7 - Lecture 7: Closed-Loop Systems Closed-Loop Systems...

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1 Lecture 7: Closed-Loop Systems • Closed-Loop Systems • Graphical Derivation Method • Examples • Reading: Chapter 5 Closed-Loop System Based on the open-loop system (feedforward path) Output can be used (feedback path) to modify the input – Feedback of continuous output c ( t ) to continuous input e ( t ) – Or feedback of discrete output c ( kT ) to discrete input e ( kT ) Signal processing in the feedback path (feedback gain) Sampler Data hold e ( t ) e ( kT ) ¹ m ( t ) Plant c ( t ) Sampler (A/D) c ( kT ) Digital Filter m ( kT )
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2 An Example of Closed-Loop System Reference input r ( t ), typically desired for the output c(t ) to track Continuous-time output c(t) is fed back to form the error signal e ( t ) Assume trivial digital controller D ( z )=1 Relation between the sampled input r ( kT ) and sampled output c ( kT )? Sampler Data hold e ( t ) e ( kT ) ¹ e ( t ) c ( t ) G p ( s ) H ( s ) r ( t ) + ¡ Example: Closed-Loop Transfer Function C ( s ) G p ( s ) H ( s ) R ( s ) + ¡ E ( s ) T 1 ¡ e ¡ Ts s ¹ E ( s ) E ¤ ( s ) C ( s ) = G ( s ) E ¤ ( s ) where G ( s ) = 1 ¡ e ¡ sT s G p ( s ) C ( z ) R ( z ) = G ( z ) 1+ GH ( z ) where GH ( z ) = Z [ G ( s ) H ( s )] 6 = G ( z ) ¢ H ( z )!
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3 Example: A Failed Attempt
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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.

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7 - Lecture 7: Closed-Loop Systems Closed-Loop Systems...

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