How to Plot a Symbolic Function in MATLAB for Full State Feedback Problem?

[maverick280857]

Hi everyone,

I have a small MATLAB problem which arose while trying to solve a full state feedback problem in control theory.

I have a system in state variable form

$$\dot{x} = Ax + Bu$$
$$y = Cx$$

where $u = -Kx$, so the system reduces to

$$\dot{x} = (A-BK)x$$

The solution is

$$x(t) = exp((A-BK)t)x(0)$$

I know $x(0)$, A, B and K and want to plot

$$y(t) = Cexp((A-BK)t)x(0)$$

as a function of time t.

This is the code I used to compute the state transition matrix

function [phi] = statetrans(A)
  t = sym('t');
  phi = expm(A * t);
end

And here is the code to compute y

A = [0, 1, 0, 0;4.4537,0,0,0;0,0,0,1;-0.5809,0,0,0];
B = [0;-0.3947;0;0.9211];
C = [0,0,1,0];
K = place(A,B,[-3,-2,-2+j,-2-j]); % this is used to determine the feedback gain after placing closed loop zeros at the desired location

x0 = [0.01;0.01;0.1;0.1]; % initial state

% The real code starts below
phi = statetrans((A-B*K));
x   = phi*x0;
y   = C*x;

The problem is that y is a symbolic function of t. How can I plot y as a function of t for t in some range (using something like t = 0:0.01:10)?

>> t = 0:0.01:10;
>> plot(t,y);
? Error using ==> plot
Conversion to double from sym is not possible.

Thanks in advance.

Cheers
Vivek

 

[maverick280857]

Got it, can use ezplot.

 

[oswaler]

Hi Vivek,

Thank you for sharing your MATLAB problem with us. It seems like you have already made good progress in solving the full state feedback problem in control theory. The issue you are facing is that y is a symbolic function and cannot be plotted directly. To plot y as a function of time, you will need to use the "subs" function in MATLAB to substitute the symbolic t with a numerical value from your desired range. Here is an example of how you can do this:

t = 0:0.01:10; % create a range of time values
y_numeric = subs(y, t, t(1)); % substitute t with the first value in the range
plot(t, y_numeric); % plot the numerical values of y against t

You can then repeat this process for each value in the time range to get a plot of y vs. t. I hope this helps you solve your problem. Good luck!

Best,