15 - Lecture 15: Frequency Response Method Frequency...

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1 Lecture 15: Frequency Response Method • Frequency Response • Nyquist Stability Criterion • Bode Diagram (next lecture) • Section 7.7-7.10 Why Frequency Response Methods? G ( s ) and H ( s ) are often not known precisely; hence the open-loop transfer function and the characteristic equation are not known. On the other hand, the open-loop frequency response , can be obtained experimentally without knowing Nyquist criterion uses experimentally obtained open-loop frequency response to determine the stability of the closed-loop system C ( s ) H ( s ) G ( s ) R ( s ) T GH ( z ) ¯ z = e j!T GH ( z ) GH ( z )
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Interpretation of Frequency Response C ( s ) G ( s ) E ¤ ( s ) C ( z ) = G ( z ) E ( z ) T E ( s ) For a stable system G ( z ), suppose the input is a sinusoid e ( t ) = sin( !t ), t ¸ 0. C ( z ) = G ( z ) z sin !T ( z ¡ e j!T )( z ¡ e ¡ j!T ) = k 1 z z ¡ e j!T + k 2 z z ¡ e ¡ j!T + C transient ( z ) steady state response C ss ( z ) transient response Steady state response of the sampled output is: c ss ( kT ) = j G ( e j!T ) j sin( k!T + 6 G ( e j!T )), k = 0 ; 1 ; 2 ;::: . which is a sinusoid of the same frequency as the sampled input e ( kT )=sin( k ! T ): • amplitude: • phase shift: j G ( e j!T ) j 6 G ( e j!T ) Obtaining Open-Loop Frequency Response Use a sinusoidal signal generator to generate the error signal e ( t ) Adjust the frequency ! of the signal generator Measure the sampled signal v ( kT ) Determine
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This note was uploaded on 04/15/2011 for the course ECE 483 taught by Professor Evens during the Spring '08 term at Purdue University-West Lafayette.

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15 - Lecture 15: Frequency Response Method Frequency...

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