Control ENG HW_Part_57

Control ENG HW_Part_57 - WT0C + q = ρCV1 (T1 − T0 ) +...

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Unformatted text preview: WT0C + q = ρCV1 (T1 − T0 ) + WT1C WT1C = ρCV2 (T2 − T1 ) + WT2 C WT2 C = ρCV3 (T3 − T2 ) + WT3C T0 (WC + ρCV1 ) + q = T1 (W C + ρCV1 ) T1 = T0 + q WC + ρCV1 T1= T2 = T3 T3 = T0 + q q( s ) ⇒ T3 ( s ) = (WC + ρCV1 )s WC + ρCV1 13.6 (b) 2 T ( s) ( s + 1)(1.25s + 1)(1.5s + 1) = 2 R( s ) 1 + k C (1 + τ D s) ( s + 1)(1.25s + 1)(1.5s + 1) ' 3 = k C (1 + τ D s) T3' ( s) 2k C (1 + τ D s) = 2 R( s) ( s + 1)(1.875s + 2.75s + 1) + 2k C (1 + τ D s) T3' ( s) 2k C (1 + τ D s) = 3 R( s) 1.875s + 4.625s 2 + (3.75 + 2k Cτ D ) s + 2k c + 1 ' c) kC=3; τ D = 0.5, offset = ?,τ 0 ( s) = 1 s T3' ( s) 1 Lt ' s →0 1.875s 3 + 4.625s 2 + (3.75 + 2k τ ) s + 2k + 1 Ti ( s) CD C = 1 2k C + 1 = 1 = 0.143 7 Offset =0.143 13.7 (a) For the control system shown in fig P 13.7, obtain the closed loop transfer function C/U. (b) Find the value of KC for whgich thre closed loop response has a ξ of 2.3. (c) find the offset for a unit-step change in U if KC = 4. s +1 1 (R − C) + U = C KC × 0.25s + 1 s C = = U 1 s 1+ KC s +1 . s 0.25s + 1 ...
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This note was uploaded on 11/13/2011 for the course COP 4355 taught by Professor Koslov during the Spring '10 term at University of Florida.

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Control ENG HW_Part_57 - WT0C + q = ρCV1 (T1 − T0 ) +...

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