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Steady-State Operating Point (Trimming)

What Is a Steady-State Operating Point?

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.

What Is an Operating Point in Simulink Control Design?

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.

BlockBlock InputBlock OperationBlock Output
Integrator  1
Square5, set by the initial conditionx0 = 5 of the Integrator block squares25
Sum25 from Square block, 1 from Constant blocksums26
Gain26multiplies by 378

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.

 Examples and How To

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Simulink Model States Included in Operating Point Object

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.

States that are excluded from the operating point object cannot be used in trimming computations. These states cannot be captured with operspec or operpoint or written with initopspec. Such states are also excluded from operating point displays or computations using Linear Analysis Tool. The following table summarizes which states are included and which are excluded from the operating point object.

State TypeIncluded in Operating Point?
Double-precision real-valued states .Yes
States whose value is not of type double. For example, complex-valued states, single-type states, int8-type states.No
States from root-level inport blocks with double-precision real-valued inputs.Yes
Internal state representations that impact block output, such as states in Backlash, Memory, or Stateflow® blocks.No (see Handling Blocks with Internal State Representation)
States that belong to a Unit Delay block whose input is a bus signal.No

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Advantages of Using Simulink Control Design vs. Simulink Operating Point Search

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 SearchSimulink Operating Point Search
Graphical-user interfaceYes
No
Only trim is available.
Multiple optimization methodsYesNo
Only one optimization method
Constrain state, input, and output variables using upper and lower boundsYesNo
Specify the output value of blocks that are not connected to root model outportsYesNo
Steady-operating points for models with discrete statesYesNo
Model reference supportYesNo
SimMechanics™ integrationYesNo

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