MATLAB: Ode23s Inputs must be floats, namely single or double.

odeode23

hi everyone
i have a problem with ode23s code
How can I fix this problem?
Is anybody here can help me please??
This the fucntion I worte:
function xp = train_feedback(t,x)
% State variable
syms x1  x2  x3  x4  x5  v1  v2  v3  v4  v5;
x = [ x1 ,  x2 ,  x3 ,  x4 ,  x5 ,  v1 ,  v2 ,   v3 ,   v4 , v5]';
A = [ 0     0     0     0     0     1      0      0     0     0
      0     0     0     0     0     1     -1      0     0     0
      0     0     0     0     0     0      1     -1     0     0
      0     0     0     0     0     0      0      1    -1     0
      0     0     0     0     0     0      0      0     1    -1
      0   -12.5   0     0     0   -0.75   0.75    0     0     0
      0    62.5  -62.5  0     0    3.75   -7.5  3.75    0     0
      0     0    62.5 -62.5   0     0     3.75  -7.5   3.75   0
      0     0     0    62.5 -62.5   0      0     3.75  -7.5   3.75
      0     0     0     0    62.5   0      0      0    3.75  -3.75];
  b1 = [0; 0; 0; 0; 0; 0.005; 0; 0; 0; 0]; % Force Input
  b2 = [0; 0; 0; 0; 0; 250; 0; 0; 0; -1250];
  vd = 25*(1 - exp(-t/40));
  % First Design R = 1/120^2
  k = [54.5333 , 16.2848 , -1.3027 , -4.3607 , 191.7414 , -40.4841 , -34.2067 , -29.7070 , -27.3437 , 52.0886];
  dx = [x(2)-20 ; x(3)-20 ; x(4)-20 ; x(5)-20];
  dv = [x(6)-vd ; x(7)-vd ; x(8)-vd ; x(9)-vd ; x(10)-vd];
  z = x(6)-vd;
  X = [dx ; dv ; z];
  u = -k*X;
  xp = A*x + b1*u +b2;
end
And then:
% Feedback LQR
clear
close all
clc
tspan = [0 30];
x0 = [0 ;20 ;20 ;20 ;20 ;0 ;0 ;0 ;0 ;0];
[t , x] = ode23s(@train_feedback , tspan , x0 , ...
            odeset('OutputFcn','odeplot','OutputSel',[2:5]));
vd = 25*(1-exp(-t/40));
k = [54.533 , 16.2848 , -1.3027 , -4.3607 , 191.7414 , -40.4841 ,-34.2067 , -29.7070 , -27.3437 , 52.0886];
Ks = 2.5e3;
Ds = 1.5e2;
N = max(size(t));
for i = 1:N
    dx = [x(i,2)-20 ; x(i,3)-20 ; x(i,4)-20 ; x(i,5)-20];
    dv = [x(i,6)-vd(i) ; x(i,7)-vd(i) ; x(i,8)-vd(i) ; x(i,9)-vd(i) ; x(i,10)-vd(i)];
    z = x(i,6)-vd(i);
    X(i , :) = [dx;dv;z];
    F(i) = -k*X(i,:)';
    Fs(:,i) = Ks*dx;
end
figure (1)
subplot(2,1,1)
plot(t,x(:,1)/1000)
grid on
xlabel('Time (sec)')
ylabel('Train Position (Km)')
subplot(2,1,2)
plot(t,vd,t,x(:,6),'-.k')
grid on
xlabel('Time (sec)')
ylabel('Train Velocity (m)')
legend('Desire Velocity','Real Velocity')
set(findall(figure(1),'type','line'),'linewidth',2)
figure(2)
subplot(2,1,1)
plot(t,F,t,Fs(1,:),'-.',t,Fs(4,:),'--')
grid on
xlabel ('Time (sec)')
ylabel ('Force (KN)')
legend ('Input Force','Spring Force 1' , 'Spring Force 4')
subplot(2,1,2)
plot(t,Ds*(x(:,6)-x(:,7)),t,Ds*(x(:,9)-x(:,10)),'-.')
grid on
xlabel ('Time (sec)')
ylabel ('Force (KN)')
legend ('Damping Force 1','Damping Force 4')
set(findall(figure(2),'type','line'),'linewidth',2)
But the program give me this error:
Error using odearguments (line 110)
Inputs must be floats, namely single or double.
Error in ode23s (line 121)
= odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);
Error in LQR_modern (line 7)
[t , x] = ode23s(@train_feedback , tspan , x0 , …

Best Answer

Delete these two lines in your function and it works:
syms x1  x2  x3  x4  x5  v1  v2  v3  v4  v5;
x = [ x1 ,  x2 ,  x3 ,  x4 ,  x5 ,  v1 ,  v2 ,   v3 ,   v4 , v5]';
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