SystemInvariant

This block receives the system invariant equations and transmits them to the numerical solver (CPODES).

The invariant equations provide additional system equations, making the system over-determined.

Models, in particular models representing physical systems, may contain invariants such as energy (conservation of energy).

Signals corresponding to invariants are often monitored to validate the model (if the energy is supposed to be constant and its corresponding signal does not look constant, then the model is not correct).

Other examples are invariants are momentum or the center of mass of a multi-body system in absence of external force.

Usually the invariants are ignored by the system dynamics and the numerical solver.

But the CPODE solver can take advantage of the invariants to improve simulation accuracy and provide improved respect of the invariants.

This feature is used internally in particular for Modelica models, but its usage is not available to the user.

In a general Activate model, an invariant signal can be designated and made available for the usage by CPODE solver by using the SystemInvariant block where the invariant signal is an input.

The CPODES solver receives the signal and adjust the states at each integration step to satisfy the invariant equations.

The invariant equations can have either zero variable , i.e., signa==0, or have a constant value (the value evaluated at the beginning of the simulation.

If the constant invariant value is chosen, the invariant checking can be enabled or disabled during the simulation using the two input activation ports of the block.