I get different results using the step response function only changing the order of the products of some parameters

1 Ansicht (letzte 30 Tage)
Hello everybody,
This is quite a simple code: I define some parameters (resistances, inductances) and after I analyse the dynamic responses. There, to obtain the kp and ki values of the PI controller, I define wn. As you can see in the code, I define two, only altering the order of the multiplications: wn = x*R/L; WN = R/L*x; The result I obtain with each one are different in the step response, as you can see in the image or compiling the code:
if true
%%Code starts here
clear all
close all
clc
%%Parameters
Rs = 1.405; % Stator resistance (Ohm)
Lls = 0.005839; % Stator Leakage inductance (H)
Llr = Lls; % Rotor Leakage inductance (H)
Rr = 1.395; % Rotor resistance (Ohm)
Lm = 0.1722; % Mutual inductance (H)
Ls = Lm + Lls; % Stator inductance
Lr = Lm + Llr; % Rotor inductance
R = Rs + Rr*(Lm^2)/(Lr^2);
sigma = 1 - Lm^2/Lr/Ls;
L = sigma*Ls;
%%Dynamics
s = tf([1 0],[1]);
x = 5; % "x" times faster dynamics (%xi = 1)
wn = x*R/L;
WN = R/L*x;
kp = 2*wn*L-R;
KP = 2*WN*L-R;
ki = wn^2*L;
KI = WN^2*L;
Ids_cl=(kp*s + ki)/L/(s^2 + (R + kp)/L*s + ki/L);
Ids_CL=(KP*s + KI)/L/(s^2 + (R + KP)/L*s + KI/L);
%%Graphs
figure()
step(Ids_cl)
hold on
step(Ids_CL)
grid on
end
Thank you for your attention,

Antworten (1)

Mischa Kim
Mischa Kim am 12 Okt. 2017
Bearbeitet: Mischa Kim am 12 Okt. 2017
Hi Mattin, welcome to the world of numerical analysis. While
wn = x*R/L;
WN = R/L*x;
are the same expressions symbolically, they are not numerically. In fact
wn - WN
ans = 2.273736754432321e-13
and, therefore
ki - KI
ans = 9.094947017729282e-12
As a result, one system is underdamped ( Ids_cl ), the other is not. In the pole zero map below you can see the Ids_cl is just "barely" underdamped, note the scale on the y-axis.
  1 Kommentar
Mattin Muniain
Mattin Muniain am 12 Okt. 2017
Bearbeitet: Mattin Muniain am 12 Okt. 2017
Thank you Mischa,but I am still surprised how that small difference in the values of ki can have so much infuence on the dynamic response of the system.

Melden Sie sich an, um zu kommentieren.

Kategorien

Mehr zu Power and Energy Systems finden Sie in Help Center und File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by