Plotting State Space Model with Disturbance

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Sam
Sam 2015-5-6
回答： Marco Boutrus 2020-3-31
Hi! I am trying to simulate a very simple dynamical system with disturbance matrix u (Dirac function).
mx''+bx'+kx=u(t)
I want to drow the displacement(position) and velocity of the system. This is my code, which seems to be not completely correct:
m=5;
c=20;
k=100;
% solves m x''+ c x' + k x = f(t)
t=0:0.1:10
A=[0 1; -(-k/m) (-c/m)];
B=[0 ; (1/m)];
C=[1 0];
D=0;
u=ones(2,1)*(heaviside(t-2)-heaviside(t-2.5));
sys1=(ss(A,B,C,D);
step (sys1)
Any suggestion for completing the code?
Thanks Sam

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采纳的回答

Sebastian Castro
Sebastian Castro 2015-5-6
I see...
In your A matrix, your spring term is -(-k/m) , and that double negative makes it positive and therefore an unstable system. Try removing one of those minus signs and you should be good.
Also, couple other things:
  1. You have an extra parenthesis when you define sys1
  2. If you want to output both position and velocity, then your C matrix should be [1 0;0 1] , or eye(2)
- Sebastian

更多回答（2 个）

Sam
Sam 2015-5-6
Dear Sebastian,
thank you for the answer. I corrected both of them, and it works now, but the excitation (U) seems not to be involved in the calculation.
U term can be a dirac impulse (as you see in my code), or a periodic function like sin. Actually I want to study the system response in underdamped, overdamped and critical situation.
  • b2<4mk - underdamping;
  • b2>4mk - overdamping;
  • b2=4mk - critical damping.
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Sebastian Castro
Sebastian Castro 2015-5-6
Your system only has 1 input (B matrix has 1 column), while you defined "u" as having 2 rows (it's a 2x101 matrix). It worked for me with these changes:
u = heaviside(t-2)-heaviside(t-2.5);
lsim(sys1,u,t);
- Sebastian

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Marco Boutrus
Marco Boutrus 2020-3-31
Hello! a very old page! but i hope u guys are still active!
i have the same formula that i need to plot (both the x and the v graphs). however i cant seem to change the stepsize, if i add
dt = 0.25; % Time step [s]
t = 0:dt:10; % Time range [s]
do i have to rewrite the whole ss form or is there a better way?
Marco

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