Differential Equations in ESDL

In ESDL, each continuous state variable supports the derivation operator ddt. Differential equations can be described with the ddt operator.

An example may be a PT2 system with the continuous state variables x and xp, the input in, and the parameters d, T, K. The mathematical description of the system is:

x’ = xp;

xp’ = (K*in – (2.0*d*T*xp) – x) / (T*T);

When modeling this PT2 system with ESDL, the derivations are specified by means of the ddt method:

x.ddt(xp);

xp.ddt( (K*in – (2.0*d*T*x.ddt()) – x) / (T*T) );

The derivatives on the left side of a differential equation (i.e., in the argument of a derivation method) cannot be accessed. If such an access is required, the system needs to be reformulated.

The ddt operator can only be used in the derivatives () method