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The operating point of a dynamic system defines its overall state at a given time. For example, in a model of a car engine, variables such as engine speed, throttle angle, engine temperature, and surrounding atmospheric conditions typically describe the operating point. It is important to specify the operating point accurately because it affects the system's behavior. For example, the behavior of a car engine can vary greatly when it operates at high or low elevations.
An equilibrium operating point remains steady and constant with time; all states in the model are at equilibrium. It is also known as a steady state or trimmed operating point. For example, a car operating on cruise control on a flat road maintains a constant speed. Its operating point is steady, or at equilibrium.
A hanging pendulum provides an example of a stable equilibrium operating point. When the pendulum hangs straight down, its position does not change with time because it is at an equilibrium position. When its position deviates slightly from this position, it always returns to the equilibrium; small changes in the operating point do not cause the system to leave the region of good approximation around the equilibrium value.
A pendulum that points upward provides an example of an unstable equilibrium operating point. As long as the pendulum points exactly upward, it is steady at this equilibrium state. However, when the pendulum deviates slightly from this state, it swings downward and the operating point leaves the region around the equilibrium value.
This section includes the following topics:
The Simulink® full model operating point includes information from all of the blocks in a Simulink model. When you use the Simulink® Control Design™ GUI or the MATLAB® command line to create operating points for a model, you are actually creating an operating point object (what is referred to as the operating point). The operating point is a subset of the Simulink full-model operating point.
The following table shows the different types of blocks that make up a full-model operating point and which types are included in the operating point.
Makeup of Simulink® Full-Model Operating Point
| Block Types | Example of Blocks | Included in Operating Point? |
|---|---|---|
| Blocks with double value states and root level inport blocks with double data type | Integrator, State Space, Transfer Function, Inport | Yes |
| Root level inport blocks with nondouble or complex data type | Inport | No |
| Blocks with internal state representation that impacts block outputs | Backlash, Memory, Stateflow | No |
| Source blocks with outputs specified by block dialog parameters | Constant, Step | No |
The operating point includes only the block information most commonly redefined by users. This information provides you with three places to make changes to the parameters of these common blocks in your model:
Directly in the Simulink Control Design Control and Estimation Tools Manager GUI
At the MATLAB command line
In the Simulink model
Note If you want to make changes to any block not included in the operating point, you must make the changes directly in the Simulink model. |
The following figure shows a simple Simulink model that has one block with state (the integrator block) and therefore one state, x1. This state depends on the initial conditions set in the integrator block. The value of this state and the input from the inport block define the operating point in the Simulink Control Design software.
The square block output is derived from just the initial condition of the integrator block while the gain block has its output derived from both the initial condition of the integrator block and output of the constant block. The derivative dx/dt of the integrator block state is defined by the output level of the root inport block.
The state, x1, defines the signal levels at the input and output of every block in the model by propagating through the blocks in the model as follows.
The integrator block initial condition of x0 = 5 sets the state x1 = 5.
The state, x1, propagates in the direction of the arrows through the blocks in the model, defining input and output signals on each block, as described in the following table.
| Block | Input Signal Level | Block Operation | Output Signal Level |
|---|---|---|---|
| Square | 5 | squares | 25 |
| Sum | 25 from square, 1 from constant | sums | 26 |
| Gain | 26 | multiplies by 3 | 78 |
The following figure shows these input and output signal levels for each block.
| Tutorial — Computing a Steady-State Operating Point for a Simulink® Model Using the Command Line | Why Are Operating Points Important? | |
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