having trouble defining a non-linear state space model

Ive been trying for the past few hours to figure out how to input a non-linear ss model and Im at a loss. the model ive been trying to input is a simple pendulum with an applied torque Tc with x1=theta and x2=thetadot

[xdot1;xdot2] = [0 x2; -9.81sin(x1) +Tc 0] y=x1

^^that is not the code i used thats the model on paper that ive been trying to input.

when i define the matricies A,B,C,and D using this code; A= [0 1;(-9.81*sin(x1)+Tc) 0]; B= [0]; C= [1]; D=[0];

then run ss(A,B,C,D)

i get an error saying: Error using ss (line 274) The value of the "a" property must be a numeric array without any Inf's or NaN's.

now im assuming the error is because of the way ive defined the A matrix with the sin(x1) in there but i have no idea how else to define that model and ive been searching the matlab guide and the internet for hours now.

anyhelp would be AWESOME

Answer 1

[Ryan G]

There are two issues here:

1) The SS model is incorrect. The applied torque should be modeled as an input which is part of the B matrix. 2) You are attempting to symbolically utilize the SS function and this cannot be done.

If you want to model the system I would suggest Simulink. Otherwise you can linaerize the model at difference points along the arc.