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Math245_SimulProject_Part1_Fall08

Math245_SimulProject_Part1_Fall08 - 0.5 on a single graph...

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Fall 2008 Math 245 Simulation Pro ject: Part 1. Date Due : Thursday, Nov. 20 The transfer function for a closed-loop system is given by ( ) ( ) 1 ( ) ( ) H s T s G s H s = + , where H(s) is the open-loop transfer function and G(s) is the controller function. Suppose H(s) and G(s) are given by the functions 2 ( ) 2 2 K H s s s = + + and 1 10 1 ( ) G s s = + . Then T(s) can be expressed as 3 2 1 10 1 1 1 10 5 5 ( ) ( ) (2 ) (2 ) ( ) K s T s s s s K + = + + + + + + . Required: a) Construct a root-locus diagram ( i.e. , a plot of the roots of the denominator of T(s) in the complex s -plane) as the gain parameter K varies from K=1 to K=8 . (Note: You should present your computed values of the roots as K is varied in increments of
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Unformatted text preview: 0.5 on a single graph of the complex s-plane). b) Determine the value of the gain K for which the system is stable. (Note: You should determine the critical value of K to at least two significant digits.) c) Select the value K=2 and separate the transfer function into two terms by an expansion in partial fractions. Then, determine the analytic form for the inverse transform ( 29 { } 1 ( ) t T s-= T L valid for K = 2 . Hint: You should seek to express T(s) in the partial fraction form 2 2 ( ) ( ) A Ms N T s s a s σ ϖ + = + + + + ....
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