( 29 Im vs. Re G j G j Indexed vs....
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ece580 lecture 15 - Nov. 1, 2011 Feedback Control Systems...

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