For the given open-loop transfer function, design a PD controller using root-locus (angle and magnitude conditions)...
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For the given open-loop transfer function, design a PD controller using root-locus (angle and magnitude conditions) to shape the closed-loop step response with a settling time of 1 second and a 10% overshoot with Matlab. You can solve it according to MATLAB script in question. s = tf('s'); Gs_1=1/((s+2)*(s+4)*(s+10)); ts= 1; % Settling time os = 0.1; % Overshoot % The open-loop transfer function and desired criteria are defined above. % Design a PD controller with F(s) = K*(sz). % Find the damping ratio and natural frequency for the desired time domain criteria. % You should find these values by writing equations. (Note: If you directly specify these values, related questions will be incorrect.) zeta = wn = % Dominant poles are located at s--sigma -+ wd*i. % Find sigma and wd. wd = sigma = % Find the angles between open-loop poles and the pole at -sigma + wd*i. theta_p1 = % Angle between s=-2 and s--sigma -wd*i theta_p2 = % Angle between s=-4 and s--sigma - wd*i theta_p3=% Angle between s=-10 and s=-sigma - wd*i % Use the angle condition to find the angle of the PD controller's zero. theta_z = % The angle should be between 0-180 degrees. % Find the location of the PD controller's zero. Z= % Find the lengths between open-loop poles and the pole at -sigma + wd*i. length_p1=% Length between s=-2 and s=-sigma + wd*i length_p2=% Length between s=-4 and s--sigma + wd*i length_p3 = % Length between s=-10 and s-sigma - wd*i % Find the length between the PD controller zero and the pole at -sigma + wd*i. length_z = % Calculate the value of K. K = G(s) = 1/((s+2)(s + 4)(s + 10)) For the given open-loop transfer function, design a PD controller using root-locus (angle and magnitude conditions) to shape the closed-loop step response with a settling time of 1 second and a 10% overshoot with Matlab. You can solve it according to MATLAB script in question. s = tf('s'); Gs_1=1/((s+2)*(s+4)*(s+10)); ts= 1; % Settling time os = 0.1; % Overshoot % The open-loop transfer function and desired criteria are defined above. % Design a PD controller with F(s) = K*(sz). % Find the damping ratio and natural frequency for the desired time domain criteria. % You should find these values by writing equations. (Note: If you directly specify these values, related questions will be incorrect.) zeta = wn = % Dominant poles are located at s--sigma -+ wd*i. % Find sigma and wd. wd = sigma = % Find the angles between open-loop poles and the pole at -sigma + wd*i. theta_p1 = % Angle between s=-2 and s--sigma -wd*i theta_p2 = % Angle between s=-4 and s--sigma - wd*i theta_p3=% Angle between s=-10 and s=-sigma - wd*i % Use the angle condition to find the angle of the PD controller's zero. theta_z = % The angle should be between 0-180 degrees. % Find the location of the PD controller's zero. Z= % Find the lengths between open-loop poles and the pole at -sigma + wd*i. length_p1=% Length between s=-2 and s=-sigma + wd*i length_p2=% Length between s=-4 and s--sigma + wd*i length_p3 = % Length between s=-10 and s-sigma - wd*i % Find the length between the PD controller zero and the pole at -sigma + wd*i. length_z = % Calculate the value of K. K = G(s) = 1/((s+2)(s + 4)(s + 10))
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To design a PD controller using rootlocus we need to follow the steps below 1 Find the damping ratio and natural frequency for the desired time domain ... View the full answer
Related Book For
Business Law Principles for Today's Commercial Environment
ISBN: 978-1305575158
5th edition
Authors: David P. Twomey, Marianne M. Jennings, Stephanie M Greene
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