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By Milne W. E.

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32*t)) Part (e): G ( s) = 1 ( s + 1) 3 G(t)= 1/2*t^2*exp(‐t) Part (f): G( s) = 2( s 2 + s + 1) s( s + 15 . 5)^2); [num,den]=tfdata(Eq,'v'); [r,p] = residue(num,den) %Part g Eq=(2*s^3+s^2+8*s+6)/((s^2+4)*(s^2+2*s+2)); [num,den]=tfdata(Eq,'v'); [r,p] = residue(num,den) %Part h Eq=(2*s^4+9*s^3+15*s^2+s+2)/(s^2*(s+2)*(s+1)^2); [num,den]=tfdata(Eq,'v'); [r,p] = residue(num,den) The solutions are presented in the form of two vectors, r and p, where for each case, the partial fraction expansion is equal to: 2‐43 Automatic Control Systems, 9th Edition Chapter 2 Solutions r r r b( s ) = 1 + 2 + ...

3. Type in Acsys 4. Then press the “transfer function Symbolic button 2‐61 Golnaraghi, Kuo Automatic Control Systems, 9th Edition Chapter 2 Solutions Golnaraghi, Kuo 5. Enter the characteristic equation in the denominator and press the “Routh‐Hurwitz” push‐ button. RH = [ 1, 10] [ 25, 450] [ -8, 0] [ 450, 0] Two sign changes in the first column. Two roots in RHP=> UNSTABLE 2-37) Use the MATLAB “roots” command same as in the previous problem. 2‐62 Automatic Control Systems, 9th Edition Chapter 2 Solutions Golnaraghi, Kuo 2-38) To solve using MATLAB, set the value of K in an iterative process and find the roots such that at least one root changes sign from negative to positive.

Two roots in RHP. 4142i Alternatively use the approach in this Chapter’s Section 2‐14: 1. Activate MATLAB 2. Go to the directory containing the ACSYS software. 3. Type in Acsys 4. Then press the “transfer function Symbolic button 2‐61 Golnaraghi, Kuo Automatic Control Systems, 9th Edition Chapter 2 Solutions Golnaraghi, Kuo 5. Enter the characteristic equation in the denominator and press the “Routh‐Hurwitz” push‐ button. RH = [ 1, 10] [ 25, 450] [ -8, 0] [ 450, 0] Two sign changes in the first column.

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