Error 'To Many Output Arguments

This is my code

clear; close; clc;

syms a1_head a2_head b hstar 

%Parameter Massa
m1 = 8095; % massa train set 1 dalam kg
m2 = 8500; % massa train set 2 dalam kg
g  = 10;

c_0_1 = 0.01176;
c_1_1 = 0.00077616;
c_2_1 = 4.48 ;

c_0_2 = 0.01176 ;
c_1_2 = 0.00077616;
c_2_2 = 4.48;

v_0 = 300;

hstar = 120;

a_1   = -1./m1.*(c_1_1 + 2.*c_2_1.*v_0);  
a_2   = -1./m2.*(c_1_2 + 2.*c_2_2.*v_0); 


a_1_head = 1-(a_1.*hstar);
a_2_head = 1-(a_2.*hstar);
b = 1;

% Model data
A = sym(zeros(4,4));
A(1,2) = a_1_head;
A(3,2) = (a_2_head) - 1;  A(3,4) = a_2_head;
display(A);

B = sym(zeros(4,2));
B(1,1) = -b*hstar;
B(2,1) = b;
B(3,2) = -b*hstar   ;
B(4,1) = -b; B(4,2) = b;
display(B);

% Q and R matrices for ARE
Q = sym(eye(4)); display(Q);
R = sym(zeros(2,2)); R(1,:) = [1 2]; R(2,:) = [2 3]; display(R);

% Matrix S to find
svar = sym('s',[1 16]);
S = [svar(1:4); svar(5:8); svar(9:12); svar(13:16)];
S(2,1) = svar(2);
S(2,2) = svar(1);
S(2,4) = svar(2);
S(3,1) = svar(3);
S(3,2) = svar(7);
S(3,3) = svar(1);
S(4,1) = svar(4);
S(4,2) = svar(2);
S(4,3) = svar(12);
S(4,4) = svar(1);
display(S);

% LHS of ARE: A'*S + S*A' - S*B*Rinv*B'*S
left_ARE = transpose(A)*S + S*A - S*B*inv(R)*transpose(B)*S; 
display(left_ARE);

% RHS of ARE: -Q
right_ARE = -Q;
display(right_ARE);

% subs(left_ARE,{s1, s2, s3}, {1, 5, 10})

% Find S in ARE
syms s1 s2 s3 s4 s7 s12
[Sol_S] = solve(left_ARE == right_ARE,s1,s2,s3,s4,s7,s12,'Real',true,'returnconditions',true)

The result like this

Sol_S = 

  struct with fields:

     s1: [0×1 sym]
     s2: [0×1 sym]
     s3: [0×1 sym]
     s4: [0×1 sym]
     s7: [0×1 sym]
    s12: [0×1 sym]

I want to find my value s using this code

D = [s1 s2 s3 s4 s7 s12];

D = [S.s1 S.s2 S.s3 S.s4 S.s7 S.s12];

But it said

Error using sym/subsref
Too many output arguments.

Error in ARE (line 78)
D = [S.s1 S.s2 S.s3 S.s4 S.s7 S.s12];

Answer 1

[Ameer Hamza]

The values of S are stored in the struct returned by solve(). The actual value of the symbolic variable does not change. So the correct syntax is

D = [Sol_S.s1 Sol_S.s2 Sol_S.s3 Sol_S.s4 Sol_S.s7 Sol_S.s12];

However, the result shows

Sol_S = 
  struct with fields:
     s1: [0×1 sym]
     s2: [0×1 sym]
     s3: [0×1 sym]
     s4: [0×1 sym]
     s7: [0×1 sym]
    s12: [0×1 sym]

that MATLAB is not able to find a solution. It is probably the case that a solution does not exist. Also, note that there are 16 equations and only 6 variables, so I guess the system is over-determined.

[Ivan Dwi Putra]

if there is 16 variabel and 16 equations it can? if the S matrix

% Matrix S to find
svar = sym('s',[1 16]);
S = [svar(1:4); svar(5:8); svar(9:12); svar(13:16)];

[Ivan Dwi Putra]

because when i run 16 equation and find 16 variables when i debug it's too long to run

[Ivan Dwi Putra]

if 16 variables it too long to run

[Ameer Hamza]

Yes, It takes a long time too, I noticed it too. However, it seems that you are trying to solve the Algebraic Riccati equation. Using Symbolic toolbox is not a good strategy. You should use a numerical solver given by MATLAB: https://www.mathworks.com/help/control/ref/icare.html. However, this requires the Control system toolbox. If you don't have the toolbox, then try these packages from FEX:

https://www.mathworks.com/matlabcentral/fileexchange/72864-the-solve-the-matrix-riccati-differential-equation

https://www.mathworks.com/matlabcentral/fileexchange/36263-algebraic-riccati-equation-solver

[Ivan Dwi Putra]

ok thank you i will try

[Ivan Dwi Putra]

I have read the code in the link, but I don't understand how I can get my s1-s16 value and how i can get the K matriks?

[Ameer Hamza]

Did you tried the icare() function?

[Ivan Dwi Putra]

i tried this link

https://www.mathworks.com/matlabcentral/fileexchange/72864-the-solve-the-matrix-riccati-differential-equation

[Ameer Hamza]

I think this package does not solve the type of Riccati equation you are trying to solve. I couldn't find a more comprehensive package related to the Algebraic Riccati equation on FEX. I guess the control toolbox function is the best option here.

[Ivan Dwi Putra]

in my state space formula i have A,B,W . where is W is placed?I have 4 state (x1,x3 is position), (x2,x4 is velocity) so my C is [0 0 1 0

0 0 0 1] like this right?

[Ivan Dwi Putra]

ok i just try icare

%Parameter Massa
m1 = 8095; % massa train set 1 dalam kg
m2 = 8500; % massa train set 2 dalam kg
g  = 10;

%Parameter Gaya
f1 = 205.10^3; % dalam N
f2 = 302.10^3; % dalam N

c_0_1 = 0.01176;
c_1_1 = 0.00077616;
c_2_1 = 4.48 ;

c_0_2 = 0.01176 ;
c_1_2 = 0.00077616;
c_2_2 = 4.48;

v_0 = 300;

hstar = 120;

a_1   = -1./m1.*(c_1_1 + 2.*c_2_1.*v_0);  
a_2   = -1./m2.*(c_1_2 + 2.*c_2_2.*v_0); 

a_1_head = 1-(a_1.*hstar);
a_2_head = 1-(a_2.*hstar);
b = 1;

p_1 = -1./m1.*(c_0_1 - c_2_1.*(v_0).^2);
p_2 = -1./m2.*(c_0_2 - c_2_2.*(v_0).^2);

A = [0  a_1_head      0        0;
     0     0          0        0;
     0 (a_2_head - 1) 0 a_2_head;
     0      0         0        0
     ];
 
B = [-b.*hstar         0;
      b                0;
      0        -b.*hstar;
     -b                b
     ];
 
U_t = [f1; f2;];
 
W = [((a_1 - 1).*v_0) - (p_1.*hstar);
     0;
     ((a_2 - 1).*v_0) - (p_2.*hstar);
     ((a_1 - 1).*v_0) - (p_1.*hstar);
     ];

 C = [0 0 1 0;
      0 0 0 1;];
 
G = -B*B';
Q = C'*C;
[X1,K1,L1] = icare(A,[],Q,[],[],[],G)

but why the result is like this

X1 =

     []


K1 =

     []


L1 =

         0
   -0.3153
   -1.0030
 -120.0037
 

x1 and k1 no value

[Ameer Hamza]

I think you should put B directly and ignore the G term. Also, you can calculate R and put it as 4th argument. Try this

[X1,K1,L1] = icare(A,B,Q,R);

It is also possible that solution does not exist. For example, read here: https://pdfs.semanticscholar.org/6b69/c5dada2e3700fa7ac6ada7cf30bf33b68136.pdf

[Ivan Dwi Putra]

do I set my own R?

i use R

R = [1 2;
     2 3;];

[X1,K1,L1] = icare(A,B,Q,R)

But still the X and K still no value

X1 =

     []


K1 =

     []


L1 =

         0
         0
   -0.3134
   -1.0087

[Ameer Hamza]

In this case, I think the equation is unsolvable for these particular matrices A, B, Q, and R.

[Ivan Dwi Putra]

ok thank you for helping me