Control ENG HW_Part_51

# Control ENG HW_Part_51 - C = 0.116-=-τ 2 1 2 2 1 tan 1 sin...

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13.1 The set point of the control system in fig P13.1 given a step change of 0.1 unit. Determine (a) The maximum value of C and the time at which it occurs. (b) the offset (c) the period of oscillation. Draw a sketch of C(t) as a function of time. ) 1 2 )( 1 ( 5 1 ) 1 2 )( 1 ( 5 + + + + + = s s K s s R C 9 3 2 8 2 + + = s s R C s R 1 . 0 = b) 0889 . 0 9 8 . 0 9 3 2 8 . 0 ) ( 2 0 = = + + = s s Lt C S offset = 0.0111 c) 2 2 1 3 1 2 ; 3 2 ; 9 8 . 0 = = = = ξ ξτ τ K

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overshoot = 305 . 0 1 exp 2 = - - ξ πξ = Maximum vslue of C = 1.0305*0.0889=0.116 Maximum value of
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Unformatted text preview: C = 0.116 -+---=--τ 2 1 2 2 1 tan 1 sin 1 1 1 9 8 . 116 . t e t 6 . 1 1 tan 1 2 1 2 =--=-t Time at which C max occurs = 1.6 (c ) Period of ociullation is 166 . 3 1 2 2 =-= πτ T T =3.166 Decay ratio = (overshoot) 2 = 0.093...
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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_51 - C = 0.116-=-τ 2 1 2 2 1 tan 1 sin...

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