Hello researchers,
I use state-space to represent a linear system (dynamic system), now i have to switch to nonlinear system.
- Is it possible to Represent an nonlinear system with State-space?
-If yes How?
Thanks
Supposing you have time- derivatives then the highest derivative order "n" is the dimension of the state vector ( taht is the order of the differential equation describing the system´s dynamics) . The state- space description can be as usual : the first state component is the solution ( or output) and the succesive derivatives uptlil order (n-1) are the remaining ones. If the dynamics is linear and the input is nonlinear with a separate nonlinearity ( for instance , a saturation) , this would be simpler. Simply describe the input to state and output mappings in the standard linerar state-space fashion and then incorporate the function descibing the nonlinearity to a feedback information mapping of the form : output or state to input.
Dear Manuel,
Can you provide us with any example of this method ? any paper or any book ?
Best regards.
It depends on the system you used but it can possible
Regards,
Cengiz Ipek
In wikipedia , at the end of this page below , you have the example of a pendulum for a sine- type nonlinearity
https://en.wikipedia.org/wiki/State-space_representation
There is no general strategy for the nonlinear case. It depends on each system.
I am adding other two papers. a) saturation with a particualr modelling of it, and b) nonlinearity being a nonlinear perturbation term in the state space. If you have a differential equation of order n then the state space has a dimension equal to n. If the nonlinear is a separate one outside the controlled plant then the control can take into account of it.
Can you please help me with transfer function of this nonlinear coupled system .