Use Matlab to produce figure Showing second order step response (similar figure
ID: 2989128 • Letter: U
Question
Use Matlab to produce figure Showing second order step response (similar figure in notes, page 94) plotted versus ''normalized time'' omegan t Taking formula derived in class y (t) = Ku(t) - K/beta e-xi omegan t sin(beta omegan t + varphi) varphi = tan-1 (beta/xi) beta = K = 1, xi = [0.4,0.5,0.6,0.7,0.8,1], normalized time omegam t =[0,12]. use legend and axes labels Same natural frequency omegan = 20, Damping factors xi to test 1.01 (close to critical) 1.41 (can check numbers for HW problem) 2.0 3.0 one plot 4 curves legend identifies damping factors and either use if in b&w; a change in line type to distinguish curves arrows from legend values to curves if in color matlab will use color to distinguish curves. Test principle of dominant pole for 4th case xi = 3.0. The principle is that the pole(s) with the more positive real part(s) will dominate the solution (assuming poles not too close). Create an approximate solution by Removal the term in the solution with the real part of pole is most negative. On a separate plot run curves for exact solution xi = 3.0 and the other approximate case term. Use legend and symbol to distinguish two curves. One plot two curves on one plot. Turn in two plots. (use axis labels, attach code)Explanation / Answer
I have tried to do your work partially since second half is not clear. I am writing down the code and steps
1)Go to Matlab -> file ->New-> Blank M file
2)Copy the following code in the editor
function []=responseplot()
zetam=[0.4,0.5,0.6,0.7,0.8,1];
function []=plotgraph(zeta)
wn_t=(0:0.01:12);
beta=sqrt(1-zeta^(2));
phi=atan(beta/zeta);
k=1;
y=k-((k/beta).*exp(-zeta.*wn_t).*sin(beta*wn_t+phi));
figure;
plot(wn_t,y);
end
plotgraph(zetam(1));
plotgraph(zetam(2));
plotgraph(zetam(3));
plotgraph(zetam(4));
plotgraph(zetam(5));
plotgraph(zetam(6));
end
3) save it
4) go to command window and type
responseplot();
5) It will give you all the plots which can then be labelled in the the figure window by going to insert-> x label or y label
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