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# lecture7_small - Direct digital design Calculating C (z )...

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Direct digital design Design methods for P ( z ) Pole placement for 1 1+ P ( z ) C ( z ) Frequency response based designs (loopshaping) Root locus Tuning PID controllers The above methods are analogous to the continuous time methods (except for the di±erent interpretation between s -plane and z -plane). The following does not have a continous time analogue. Finite settling time (deadbeat) control. Roy Smith: ECE 147b 7 :2 Direct digital design Calculating C ( z ) to control P ( z ) P ( s ) C ( s ) C ( z ) P ( z ) Approximation of C ( s ) with C ( z ) Model P ( s ), and sample/hold as P ( z ) Continuous-time design Discrete-time design ZOH equivalence gives P ( z ). Design C ( z ) for good closed-loop control of P ( z ) Roy Smith: ECE 147b 7 :1

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Deadbeat control Approach: P ( z ) C ( z ) ±² ³´ + - µ ± ± ± ± ² r ( z ) y ( z ) The closed-loop response is: M ( z )= P ( z ) C ( z ) 1+ P ( z ) C ( z ) . So: Choose M ( z ), the desired closed-loop response. Solve the above to get C ( z ). Roy Smith: ECE 147b 7 :4 Deadbeat control Ideal closed-loop response: M ( z ) ¶¶ r ( k ) y ( k ) Consider the best possible closed-loop response: M ( z z - 1 A step input, r ( z z z - 1 Gives y ( z 1 z - 1 (a delayed step output).
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## This note was uploaded on 04/06/2010 for the course ECE 145 taught by Professor Rodwell during the Spring '07 term at UCSB.

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lecture7_small - Direct digital design Calculating C (z )...

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