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blockdiagram4 - 30 ln ln 100 100 OS OS π = = = (3...

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Block Diagrams Q UESTION 4 For the block diagram shown in Figure 4.1, determine K and α such that the 2% settling time and percent overshoot of the closed–loop system are 0.2 s and 30%, respectively. ( 29 K s s α + R(s) E(s) Y(s) + - Figure 4.1 The closed–loop transfer function is ( 29 ( 29 2 1 K s s Y K K R s s K s s α α α + = = + + + + (1) The closed–loop characteristic equation is 2 2 2 2 n n s s K s s α ζϖ ϖ + + = + + (2) From the specifications, the damping ratio is 2 2 2 2 % 30 ln ln 100
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Unformatted text preview: % 30 ln ln 100 100 OS OS ζ π -- ÷ ÷ = = = + + ÷ ÷ (3) The natural frequency is used to determine the value of K ( 29 2 4 4 4 0.2 3121 0.358 0.2 n K K = = → = = ÷ ÷ (4) The value of α is 2 40 n = = (5) Block Diagram 2...
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