Solve state space equation and initial conditions

Asked by Eloy Pena Asensio

Eloy Pena Asensio (view profile)

on 20 Aug 2018
Latest activity Commented on by Aquatris

Aquatris (view profile)

on 29 Aug 2018
Hello everybody.
I am trying to implement an adaptive filter identification system. The mass is variable so I have to calculate with Matlab (no Simulink) each transfer function for each mass. The problem is the continuity: I have all the state spaces but I can not solve de last "position" in order to introduce it as initial condition in the next state space.
I have state space equation like:
xdot=A.x+B.u(t) where u=sen(t)
y= C.x where C is [0 C2] so I can solve x2 because I know the value of the amplitude y(t).
The problem is that I can not solve x1, I dont know how to use ode45 for this.
The purpose is to use lsim(sys,u,t,x0) where x0=[x1 x2]
How could I resolve the value of x1 in the last position of my last state space?
A =
x1 x2
x1 -4 -12.5
x2 8 0
B =
u1
x1 4
x2 0
C =
x1 x2
y1 0 3.125
D =
u1
y1 0
As aspicted in the attached figure, the next state space starts in the correct position (last state space position) because I solved x2 but not with the proper velocity and acceleration because I didnt solve x1. The mass changes in each vertical line, the mass change point is marked with a circle

Aquatris

Aquatris (view profile)

on 29 Aug 2018
First, the thing you solve with ode is xd = Ax+Bu, which is the differential equation part of state space. The part y = Cx is not a differential equation. It is a simple linear equation. The only purpose of y = Cx is to extract the output value using the states. I recommend you review state space again.
Eloy Pena Asensio

Eloy Pena Asensio (view profile)

on 29 Aug 2018
But the initial condiction x0, x1 express the velocity and the position. That is why i am confusse about to extrat from y=Cx. What parameter should I uso in y to extract x1?
Aquatris

Aquatris (view profile)

on 29 Aug 2018
That depends on your system. How did you find the "3.125" number in your C matrix to get the position? You will use the same method to get C value for velocity.