Hi all, this is my first post here! I posted this already on the matlab newsgroup, but no answers yet...
I'm working on a simulation in Simulink, it involves the stability of an electric power system. I'm using the Lyapunov stability equation to determine the stability of the system, dependent of two variables, current (I) and voltage (V), so we're talking about a 3-D function. The system consists of two differential equations of the first order, so I've got two integrators in Simulink (and some constants, sums etc), that's where I input my starting points. I view the V and I using the XY scope.
In my Lyapunov equation, for a certain value where V equals a constant number, let's call it n, the value of the equation is infinite, since there is a term [1/(V-n)] in the equation.
So there's basically a huge infinite wall in V=n. Basic stability theory says that if I set my initial point below V=n, there is no way my system should return to the origin (and thus to the point of stability) because there is no way it could cross over that wall (or at least not with the limited power that my system can provide).
However, I've ran dozens of simulations and no matter where I put the starting point, it always returns to the origin. I've tried reducing the fixed-step in the solver down to 10^-9, but no luck, it always crosses the barrier.
I hope I've explained myself decenlty.
Does anyone have an idea as to what to do?
Thank you in advance for your suggestions!
I'm working on a simulation in Simulink, it involves the stability of an electric power system. I'm using the Lyapunov stability equation to determine the stability of the system, dependent of two variables, current (I) and voltage (V), so we're talking about a 3-D function. The system consists of two differential equations of the first order, so I've got two integrators in Simulink (and some constants, sums etc), that's where I input my starting points. I view the V and I using the XY scope.
In my Lyapunov equation, for a certain value where V equals a constant number, let's call it n, the value of the equation is infinite, since there is a term [1/(V-n)] in the equation.
So there's basically a huge infinite wall in V=n. Basic stability theory says that if I set my initial point below V=n, there is no way my system should return to the origin (and thus to the point of stability) because there is no way it could cross over that wall (or at least not with the limited power that my system can provide).
However, I've ran dozens of simulations and no matter where I put the starting point, it always returns to the origin. I've tried reducing the fixed-step in the solver down to 10^-9, but no luck, it always crosses the barrier.
I hope I've explained myself decenlty.
Does anyone have an idea as to what to do?
Thank you in advance for your suggestions!