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
An Integrator block state set to
The following table summarizes the signal values for the model at this operating point.
|Block||Block Input||Block Operation||Block Output|
|Gain||Multiply input by 3|
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.
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.
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
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 Type||Included in Operating Point?|
|Double-precision real-valued states||Yes|
|States whose value is not of type
|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 Handle Blocks with Internal State Representation)|
|States that belong to a Unit Delay block whose input is a bus signal||No|