Class method.


Converts index-1 DAE system to ODE system.

This method utilizes the differentiation method of converting index-1 DAE systems to ODE systems. This method cannot handle higher index DAE systems. The DAE system is as follows:

\[\begin{split}\dot{x} = f(x,u,z) \\ 0 = g(x,u,z)\end{split}\]

where \(x\) is the states, \(u\) is the input and \(z\) is the algebraic states of the system. Differentiation method is as follows:

\[\dot{z} = -\frac{\partial g}{\partial z}^{-1}\frac{\partial g}{\partial x}f-\frac{\partial g}{\partial z}^{-1}\frac{\partial g}{\partial u}\dot{u}\]

Therefore the converted ODE system looks like:

\[\begin{split}\begin{pmatrix} \dot{x} \\ \dot{u} \\ \dot{z} \end{pmatrix} = \begin{pmatrix} f(x,u,z) \\ q \\ g(x,u,z) \end{pmatrix}\end{split}\]

where \(\dot{x},\dot{u},\dot{z}\) are the states of the model and q is the input to the model. Similarly, it can be extended to discrete time systems. The dae to ode converted model assumes that converted algebraic states and states measurements are available.


model (Model) – Index-1 DAE model


Model – Converted ODE Model

This page is auto-generated. Page source is not available on Github.