Undefined function 'Poles' for input arguments of type 'double'.

I run into the problem where my code produces the error message as stated above. I've searched around and 1 possible problem has something to do with my file path. I have since fixed that but I am still receiving the same problem. Am hoping somebody could help point out my error in the code. I am trying to apply Lyapunov stability analysis to my state space system and plot a phase portrait with the program below.

Any help is much appreciated! Thanks in advance.

% Using Lyapunov analysis, assess the stability properties of the
% system; any case will do since the A matrix is identical for all
% input/ouput cases, the stability condition does not change. 
% Check your results via eigenvalue analysis. Plot the phase portraits to
% reinforce your results. 

% Values used from chapter 1.
% Mass values 
m1 = 1; 
m2 = 2;
m3 = 3; 

% Spring Coefficients 
k1 = 1; 
k2 = 2; 
k3 = 3; 
k4 = 4; 

% Damping Coefficients 
c1 = 1; 
c2 = 2;
c3 = 3; 
c4 = 4;

% A, B, C and D matrix generated from chapter 1. 
A = [0 0 0 1 0 0; 
     0 0 0 0 1 0; 
     0 0 0 0 0 1; 
     ((-1)*((k1+k2)/m1)) (k2/m1) 0 ((-1)*((c1+c2)/m1)) (c2/m1) 0; 
     (k2/m2) ((-1)*((k2+k3)/m2)) (k3/m3) (c2/m2) ((-1)*((c2+c3)/m2)) (c3/m2); 
     0 (k3/m3) ((-1)*((k3+k4)/m3)) 0 (c3/m3) ((-1)*((c3+c4)/m3))];

B = [0 0 0;
     0 0 0; 
     0 0 0;
     (1/m1) 0 0;
     0 (1/m2) 0;
     0 0 (1/m3)];
  
 C = [1 0 0 0 0 0; 
      0 1 0 0 0 0; 
      0 0 1 0 0 0];
 
 D = [0 0 0; 
      0 0 0; 
      0 0 0];

sys_1 = ss(A,B,C,D);
X0(101,:);

if (real(Poles(1))==0 | real(Poles(2))==0) % lyap will fail
    if (real(Poles(1)) <=0 | real(Poles(2)) <=0)
        disp('System is marginally stable'); 
    else 
        disp('System is unstable');
    end
else % lyap succeeds 
    Q = eye(6);         % Given positive definite matrix 
    P = lyap(A',Q);     % Solve for P 
    pm1 = det(P(1,1));  % Sylvester's method to see if P is positive definite 
    pm2 = det(P(1:6,1:6)); 
    
    if (pm1>0 & pm2>0)
        disp('System is asymptotically stable.'); 
    else 
        disp('System is unstable');
    end 
    
end

figure;
plot(Xo(:,1),Xo(:,2),'k');
    axis([-1.5 -1.5 -2 1]);
set(gca,'Fontsize',18);
xlabel('\itx_1(rad)');
ylabel('\itx_2 (rad/s)');

Answer 1

[Paul]

From the way the code is written it looks like Poles is supposed to be a variable. But the code never actually computes Poles. So Matlab can't find a variable called Poles, so it next assumes it's a function. But Matlab doesn't have a function called Poles and the error results. I suspect that you meant to do

Poles = pole(sys)
% doc pole  % for more information

before executing the if statement. Of course, Poles will have six elements because the system is 6th order.

Also, you might want to take another look at that if logic. I don't know exactly what it's trying to do, but it looks peculiar.

[Justin Goh]

Thank you Paul. I feel like a fool for not realizing that. I managed to fix my program and it now does not produce that problem.