## Documentation Center |

An *operating point* of a dynamic system
defines the overall *state* of this system at a
specific time. For example, in a car engine model, variables such
as engine speed, throttle angle, engine temperature, and surrounding
atmospheric conditions typically describe the operating point.

A *steady-state operating point* of the model,
also called equilibrium or *trim* condition, includes
state variables that do not change with time.

A model might have several steady-state operating points. For
example, a hanging pendulum has two steady-state operating points.
A *stable steady-state operating point* occurs
when a pendulum hangs straight down. That is, the pendulum position
does not change with time. When the pendulum position deviates slightly,
the pendulum always returns to equilibrium; small changes in the operating
point do not cause the system to leave the region of good approximation
around the equilibrium value.

An *unstable steady-state operating point* occurs
when a pendulum points upward. As long as the pendulum points *exactly* upward,
it remains in equilibrium. However, when the pendulum deviates slightly
from this position, it swings downward and the operating point leaves
the region around the equilibrium value.

When using optimization search to compute operating points for a nonlinear system, your initial guesses for the states and input levels must be in the neighborhood of the desired operating point to ensure convergence.

When linearizing a model with multiple steady-state operating points, it is important to have the right operating point. For example, linearizing a pendulum model around the stable steady-state operating point produces a stable linear model, whereas linearizing around the unstable steady-state operating point produces an unstable linear model.

The *operating point* of a model consists
of the model initial states and root-level input signals.

For example, this Simulink^{®} model has an operating point
that consists of two variables:

Root input level set to 1

Integrator block state set to 5

The next table summarizes the operating point values of this Simulink model.

Block | Block Input | Block Operation | Block Output |
---|---|---|---|

Integrator | 1 | ||

Square | 5, set by the initial conditionx0 = 5 of
the Integrator block | squares | 25 |

Sum | 25 from Square block, 1 from Constant block | sums | 26 |

Gain | 26 | multiplies by 3 | 78 |

The next block diagram shows how the model input and the initial state of the Integrator block propagate through the model during simulation.

If your model initial states and inputs already represent the desired steady-state operating conditions, you can use this operating point for linearization or control design.

The operating point object in Simulink Control Design™ includes the tunable states in your Simulink model.

The operating point object excludes states of blocks that have internal representation, such as Backlash, Memory, and Stateflow blocks.

Block Type | Block Example | Included in Operating Point? |
---|---|---|

Blocks with double-precision real-valued states | Integrator, State Space, Transfer Function | Yes |

Root-level inport blocks with double-precision real-valued inputs | Inport | Yes |

Blocks with internal state representation that impact block output | Backlash, Memory, Stateflow | No |

Simulink provides `trim` for steady-state
operating point search. How is `trim` different
from `findop` in Simulink Control Design for
performing an optimization-based operating point search?

Simulink Control Design operating point search provides these
advantages to using `trim`:

Simulink Control Design Operating Point Search | Simulink Operating Point Search | |
---|---|---|

Graphical-user interface | Yes | No Only trim is available. |

Multiple optimization methods | Yes | No Only one optimization method |

Constrain state, input, and output variables using upper and lower bounds | Yes | No |

Specify the output value of blocks that are not connected to root model outports | Yes | No |

Steady-operating points for models with discrete states | Yes | No |

Model reference support | Yes | No |

SimMechanics™ integration | Yes | No |

Was this topic helpful?