MATLAB: Pzmap says the poles have an imaginary part when they shouldn’t have it

polepolespzmapzerozeros

I have the following transfer function:

48600/((s+90)^2 * (s+15) * (s+0.4))

and my poles should all have no imaginary part… Why I'm getting for my poles of real part's value of -90 an imaginary part different from zero that is what it should have? I got the fact that is very little and it can be considered zero, but why this function says it even exists?

Best Answer

Round off error.

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

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MATLAB: Acos(x) returns complex values. Why do they describe

But why do these complex values describe?

To understand this, you need to study calculus. This is not just limited to cos(), all trigonometric functions exhibit this behaviour. In short, the domain of trigonometric functions can be extended to the complex plane, in which case the range of those functions will also span the complex plane (instead of usual [-1, 1]). The following are some links to show how trigonometric functions and complex numbers are interconnected

https://en.wikipedia.org/wiki/Euler%27s_formula

https://en.wikipedia.org/wiki/Taylor_series

https://www.livescience.com/51399-eulers-identity.html

https://en.wikipedia.org/wiki/Sine#Relationship_to_complex_numbers

MATLAB: Values Stops Somewhere that it shouldn’t

Hi Atahan,

Your graph doesn't stop in the middle. The figure is the same with the original. Your months labeling is wrong. Change the axis limits from

ax.XAxis.Limits = [0 500];

ax.XAxis.Limits = [0 360];

I think this would resolve the problem.

Selamlar :)

--- edit -------

Although your graph is now scaled properly, your labeling for months is still wrong. In order to correct it, one way could be using text commands instead of modifying the xaxis. The code is as follows:

 days = 1:365;
%Formulas of the Equation of Time
earth_tilt = -7.655*sin(2*pi*days/365);
elliptical_orbit = 9.873*sin(4*pi*days/365+3.588);
time_variation = earth_tilt + elliptical_orbit;
plot(days,earth_tilt,'g--')
hold on
plot(days,elliptical_orbit,'r-.')
plot(days,time_variation,'black')
%deleted part
%ax = gca;
%ax.XAxisLocation = 'origin';
%ax.XAxis.TickLabels = {'Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec'}';
%ax.XAxis.Limits = [0 500];
%added part
axis([0 370 -20 20]);
months={'Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec'};
for i=1:length(months)
text(15+(i-1)*30,-19,months(i));
end
%rest
title('Time Variation')
xlabel('Day of The Year','FontWeight','bold')
ylabel('Minutes','FontWeight','bold')
legend({'Earth Elliptic Orbit','Tilt of Earth Axis','Orbit+Tilt'},'FontSize',14)
% Location information of legend
set(legend, 'Location', 'NorthWest')

Best Answer

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MATLAB: Acos(x) returns complex values. Why do they describe

MATLAB: Values Stops Somewhere that it shouldn’t

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