## Create a Simple Model

You can use Simulink® to model a system and then simulate the dynamic behavior of that system. The basic techniques you use to create a simple model in this tutorial are the same as those you use for more complex models. This example simulates simplified motion of a car. A car is typically in motion while the gas pedal is pressed. After the pedal is released, the car idles and comes to a stop.

A Simulink block is a model element that defines a mathematical relationship between its input and output. To create this simple model, you need four Simulink blocks.

Block NameBlock PurposeModel Purpose
Pulse GeneratorGenerate an input signal for the modelRepresent the accelerator pedal
GainMultiply the input signal by a constant valueCalculate how pressing the accelerator affects the car acceleration
Integrator, Second-OrderIntegrate the input signal twiceObtain position from acceleration
OutportDesignate a signal as an output from the modelDesignate the position as an output from the model

Simulating this model integrates a brief pulse twice to get a ramp. The results display in a Scope window. The input pulse represents a press of the gas pedal — 1 when the pedal is pressed and 0 when it is not. The output ramp is the increasing distance from the starting point.

### Open New Model

1. Start MATLAB®. From the MATLAB toolstrip, click the Simulink button .

2. Click the Blank Model template.

3. From the Simulation tab, select Save > Save as. In the File name text box, enter a name for your model. For example, `simple_model`. Click . The model is saved with the file extension `.slx`.

Simulink provides a set of block libraries, organized by functionality in the Library Browser. The following libraries are common to most workflows:

• Continuous — Blocks for systems with continuous states

• Discrete — Blocks for systems with discrete states

• Math Operations — Blocks that implement algebraic and logical equations

• Sinks — Blocks that store and show the signals that connect to them

• Sources — Blocks that generate the signal values that drive the model

1. From the Simulation tab, click the Library Browser button .

2. Set the Library Browser to stay on top of the other desktop windows. On the Simulink Library Browser toolbar, select the Stay on top button .

To browse through the block libraries, select a category and then a functional area in the left pane. To search all of the available block libraries, enter a search term.

For example, find the Pulse Generator block. In the search box on the browser toolbar, enter `pulse`, and then press Enter. Simulink searches the libraries for blocks with `pulse` in their name or description and then displays the blocks.

Get detailed information about a block. Right-click the Pulse Generator block, and then select Help for the Pulse Generator block. The Help browser opens with the reference page for the block.

Blocks typically have several parameters. You can access all block parameters by double-clicking the block.

### Add Blocks to a Model

To start building the model, browse the library and add the blocks.

1. From the `Sources` library, drag the Pulse Generator block to the Simulink Editor. A copy of the Pulse Generator block appears in your model with a text box for the value of the Amplitude parameter. Enter `1`.

Parameter values are held throughout the simulation.

2. Add the following blocks to your model using the same approach.

BlockLibraryParameter
Gain```Simulink/Math Operations```

Gain: `2`

Integrator, Second-Order`Simulink/Continuous`

Initial condition: `0`

Outport`Simulink/Sinks`

Port number: `1`

Add a second Outport block by copying the existing one and pasting it at another point using keyboard shortcuts.

Your model now has the blocks you need.

3. Arrange the blocks by clicking and dragging each block. To resize a block, drag a corner.

### Connect Blocks

Connect the blocks by creating lines between output ports and input ports.

1. Click the output port on the right side of the Pulse Generator block.

The output port and all input ports suitable for a connection are indicated by a blue chevron symbol.

2. Point to to see the connection cue.

Click the cue. Simulink connects the blocks with a line and an arrow indicating the direction of signal flow.

3. Connect the output port of the Gain block to the input port on the Integrator, Second-Order block.

4. Connect the two outputs of the Integrator, Second-Order block to the two Outport blocks.

5. Save your model. In the Simulation tab, click Save.

To view simulation results, connect the first output to a Signal Viewer.

Click the signal. In the Simulation tab under Prepare, click Add Viewer. Select Scope. A viewer icon appears on the signal and a scope window opens.

You can open the scope at any time by double-clicking the icon.

### Run Simulation

After you define the configuration parameters, you are ready to simulate your model.

1. In the Simulation tab, set the simulation stop time by changing the value in the toolbar.

The default stop time of `10.0` is appropriate for this model. This time value has no unit. The time unit in Simulink depends on how the equations are constructed. This example simulates the simplified motion of a car for 10 seconds — other models could have time units in milliseconds or years.

2. To run the simulation, click the button .

The simulation runs and produces the output in the viewer.

### Refine Model

This example takes an existing model, `moving_car.slx`, and models a proximity sensor based on this motion model. In this scenario, a digital sensor measures the distance between the car and an obstacle 10 m (30 ft) away. The model outputs the sensor measurement and the position of the car, taking these conditions into consideration:

• The car comes to a hard stop when it reaches the obstacle.

• In the physical world, a sensor measures the distance imprecisely, causing random numerical errors.

• A digital sensor operates at fixed time intervals.

#### Change Block Parameters

To start, open the `moving_car` model. At the MATLAB command line, enter:

```open_system('moving_car.slx') ```

You first need to model the hard stop when the car position reaches `10` . The Integrator, Second-Order block has a parameter for that purpose.

1. Double-click the Integrator, Second-Order block. The Block Parameters dialog box appears.

2. Select Limit x and enter `10` for Upper limit x. The background color for the parameter changes to indicate a modification that is not applied to the model. Click OK to apply the changes and close the dialog box.

#### Add New Blocks and Connections

Add a sensor that measures the distance from the obstacle.

1. Modify the model. Expand the model window to accommodate the new blocks as necessary.

• Find the actual distance. To find the distance between the obstacle position and the vehicle position, add the Subtract block from the `Math Operations` library. Also add the Constant block from the `Sources` library to set the constant value of `10` for the position of the obstacle.

• Model the imperfect measurement that would be typical to a real sensor. Generate noise by using the Band-Limited White Noise block from the `Sources` library. Set the Noise power parameter to `0.001`. Add the noise to the measurement by using an Add block from the `Math Operations` library.

• Model a digital sensor that fires every 0.1 seconds. In Simulink, sampling of a signal at a given interval requires a sample and hold. Add the Zero-Order Hold block from the `Discrete` library. After you add the block to the model, change the Sample Time parameter to `0.1`.

• Add another Outport to connect to the sensor output. Keep the default value of the Port number parameter.

2. Connect the new blocks. The output of the Integrator, Second-Order block is already connected to another port. To create a branch in that signal, left-click the signal to highlight potential ports for connection, and click the appropriate port.

#### Annotate Signals

Add signal names to the model.

1. Double-click the signal and type the signal name.

2. To finish, click away from the text box.

3. Repeat these steps to add the names as shown.

#### Compare Multiple Signals

Compare the `actual distance` signal with the `measured distance` signal.

1. Create and connect a Scope Viewer to the `actual distance` signal. Right-click the signal and select Create & Connect Viewer > Simulink > Scope. The name of the signal appears in the viewer title.

2. Add the `measured distance` signal to the same viewer. Right-click the signal and select Connect to Viewer > Scope1. Make sure that you are connecting to the viewer you created in the previous step.

3. Run the model. The Viewer shows the two signals, ```actual distance``` in yellow and ```measured distance``` in blue.

4. Zoom into the graph to observe the effect of noise and sampling. Click the button . Left-click and drag a window around the region you want to see more closely.

You can repeatedly zoom in to observe the details.

From the plot, note that the measurement can deviate from the actual value by as much as 0.3 m. This information becomes useful when designing a safety feature, for example, a collision warning.