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blockdiagram11

# blockdiagram11 - Block Diagrams 29 29 2 100 4 100 Y s R s s...

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Block Diagrams Q UESTION 11 For the block diagram shown in Figure 11.1, determine the transfer function ( 29 ( 29 Y s R s , damping ratio, natural frequency, damped natural frequency, percent overshoot, 2% settling time, and peak time when K 1 = 10 and K 2 = 0.2. 1 K ( 29 10 2 s s + 2 K s Y(s) R(s) + - + - Figure 11.1 Denoting the output of the left summing junction by E 1 ( s ) ( 29 ( 29 ( 29 1 E s R s Y s = - (1) Denoting the output of the right summing junction by E 2 ( s ) ( 29 ( 29 ( 29 2 1 10 0.2 E s E s sY s = - (2) Writing an equation for the output ( 29 ( 29 ( 29 2 10 2 Y s E s s s = + (3) Combining equations (1) and (2) ( 29 ( 29 ( 29 ( 29 2 10 0.2 E s R s Y s sY s = - - (4) Combining equations (3) and (4) ( 29 ( 29 ( 29 ( 29 ( 29 10 10 0.2 10 2 Y s R s s Y s s s = - + + (5) Rearranging equation (5), the closed–loop transfer function is

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Unformatted text preview: Block Diagrams ( 29 ( 29 2 100 4 100 Y s R s s s = + + (6) The closed–loop characteristic equation is 2 2 2 4 100 2 n n s s s ζϖ ϖ + + = + + (7) The closed–loop natural frequency is rad 100 10 s n = = (8) The closed–loop damping ratio is 4 0.2 2 n ζ = = (9) The closed–loop percent overshoot is ( 29 2 / 1 % 100 52.66% OS e ζπ--= = (10) The closed–loop 2% settling time is 4 2 s s n T = = (11) The closed–loop peak time is 2 0.3206 s 1 p n T π = =-(12) The closed–loop damped natural frequency is 2 rad 1 9.798 s d n =-= (13) 2...
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