## About Operating Points

### What Is an Operating Point?

An operating point of a dynamic system defines the states and root-level input signals of the model 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.

The following Simulink® model has an operating point that consists of two variables:

• A root-level input signal set to `1`

• An Integrator block state set to `5`

The following table summarizes the signal values for the model at this operating point.

BlockBlock InputBlock OperationBlock Output
Integrator`1`Integrate input`5`, set by the initial condition`x0 = 5`
Square`5`, set by the initial condition of the Integrator block Square input`25`
Sum`25` from Square block, `1` from Constant blockSum inputs`26`
Gain`26`Multiply input by 3`78`

The following 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.

### What Is a Steady-State Operating Point?

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

A model can have several steady-state operating points. For example, a hanging damped pendulum has two steady-state operating points at which the pendulum position does not change with time. A stable steady-state operating point occurs when a pendulum hangs straight down. When the pendulum position deviates slightly, the pendulum always returns to equilibrium. In other words, 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 nonlinear systems, your initial guesses for the states and input levels must be near 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.

### Simulink Model States Included in Operating Point Object

In Simulink Control Design™ software, an operating point for a Simulink model is represented by an operating point (`operpoint`) object. The object stores the tunable model states and their values, along with other data about the operating point. The states of blocks that have internal representation, such as Backlash, Memory, and Stateflow® blocks, are excluded.

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 Model Linearizer. 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 statesYes
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 inputsYes
Internal state representations that impact block output, such as states in Backlash, Memory, or Stateflow blocks.No (see Handle Blocks with Internal State Representation)
States that belong to a Unit Delay block whose input is a bus signalNo