ps4_soln

# ps4_soln - EE 428 Problem Set 4 Solutions -3- Problem 14:...

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EE 428 Problem Set 4 Solutions -3- Problem 14: (part 2)

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EE 428 Problem Set 4 Solutions -4- Problem 14: % m-file for Problem Set 4, Problem 14 Part 1 % clear the workspace and close all figures clear close all % define the denominator of the system transfer function zeta = 0.5; omega_n = 1; den = [1/omega_n^2, 2*zeta*omega_n, 1]; % define the numerator and system for each value of alpha alpha = 1; num = [1/(alpha*zeta*omega_n), 1]; sys1 = tf(num, den); alpha = 2; num = [1/(alpha*zeta*omega_n), 1]; sys2 = tf(num, den); alpha = 4; num = [1/(alpha*zeta*omega_n), 1]; sys3 = tf(num, den); alpha = 100; num = [1/(alpha*zeta*omega_n), 1]; sys4 = tf(num, den); alpha = -1; num = [1/(alpha*zeta*omega_n), 1]; sys5 = tf(num, den); % Compute the zero-state unit-step response for each system, show % time-response characteristics t = linspace(0,20,10000)'; y(:,1) = step(sys1, t); [tr1, ts1, Mp1, tp1, yss] = find_resp_char(y(:,1),t) y(:,2) = step(sys2, t); [tr2, ts2, Mp2, tp2, yss] = find_resp_char(y(:,2),t) y(:,3) = step(sys3, t); [tr3, ts3, Mp3, tp3, yss] = find_resp_char(y(:,3),t) y(:,4) = step(sys4, t); [tr4, ts4, Mp4, tp4, yss] = find_resp_char(y(:,4),t) y(:,5) = step(sys5, t); % plot the step responses figure(1) handle = plot(t, y(:,1), '-r' , t, y(:,2), ':b' , t, y(:,3), '-.g' , ... t, y(:,4), '--k' , t, y(:,5), '-m' ); set(handle, 'LineWidth' , 2, 'MarkerSize' , 10); set(gca, 'FontSize' , 14, 'FontName' , 'times new roman' ); legend( '\fontsize{14}\fontname{times new roman} zero at s = -0.5' , ... '\fontsize{14}\fontname{times new roman} zero at s = -1.0' , ... '\fontsize{14}\fontname{times new roman} zero at s = -2.0' , ... '\fontsize{14}\fontname{times new roman} zero at s = -50' , ... '\fontsize{14}\fontname{times new roman} zero at s = 0.5' ); title( 'Effect of Zero Location on the Zero-State Unit-Step Response' , ... 'FontSize' , 14, 'FontName' , 'Times New Roman' ) ylabel( 'Amplitude' , 'FontSize' , 14, 'FontName' , 'Times New Roman' ) xlabel( 'Time' , 'FontSize' , 14, 'FontName' , 'Times New Roman' )

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EE 428 Problem Set 4 Solutions -6- Problem 15:
EE 428 Problem Set 4 Solutions -7- Problem 15: % m-file for Problem Set 4, Problem 15 % clear the workspace and close all figures clear close all % define the common numerator and denominator terms num = 1; den = [1,1,1]; % generate the system representation for each value of the alpha alpha = 0.1; sys1 = tf(num, conv(den, [2/alpha, 1]) ); alpha = 1.0; sys2 = tf(num, conv(den, [2/alpha, 1]) ); alpha = 10.0; sys3 = tf(num, conv(den, [2/alpha, 1]) ); % Compute the zero-state unit-step response for each system

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## This note was uploaded on 07/23/2008 for the course EE 428 taught by Professor Schiano during the Fall '07 term at Penn State.

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ps4_soln - EE 428 Problem Set 4 Solutions -3- Problem 14:...

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