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Assignment 3 Solutions 2009

# Also find the transfer funct ion model for this

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Unformatted text preview: s = 2) b1 s - a 2 b1 + a b1 a 3 b 2 1 F ( s + ) Q ( s ) (s - b 3 )(s - a 2 ) (s - b 3 )(s - a 2 ) 2. Following state­space model is given, é - 2 1 0 ù é 0 ù x = Ax + Bu ê - 3 0 3 ú; B = ê3ú; C = [1 0 0 ; A = ê ú ê ú y = Cx ê - 1 0 - 3 ú ê1 ë û ëú û Determine the eigenvalues of the state matrix. Also, find the transfer funct ion model for this system. Report the poles and zeros of this transfer function. Obtain the response of this model to a step­change in the input. Solution: We need to define the matrix A first and then issue the eig command in MATLAB: » A=[­2 1 0;­3 0 3;­1 0 ­3] A = ­2 1 0 ­3 0 3 ­1 0 ­3 To find the transfer function model we can use the fo llo wing sequence (after defining B and C also): » [num,den]=ss2t f(A,B,C,0); » g=tf(num,den) Transfer function: 3 s + 12 ­­­­­­­­­­­­­­­­­­­­­­ s^3 + 5 s^2 + 9 s + 12 The poles and zeros can be obtained in various ways. Here is one: » pole(g) ans = ­3.3892 ­0.8054 + 1.7006i ­0.8054 ­ 1.7006i...
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