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Some Operating Point Search Methods Finding Operating Points with Simscape, Simulink, and Related Products |
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.
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.
See Linearizing at an Operating Point.
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.
You can provide predefined state and input vectors, x0 and u0, to specify an operating point. If you do not know an operating point in advance, you have two methods of identifying an operating point that satisfies operating specifications.
Time-Based Search: Observing the actual or simulated behavior of the system in time is more general, but less precise, and usually requires a trial-and-error process to find a precise operating point.
State-Based Search: If you know the system dynamics, you can solve for steady states, at least in principle.
You can sometimes find operating points and steady states by trial and error while operating or simulating over some length of time and varying the system parameters, inputs, and initial conditions. In such a time-based approach, you isolate and study instants or intervals of time when a system satisfies the operating specifications. The system state and inputs under those conditions constitute the operating point, which you can also specify by an operating or simulation time.
The alternative to trial-and-error searching for steady states is trimming. In this state-based approach, you bypass time-based simulation and find solutions for inputs, outputs, states, and state derivatives satisfying an operating specification. Trimming specifies inputs and part of a state and solves the system dynamics for the rest of the state. The resulting full state and input vectors, x0 and u0, constitute the operating point.
In general, there is no guarantee that such solutions, x0, exist for given operating specifications and inputs, u0.
An operating point includes the state of discrete system variables that change in a discontinuous way. In general, you cannot find these states by small, continuous changes of system variables. Such states usually require systematic exploration of the discrete variables over the full range of their possible values.
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, MathWorks recommends Simulink Control Design™ software. |
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.
One way to identify operating points is to simulate your model and inspect its state x and output y as a time series.
In your Simscape model, set up sensor outputs for whatever block outputs you want to observe.
Connect Scope blocks, To Workspace blocks, or both, to your Simscape block outputs to observe and record simulation behavior.
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.
Most commonly, the operating point that you want is a steady state. The Simscape steady-state solver allows you to isolate steady states more exactly than you can with ordinary simulation. It is the only practical method to isolate steady states of a strongly nonlinear character. You can search for multiple steady states with the steady-state solver by varying the model inputs, parameters, and initial conditions.
Before simulation starts, the steady-state solver determines the model steady state x(t=0) = x0. In general, the system does not remain in this initial steady state x0 during simulation, because the system inputs u change independently, and the system has to respond by changing its state x(t).
To implement the steady-state solver:
In each, some, or all of the physical networks in your Simscape model, open the Solver Configuration block.
In each block dialog box, select the Start simulation from steady state check box.
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.
Close these dialog boxes and start 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). |
Note The techniques described in this section require the Simulink Control Design product. You must use the features of this product on the Simulink lines in your model, not directly on Simscape physical network lines or blocks. Simulink Control Design offers both command line and graphical interfaces for finding and analyzing operating points. |
Simulink Control Design methods are state-based, giving you full access to state names and values, and allow you to impose operating specifications or use simulation snapshots. They work well for simple to moderately complex Simscape models. MathWorks does not recommend these methods for highly complex Simscape models.
To find operating points, it is simplest to use the operspec and findop functions, customizing where necessary. Create an operating specification object with operspec, then compute an operating point object with findop. The findop function attempts to find an operating point that satisfies the operating specifications and reports on its success or failure. If the search is successful, find_op returns state values satisfying the operating specifications.
You have several choices for operating specifications for the components of the state vector.
| Assumed Operating Condition | Operating Specification |
|---|---|
| Default | Request that all state component derivatives be zero. This is a steady-state for the whole model, not just a Simscape network within the model. |
| Nondefault | Request any value you want independently for each state component. |
| Nondefault | Request that a particular state component derivative be zero. This is a steady-state condition for that state component. |
Tip Making full use of Simulink Control Design software to locate operating points requires that the model be able to run without trying to start in a steady state. In the Solver Configuration blocks of your model, ensure that the Start simulation from steady state check boxes are cleared. |
Additional Simulink Control Design Methods. You can also use the graphical user interface, through the model menu bar: Tools > Control Design > Linear Analysis. This interface gives you access to state, input, and output names, structure, and initial values.
For more details on the use of operating point specification objects, related functions, and the graphical interface, see the Simulink Control Design documentation.
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.
The Simulink trim function is not supported for models containing Simscape components.
 | Real-Time Simulation | Linearizing at an Operating Point |  |
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