design-lead-RL0

design-lead-RL0 - ECE 382 Lead Compensator Design...

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Unformatted text preview: ECE 382 Lead Compensator Design (Root-Locus) G ( s ) = 4 s ( s + 2 ) Design Objective: = . 5 and n = 4 rad/sec. ( Interpret the design objective in terms of performance specification. ) Procedure : 1) General form of a lead compensator G c ( s ) = K c ( s + 1 ) ( s + 1 ) , K c , > , < < 1 Determine the closed-loop poles of the uncompensated system. T ( s ) = G ( s ) 1 + G ( s ) = 4 s 2 + 2 s + 4 4 = 2 n s 2 + 2 n s + 2 n Closed-loop poles of the uncompensated system are at s 1 , s 2 =- n j n q 1- 2 =- 1 j 3 =- 1 j 1 . 732 Also K v = lim s sG ( s ) = 2. 2) Determine the desired dominant closed-loop poles location of the compensated system. T d ( s ) = G d 1 + G d ( s ) = G c ( s ) G ( s ) 1 + G c ( s ) G ( s ) = 2 n s 2 + 2 n s + 2 n where, from the design objective, we have = . 5 and n = 4 rad/sec. Then we have, s ? 1 , s ? 2 =- n j n q 1- 2 =- 2 j 2 3 =- 2 j 3 . 464 3) Use MATLABs rlocus(num,den) function to plot the root locus of the uncompensated...
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design-lead-RL0 - ECE 382 Lead Compensator Design...

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