Control Tutorials for MATLAB and Simulink. Simulink is a graphical extension to MATLAB for modeling and simulation of systems. One of the main advantages of Simulink. Another advantage of Simulink is the. When a transfer function is built, the initial conditions are assumed to be zero. Contents. In Simulink, systems are drawn on screen as block diagrams.
Many elements of block diagrams are available, such as transfer. Simulink is integrated with MATLAB and data can be easily transfered between the programs. In these tutorials, we will apply. Simulink to the examples from the MATLAB tutorials to model the systems, build controllers, and simulate the systems. Simulink. is supported on Unix, Macintosh, and Windows environments; and is included in the student version of MATLAB for personal computers. For more information on Simulink, please visit the Mathworks link at the top of the page.
The idea behind these tutorials is that you can view them in one window while running Simulink in another window. System. model files can be downloaded from the tutorials and opened in Simulink. You will modify and extend these system while learning. Simulink for system modeling, control, and simulation.
Do not confuse the windows, icons, and menus in the tutorials. Simulink windows. Most images in these tutorials are not live - they simply display what you should see in. Simulink windows. All Simulink operations should be done in your Simulink windows. Starting Simulink.
Simulink is started from the MATLAB command prompt by entering the following command: simulink. Alternatively, you can hit the Simulink button at the top of the MATLAB window as shown here. When it starts, Simulink brings up a single window, entitled Simulink Library Browser which can be seen here. Model Files. In Simulink, a model is a collection of blocks which, in general, represents a system. In addition, to drawing a model into. File menu or from the MATLAB command prompt.
As an example, download the following model file by clicking on the following link. MATLAB from. simple. Open this file in Simulink by entering the following command in the MATLAB command window. Alternatively, you can load this. Open option in the File menu in Simulink, or by hitting Ctrl- O in Simulink). The following model window should appear.
A new model can be created by selecting New from the File menu in any Simulink window (or by hitting Ctrl- N). Basic Elements. There are two major classes of items in Simulink: blocks and lines. Blocks are used to generate, modify, combine, output, and display signals. Lines are used to transfer signals from one. Blocks. There are several general classes of blocks within the Simulink library: Sources: used to generate various signals.
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Sinks: used to output or display signals. Continuous: continuous- time system elements (transfer functions, state- space models, PID controllers, etc.)Discrete: linear, discrete- time system elements (discrete transfer functions, discrete state- space models, etc.)Math Operations: contains many common math operations (gain, sum, product, absolute value, etc.)Ports & Subsystems: contains useful blocks to build a system. Blocks have zero to several input terminals and zero to several output terminals.
Unused input terminals are indicated by. Unused output terminals are indicated by a small triangular point.
The block shown below has an unused. Lines. Lines transmit signals in the direction indicated by the arrow. Lines must always transmit signals from the output terminal. On exception to this is a line can tap off of another line, splitting. Lines can never inject a signal into another line; lines must be combined through the use of a block such as a summing junction. A signal can be either a scalar signal or a vector signal. For Single- Input, Single- Output (SISO) systems, scalar signals.
For Multi- Input, Multi- Output (MIMO) systems, vector signals are often used, consisting of two or more. The lines used to transmit scalar and vector signals are identical. The type of signal carried by a line. Simple Example. The simple model consists of three blocks: Step, Transfer Function, and Scope.
The Step is a Source block from which a step input signal originates. This signal is transferred through the line in the direction indicated by the arrow to the Transfer Function. Continuous block. The Transfer Function block modifies its input signal and outputs a new signal on a line to the Scope. The Scope is a Sink block used to display a signal much like an oscilloscope. There are many more types of blocks available in Simulink, some of which will be discussed later.
Right now, we will examine. Modifying Blocks. A block can be modified by double- clicking on it. For example, if you double- click on the Transfer Function block in the Simple model, you will see the following dialog box. This dialog box contains fields for the numerator and the denominator of the block's transfer function. By entering a vector.
For example, to change the denominator to. The Step block can also be double- clicked, bringing up the following dialog box. The default parameters in this dialog box generate a step function occurring at time = 1 sec, from an initial level of zero.
Each of these parameters can be changed. Close this dialog before. The most complicated of these three blocks in the Scope block. Double- clicking on this brings up a blank oscilloscope screen. When a simulation is performed, the signal which feeds into the scope will be displayed in this window.
Detailed operation. The only function we will use is the autoscale button, which appears as. Running Simulations.
To run a simulation, we will work with the following model file: simple. Download and open this file in Simulink following the previous instructions for this file.
You should see the following model. Before running a simulation of this system, first open the scope window by double- clicking on the scope block. Then, to start. the simulation, either select Start from the Simulation menu, click the Play button at the top of the screen, or hit Ctrl- T. The simulation should run very quickly and the scope window will appear as shown below.
Note that the simulation output (shown in yellow) is at a very low level relative to the axes of the scope. To fix this. hit the autoscale button (binoculars), which will rescale the axes as shown below. Note that the step response does not begin until t = 1. This can be changed by double- clicking on the step block. Now, we will change the parameters of the system and simulate the system again.
Double- click on the Transfer Function block in the model window and change the denominator to. Re- run the simulation (hit Ctrl- T) and you should see what appears as a flat line in the scope window. Hit the autoscale button, and you should see the following in the scope window. Notice that the autoscale button only changes the vertical axis. Since the new transfer function has a very fast response, it compressed into a very. This is not really a problem with the scope, but with the simulation itself.
Simulink simulated. To correct this, you need to change the parameters of the simulation itself. In the model window, select Configuration Parameters from the Simulation menu. You will see the following dialog box.
There are many simulation parameter options; we will only be concerned with the start and stop times, which tell Simulink. Chnage Start time from 0. Change Stop time from 1. Close the dialog box and rerun the simulation. After hitting the autoscale button, the scope window should provide a much better display of the step response as shown below. Building Systems.
In this section, you will learn how to build systems in Simulink using the building blocks in Simulink's Block Libraries. You will build the following system. If you would like to download the completed model, click here. First, you will gather all of the necessary blocks from the block libraries. Then you will modify the blocks so they correspond. Finally, you will connect the blocks with lines to form the complete system.
After this. you will simulate the complete system to verify that it works. Gathering Blocks. Follow the steps below to collect the necessary blocks: Create a new model (New from the File menu or hit Ctrl- N).
You will get a blank model window. Click on the Sources listing in the main Simulink window. This will bring up the Sources block library.
Sources are used to generate signals. Drag the Step block from the Sources window into the left side of your model window. Click on the Math Operations listing in the main Simulink window. From this library, drag a Sum and Gain block into the model window and place them to the right of the Step block in that order.
Click on the Continuous listing in the main Simulink window. First, from this library, drag a PID Controller block into the model window and place it to the right of the Gain block.
From the same library, drag a Transfer Function block into the model window and place it to the right of the PID Controller block. Click on the Sinks listing in the main Simulink window. Drag the Scope block into the right side of the model window. Modify Blocks. Follow these steps to properly modify the blocks in your model. Double- click on the Sum block.
Since you will want the second input to be subtracted, enter +- into the list of signs field. Close the dialog box. Double- click the Gain block. Change the gain to 2. Double- click the PID Controller block and change the Proportional gain to 1 and the Integral gain to 2.
Close the dialog box. Double- click the Transfer Function block. Leave the numerator , but change the denominator to [1 2 4]. Close the dialog box.
The model should appear as. Change the name of the PID Controller block to PI Controller by double- clicking on the word PID Controller.
Similarly, change the name of the Transfer Function block to Plant. Now, all the blocks are entered properly. Your model should appear as. Connecting Blocks with Lines. Now that the blocks are properly laid out, you will now connect them together.