Answer Happy

Homework Task #4 from the P4 sample code • The system in problem 9.40 of the textbook has input-output relation y""(t) + 6y"(t) + 11y' (t) + 6y(t) = x(t) Assume that this system is causal and use the Laplace transform to find the transfer function H(s) by hand. Write Matlab code similar to P4 to do the following: 1) use tf to compute a transfer function system model H1 2) use zpk to convert the transfer function system model to a zero-pole-gain system model H2; 3) use pzmap to produce a pole-zero plot; 4) use pole to find the poles; 5) use isstable to determine if the system is stable; 6) use residue to compute a partial fraction expansion and find the impulse response h(t). Hint: because the system is causal, the ROC must be the right half-plane to the right of the rightmost pole.
clear close all clear; z = [-1 2]; % zeros (roots of numerator) P = [-2 -3 1]; % poles (roots of denominator) 8 = 2; % transfer function gain H1 = zpk (z,p,g) % zero-pole-gain system model H2 = tf(H1) % convert to transfer function [numer,denom] = tfdata (H1, 'v') [numer, denom] = tfdata (H2, 'v') H3= tf(numer, denom) % H3 is the same as H1 H4 = zpk (H3) % H4 is the same as H1 printsys (numer, denom) P = pole (H1) P= pole (H2) % same result as the line above Z = zero (H1) Z = zero (H2) % same result as the line above [p z]= pzmap (H1) [p z]= pzmap (H2) % same result as the line above figure (1); pzmap (H1); figure (2); pzmap (H2); figure (3); pzmap (numer, denom); isstable (H1) [r p k] = residue (numer, denom)| whos