## Finding an Operating Point

### What Is an Operating Point?

An operating point of a system is a dynamic configuration that satisfies design and use requirements called operating specifications. You can express such operating specifications as requirements on the system state x and inputs u. It is not always possible to find a dynamic state that satisfies all operating conditions. Also, a system might have multiple operating points satisfying the same requirements.

Operating points are essential for designing and implementing system controllers. You can optimize a system at an operating point for performance, stability, safety, and reliability.

The most important and common type of operating point is a steady state, where some or all of the system dynamic variables are constant.

#### Using Operating Points for Linearization

An important motive for finding operating points is linearization, which determines the system response to small disturbances at an operating point. Linearization results influence the design of feedback controllers to govern dynamic behavior near the operating point. A full linearization analysis requires one or more system outputs, y, in addition to inputs.

#### Example

A pilot flying an aircraft wants to find, for a given environment, a state of the aircraft engine and control surfaces that produces level, constant-velocity, and constant-altitude flight relative to the ground. The requirements of "level," "constant velocity," "constant altitude," and "relative to the ground" constitute operating specifications. This operating point is a steady state of the aircraft velocity, altitude, and orientation in space.

### Finding Operating Points in Physical Models

You have a number of ways to find an operating point in a Simscape™ model. You can impose operating specifications and isolate operating points using Simscape and Simulink® features.

Tip

To find a steady state, the Simscape steady-state solver is the most direct method. For a comprehensive suite of operating point and linearization tools, Simulink Control Design™ software is recommended.

To analyze operating points, you work with the full state vector of your model, which contains:

• Simulink components, which can be continuous or discrete.

• Simscape components, which are continuous.

Whichever method that you choose to find an operating point, if you want to use it for linearization, you must save the operating point information in the form of an operating point object, a simulation time t0, or a state vector x0 and input vector u0.

#### Simulating in Time to Search for an Operating Point

One way to identify operating points is to simulate your model and inspect its state x and output y as a time series.

1. In your Simscape model, set up sensor outputs for whatever block outputs you want to observe.

2. Connect Scope blocks, To Workspace blocks, or both, to your Simscape block outputs to observe and record simulation behavior.

3. In the Data Import/Export pane of your model Configuration Parameters settings, select the Time, States, and Output check boxes to record this simulation information in your workspace.

#### Using the Simscape Initial Condition Solver

Simscape software provides two workflows to initialize a physical model. The first solves for steady state, where all differential variables have zero derivative. Using this approach you can search for multiple steady states with the steady-state solver by varying the model inputs, parameters, and initial conditions. The second approach is to directly specify initial conditions by specifying initialization priority and targets for block variables. For more information on this approach, see Variable Initialization.

To use the first approach, enable the steady-state solver:

1. In each, some, or all of the physical networks in your Simscape model, open the Solver Configuration block.

2. In each of these block dialog boxes, select the Start simulation from steady state check box.

3. In the model Configuration Parameters settings, on the Data Import/Export pane, select the States check box to record the time series of x values in your workspace.

If you also have input signals u in the model, you can capture those inputs by connecting To Workspace blocks to the input Simulink signal lines.

4. Close these dialog boxes and start the simulation.

The first vector of values x(t=0) that you capture during simulation reflects the steady state x0 that the Simscape solver identified.

Tip

Finding an initial steady state is part of the nondefault Simscape simulation sequence. See Initial Conditions Computation.

You can simplify the initial steady-state computation by setting the simulation time to `0`. The simulation then solves for one time step only (time zero) and returns a single state vector x(t=0).

#### Using Simulink Control Design Techniques to Find Operating Points

You can use Simulink Control Design software to find operating points for models with Simscape components. Simulink Control Design provides both command-line and graphical interfaces for finding and analyzing operating points.

For more information, see Find Steady-State Operating Points for Simscape Models (Simulink Control Design).

#### Using Sources to Find Operating Points Not Recommended

You can impose an operating specification on part of a Simscape model by inserting source blocks from the Simscape Foundation Library. These impose specified values of system variables in parts of the model. You can simulate and save the state vector.

However, you cannot obtain an operating point for the original system (without the source blocks) by saving the state values from the model and then removing the source blocks. In general, the number, order, and identity of state components change after adding and removing Simscape blocks in a model.

#### Simulink`trim` Function Not Supported with Simscape Models

The Simulink `trim` function is not supported for models containing Simscape components.