Simulation-based computations produce poor operating point results when you specify:
- A simulation time that is insufficiently long to drive the model to steady state.
- Initial conditions that do not cause the model to reach true equilibrium.
You can usually combine a simulation snapshot and an optimization-based search to
improve your operating point results. For example, simulate your model until it reaches
the neighborhood of steady state and use the resulting simulation snapshot to define the
initial conditions for an optimization-based search.
NoteIf your Simulink model has internal states, do not linearize this model at the
operating point you compute from a simulation snapshot. Instead, try linearizing the
model using a simulation snapshot or at an operating point from optimization-based
search.
Which Model States Must Be at Steady State?
When computing a steady-state operating point, not all states are required to be at
equilibrium. A pendulum is an example of a system where it is possible to find an
operating point with all states at steady state. However, for other types of systems, there
may not be an operating point where all states are at equilibrium, and the application
does not require that all operating point states be at equilibrium.
For example, suppose that you build an automobile model for a cruise control application
with these states:
- Vehicle position and velocity
- Fuel and air flow rates into the engine
If your goal is to study the automobile behavior at constant cruising velocity, you need an
operating point with the velocity, air flow rate, and fuel flow rate at steady state. However,
the position of the vehicle is not at steady state because the vehicle is moving at constant
velocity. The lack of a steady-state position variable is fine for the cruise control
application because the position does not have significant impact on the cruise control
behavior. In this case, you do not need to overconstrain the optimization search for an
operating point by requiring that all states be at equilibrium.
Similar situations also appear in aerospace systems when analyzing the dynamics of an
aircraft under different maneuvers.
Compute Steady-State Operating Points