Lecture7

Design search for good trade off example 52 gs 1 s1 d

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Unformatted text preview: ( s) s+1 e=r−y G(s) = ⇒ 4 y + y − 2y = r − r ¨˙ ˙ Performance: Four fundamental transfer functions are small. 1 1 + GD G 1 + GD D 1 + GD GD 1 + GD Tracking E/R Regulation E/W Control effort U/R Regulation/Control effect E/V, U/W small when D → ∞ small when D → 0 . Conflicting Objectives . Design = Search for good trade-off Example 5.2 G(s) = 1 , s+1 D ( s) = k Y GD k = = R 1 + GD s+1+k Step response: Y ( s) = y (t) = 1 k k 1 1 · = (− ) s s+1+k k+1 s s+k+1 k (1 − e−(k+1)t )1(t). k+1 Time constant = 1 k+1 Larger k ⇒ Faster tracking U D k (s + 1) = = R 1 + GD s+k+1 Step response: U (s ) = u( t ) = 1 k (s + 1) k 1 k · = (+ ) s s+1+k k+1 s s+k+1 k (1 + ke−(k+1)t )1(t). k+1 Large...
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