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MIT16_30F10_lec24

# MIT16_30F10_lec24 - Topic#24 16.30/31 Feedback Control...

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Topic #24 16.30/31 Feedback Control Systems Closed-loop system analysis Bounded Gain Theorem Robust Stability

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Fall 2010 16.30/31 24–1 SISO Performance Objectives Basic setup: d i d o G c ( s ) y r e u G ( s ) n Where the tracking error can be written as: e = r ( y + n ) = r ( d o + G ( d i + G c e ) + n ) = S ( r d o n ) SG d i y = T ( r n ) + S d o + SG d i with L = GG c , S = ( I + L ) 1 T = L ( I + L ) 1 For good tracking performance of r (typically low frequency), require e small I S ( j ω ) I small 0 ω ω 1 To reduce impact of sensor noise n (typically high frequency), require I T ( j ω ) I small ω ω 2 Since T ( s ) + S ( s ) = I s cannot make both I S ( j ω ) I and I T ( j ω ) I small at the same frequen- cies fundamental design constraint December 29, 2011
Fall 2010 16.30/31 24–2 SISO Design Approaches There are two basic approaches to design: Indirect that works on L itself classical control does this Direct that works on S and T For the Indirect , note that If | L ( j ω ) | » 1 S = (1 + L ) 1 L 1 | S | « 1 , | T | ≈ 1 If | L ( j ω ) | « 1 S = (1 + L ) 1 1 and T L | T | « 1 So we can convert the performance requirements on S , T into spec- ifications on L (A) High loop gain Good command following & dist rejection (B) Low loop gain Attenuation of sensor noise. Of course, we must be careful when | L ( j ω ) | ≈ 1 , require that arg L = ± 180 to maintain stability December 29, 2011

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Fall 2010 16.30/31 24–3 Direct approach works with S and T . Since e = r y , then for perfect tracking, we need e 0 want S 0 since e = Sr + . . .
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MIT16_30F10_lec24 - Topic#24 16.30/31 Feedback Control...

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