1. ECEN/MAE 3723 – Systems I MATLAB Lecture 2

2. Lecture Overview What is Simulink? How to use Simulink  Getting Start with Simulink  Building a model Example 1 (Differential Equations ) Example 2 (Transfer Function) Creating Subsystems Useful Information

3. What is Simulink? (1) A software package for modeling, simulating, and analyzing dynamic systems. Supports linear and nonlinear systems, modeled in continuous time, sample time, or a hybrid of the two. Systems can also be multirate (i.e. different parts that are sampled or updated at different rates)

4. What is Simulink? (2) For modeling, it provides a graphical user interface (GUI) for building models as block diagrams (using click-and-drag mouse operations) Can build models in hierarchical fashion (using both top-down and bottom-up approaches) You can simulate, analyze the output results, explore, revise your models and have FUN!

5. Lecture Overview What is Simulink? How to use Simulink  Getting Start with Simulink  Building a model Example 1 (Differential Equations ) Example 2 (Transfer Function) Creating Subsystems Useful Information

6. Start a Simulink Session Type simulink on Matlab command window Click on the SIMULINK icon on toolbar

7. Simulink Library Browser SEARCH window CREAT NEW MODEL icon BLOCK set for model construction LIBRARY

8. Create a New Model CREAT NEW MODEL icon Workspace where you construct your model

9. Lecture Overview What is Simulink? How to use Simulink  Getting Start with Simulink  Building a model Example 1 (Differential Equations ) Example 2 (Transfer Function) Creating Subsystems Useful Information

10. Building a Model Simulink Block Diagram – pictorial model of a dynamic system Each block represents an elementary dynamic system that produces an output (either continuous or discrete output) Lines represent connections of block inputs to block outputs u (Input) x (states) y (Output)

11. Building a Model (2) The following steps will guide you to construct a system/model: STEP 1: Creating Blocks STEP 2: Making connections STEP 3: Set Parameters STEP 4: Running Simulation

12. Building a Model (3) Step 1: Creating Blocks Click-Drag-Drop the Sine Wave block to Workspace Window This is the Sine Wave block is from the Sources library Sources library Save this model

13. Building a Model (4) Step 1: Creating Blocks These are from the Sinks library The Gain block is from the Math library The Mux block is from the Signals &Systems library

14. Building a Model (5) Step 2: Making connections To make connection: left-click while holding down control key (on keyboard) and drag from source port to a destination port A connected Model

15. Building a Model (6) Gain value = 5 Name the output parameter as “out1” Double click the Gain block to set the parameter for the Gain block Step 3: Set Parameters

16. Building a Model (7) click “simulation parameters” to set up the desired parameters You can change the “stop time” and then click the “OK button” Click here to run the simulation Step 4: Running Simulation

17. Building a Model (8) View output via Scope block Double click on Scope block to display output of the scope Note: Scope block is similar to oscilloscope! Output of the scope Yellow: Input sine wave Purple: Output (sine wave with gain of 5 To fit graph to frame

18. Building a Model (9) Three outputs show here View output (workspace) You can plot the output using the plot function

19. Lecture Overview What is Simulink? How to use Simulink  Getting Start with Simulink  Building a model Example 1 (Differential Equations ) Example 2 (Transfer Function) Creating Subsystems Useful Information

20. Example 1:Differential Equations (1) Example of a dynamic system: A mass- spring-damper system The Mathematical model of the system is describe by: M KB x Lets M=2kg; B = 2 Ns/m; K=2 N/m

21. Unit Step Input Example 1:Differential Equations (2) Use Simulink to simulate the step response of the system, i.e. STEP 1: Creating Blocks f(t), N 1 0 Time, s Select BLOCK setLocation in Simulink Library StepSources SumMath Operation GainMath Operation IntegratorContinuous Scope & To WorkspaceSinks

22. Example 1:Differential Equations (2) STEP 2: Making connections

23. Example 1:Differential Equations (3) STEP 3: Set Parameters Set Step time =0 Note: Assume all initial conditions = 0

24. Example 1:Differential Equations (4) STEP 4: Running Simulation Open “simulation parameters” window Set “Stop time” = 30 1 2 RUN Simulation

25. Example 1:Differential Equations (5) Step Response for the mass-spring-damper system example Output from Scope block Plot system response

26. Lecture Overview What is Simulink? How to use Simulink  Getting Start with Simulink  Building a model Example 1 (Differential Equations ) Example 2 (Transfer Function) Creating Subsystems Useful Information

27. Example 2: Transfer Function (1) Use the same mass-spring-damper system example and simulate the response using transfer function approach The transfer function of the equation (assume all initial conditions =0)

28. Example 2: Transfer Function (2) STEP 1: Creating Blocks Select BLOCK setLocation in Simulink Library StepSources Transfer FunctionContinuous Scope & To WorkspaceSinks

29. Example 2: Transfer Function (3) STEP 2: Making connections

30. Example 2: Transfer Function (4) Set Step time =0 STEP 3: Set Parameters

31. Example 2: Transfer Function (5) STEP 4: Running Simulation Open “simulation parameters” window Set “Stop time” = 30 1 2 RUN Simulation

32. Example 2: Transfer Function (6) Same output as before (Slide 21) Output from Scope block Plot system response

33. Lecture Overview What is Simulink? How to use Simulink  Getting Start with Simulink  Building a model Example 1 (Differential Equations ) Example 2 (Transfer Function) Creating Subsystems Useful Information

34. Creating Subsystems (1) Subsystem – similar to “Subroutine” Advantage of Subsystems:  Reduce the number of blocks display on the main window (i.e. simplify the model)  Group related blocks together (i.e. More organized)  Can create a hierarchical block diagram (i.e. you can create subsystems within a subsystem )  Easy to check for mistakes and to explore different parameters

35. Creating Subsystems (2) Create Subsystem using model in Example 1 STEP 1: Creating Blocks (Main window) This is the Subsystem block is from the Subsystems library

36. Creating Subsystems (3) STEP 2: Double click Subsystem block and create a model in the Subsystem block Inport (named from “sum” Outport (three outports)

37. Creating Subsystems (4) STEP 3: Making connections (Main window)

38. Creating Subsystems (5) STEP 4: Set Parameter (Main window) STEP 5: Running Simulation Then view output response Output from Scope block

39. Lecture Overview What is Simulink? How to use Simulink  Getting Start with Simulink  Building a model Example 1 (Differential Equations ) Example 2 (Transfer Function) Creating Subsystems Useful Information

40. Useful Information (1) Ramp Function Set Slope Set Start time for Ramp function Set initial value

41. Useful Information (2) Unit Step Function or Impulse t(s) 5 0 5 Input(t) Start at 5.01 s Start at 0 s

42. Useful Information (3) To run programs, have to be in the current active directory or in a directory in the path (goto File  Set path...  ) To copy the SIMULINK Model from Simulink Workspace and add to report (Edit  Copy model to clipboard) Need help on SIMULINK (At Simulink Library Browser  Click Help)