Using 'solve' function with variables:

Hello I'm using the following code to get a state space model, but having a trouble using 'solve' function.

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%Declaration of Variables
syms x(t) t M m ddx(t) l th(t) ddth(t) dth(t) b1 b2 dx(t) F(t) I
%Nonlinear Equations
eqn1=eq((I+m*l^2)*ddth+m*l*cos(th)*ddx-m*g*l*sin(th)+b2*dth,0)
eqn2=eq((M+m)*ddx+m*l*cos(th)*ddth-m*l*sin(th)*(dth)^2+b1*dx,F)
%Linear Equations
eqn1L=subs (eqn1,[cos(th),sin(th(t)),dth(t)^2],[1,th(t),0])
eqn2L=subs (eqn2,[cos(th),sin(th(t)),dth(t)^2],[1,th(t),0])
%Finding State Space Model
syms x_ dx_ ddx_ th_ dth_ ddth_
X = [x(t),dx(t),ddx(t),th(t),dth(t)];
X_ = [x_,dx_,th_,ddx_,dth_];
eqndx_=eq(dx_,dx_)
ddx_solution=solve(subs(eqn2L,X,X_),ddx_)
eqndth_=eq(dth_,dth_)
ddth_solution=solve(subs(eqn1L,X,X_),ddth_)
eqns_=[eqndx_,ddx_solution,eqndth_,ddth_solution];
[A,B]=equationsToMatrix(eqns_,[x_,dx_,th_,dth_])
C=[1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1];
D=[0;0;0;0];
sys = ss(A,B,C,D) 
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and this is the output for lines 13..22(end)
|eqndx_ =
dx_ == dx_
ddx_solution =
Empty sym: 0-by-1
eqndth_ =
dth_ == dth_
ddth_solution =
Empty sym: 0-by-1
A =
[ 0, 0, 0, 0]
[ 0, 0, 0, 0]
[ 0, 0, 0, 0]
[ 0, 0, 0, 0]
B =
0
0
0
0
Error using ss (line 260)
The value of the "a" property must be a numeric array without any Inf's or NaN's.
Error in Linearization_Test (line 22)
sys = ss(A,B,C,D)|

Answer 1

[Nicolas Schmit]

Replace

X = [x(t),dx(t),ddx(t),th(t),dth(t)];
X_ = [x_,dx_,th_,ddx_,dth_];

with

X = [x(t),dx(t),ddx(t),th(t),dth(t), ddth(t)];
X_ = [x_, dx_,ddx_,th_, dth_, ddth_];

Note that ss() does not work on symbolic variables.