delayss - State Space Model with two states

Dear comunnity:

Nowadays i am trying to create a state space model of a system with two states (x1,x2) and a delay in the state x2. The state space representation of my system is as follows:

dx1/dt = x2(t)/LS

dx2/dt = -x1(t)/CF - (1/CF*K)*x2(t-Td) + u/CF

Where x1,x2 are the states, x2(t-Td) is the delayed state by a time Td and u is the input of the system.

Even due the help file of delayss.m is helpful, the example is given for a system with a single state x1 only. I tried the following code:

% Clear the workspace
clc
clear all

% Electrical Parameters Values
LS = 32.6e-06  ; % H
CF = 300e-06   ; % F
K = 100e-03;   ; % Ohms
Td = 1e-06;

%Definition of the State Matrices
% States defined as:

A = [0          (1/LS);
    (-1/CF)         0];

Ad = [0             0;
    (-1/(CF*K))     0];

B = [0;
     (1/CF)];
 
C = [0  1];

D = 0;

%System Definition in SS
DelayT(1) = struct('delay',Td,'a',Ad,'b',[0;0],'c',[0 0],'d',0);
sys = delayss(A,B,C,D,DelayT) 
step(sys);

But the step response of the system is not as expected, therefore i know that there is a error on how i defined the system. Could anybody support me with the correct way to define my system using delayss.

Kinds Regards

Rodrigo Guzman

Answer 1

[Ameer Hamza]

The value of Ad is wrong according to your equations. Change it to

Ad = [0             0;
      0  (-1/(CF*K))];

Similarly, do you want to output x1 or x2 as output? If you want to output x1, then change C to

C = [1  0];

Apart from that, your code is correct.

[Rodrigo Zenon Guzman Iturra]

I truly apologize, it was a foolish mistake. Thank you for your support.

Rodrigo Guzman

[Ameer Hamza]

Glad to be of help.