State variable

State variable

Simcenter Amesim uses a very broad definition of a state variable so that, if the states are , then a state may be:

Type	Description	Example
An explicit state State variable explicit	The state is defined by a starting or initial value and an explicit expression for the derivative
An implicit state State variable implicit	The state is defined by a starting or initial value and an implicit expression for the derivative
A constraint State variable constraint constraint	The state is defined by an algebraic expression not involving	find v such that

In a dynamic run the integrator attempts to estimate the evolution of these state variables with time.

A successful stabilizing run leads to an equilibrium position. In an equilibrium position, if all inputs are held constant the state variables will also be constant with time or their derivatives will be constant.

We now continue with the current example.

Procedure

1. Set the signal source value after step to 0.1.

2. Open the Run Parameters dialog box .

3. Select the Standard options tab, and select the Stabilizing + Dynamic radio button in the Simulation mode area.

4. Start a run .

5. Plot the body displacement and the body velocity.

Figure 60: Body displacement and body velocity

The run correctly produces an equilibrium position at the start of the run then gives the dynamics of the motion induced by the step. Thus we have two approaches for starting in an equilibrium position:

• Use of Hold inputs constant Hold inputs constant in combination with the Use old final values facility.

• Use of a stabilizing run.

Both these techniques are useful. The first technique approaches equilibrium using the natural dynamics of the system. In other words it uses the free response of the system. The stabilizing run uses a much more aggressive method. The table below summarizes the relative merits of the techniques.

	Hold inputs constant	Stabilizing run
Reliability	If the system is stable, the method is normally reliable.	The method does not always work and when it does work, it may give an equilibrium position which is not accessible from the starting value.
Uniqueness of solution	Normally if a solution is obtained, it does not vary significantly with parameters such as integrator tolerance.	If there are multiple equilibrium positions, it is difficult to tell in advance which one will be found.
CPU time	Can be significantly higher.	If the method works, CPU times are normally lower.
Parameters available to aid convergence	We can vary all the dynamic run parameters: tolerance, error type, maximum step size, standard/cautious, final time.	The following parameters will influence the success of the run and the CPU time: tolerance, error type, standard/cautious.

We now give a brief note on some of these points.