Question

Consider a simple direct current motor with transfer function 10 P(s) = 2s2+s (a) Plot a Bode plot for the plant's transfer function. (b) Design a PD-controller that gives a closed loop bandwidth, wBw, of at least 10 rad/sec and has a phase margin of at least 30°· Using Matlab's bode or margin, find and verify that bandwidth and phase margin requirements have been met. Remember that margin is found using the OLTF but bandwidth is found using the CLTF (c) Use Isin to plot the output response to a sinusoidal input with w = aBw and find the amplitude of the output sinusoids (at steady state). Is this as you expected? (d) Plot the step response for the closed loop system with your PD-controller.

Please help as much as you can, I want to use this probem as a study guide for the final so any and all help / code is super appreciatted. Thanks

Answer 1

matlab plot all parts:

clc;

clear all;

s=tf('s');

p=10/(2*s^2+s);% plant

gc=1.1*(s+19.3847);%controller

margin(p);grid % bode plot without controller

figure

margin(p*gc);grid%bode plot with controller

pcl=bandwidth(feedback(p*gc,1));%closed loop transfer function bandwidth

disp(pcl);

figure

step(feedback(p*gc,1));grid % step response