1. M ATLAB T UTORIAL Simulink & Control System Design ToolBox and GUIs 1

2. C ONTENTS Simulink What’s Simulink? Constructing and running a simple model Working with MATLAB Creating subsystems Block help Control System ToolBox CST Basic Commands CST design GUIs 2

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4. C ONSTRUCTING AND R UNNING A SIMPLE M ODEL Starting Simulink Creating a new model Constructing a simple system Running a simulation Step-size of simulation Saving / opening a model 4

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6. C REATING A NEW MODEL 6

7. C ONSTRUCTING A SIMPLE SYSTEM Adding blocks to your model Connecting blocks Defining block parameters Changing Simulink parameters and Defining in Matlab Labeling blocks and signals 7

8. R UNNING A SIMULATION Time is built-in during Simulink simulation. 8

9. C HANGING THE STEP SIZE 9

10. S AVING A MODEL 10

11. W ORKING WITH M ATLAB Importing from and exporting to MATLAB 11

12. C REATING A SUBSYSTEMS 12

13. B LOCK HELP 13

14. M ODELING 14

15. M ODELING A SYSTEM OF TRANSFER FUNCTIONS 15

16. M ODELING A SYSTEM OF DIFFERENTIAL EQUATIONS This representation is more general and can be used for nonlinear systems as well 16

17. F EEDBACK CONTROL 17

18. EXAMPLE Train System [1] 18 - Free Body Diagram and Newton’s Law

19. EXAMPLE 19 State variable and output equation Transfer Function

20. EXAMPLE State-Space 20

21. EXAMPLE Simulink Model 21

22. Running the model: 22 - Defining the input: EXAMPLE

23. 23 - Simulating the model for 1000 seconds EXAMPLE

24. Obtaining the MATLAB Model 24

25. M ATLAB CONTROL SYSTEM TOOLBOX AND DESIGN GUI S - Control System ToolBox Basic commands - Sisotool GUI - Rltool GUI 25

26. C ONTROL S YSTEM T OOL B OX B ASIC COMMANDS Implementation of a Control Strategy using MATLAB Control System ToolBox 26 1- Modeling 2- PID Control 3- Root Locus 4- Frequency 5- State-Space

27. C ONTROL S YSTEM T OOL B OX B ASIC COMMANDS Modeling: a Pitch Controller [1] 27 -The state equations and transfer function of the system: Angle of attack Pitch rate Pitch angle

28. M ODELING : A P ITCH C ONTROLLER 28 - State-Space Representation - MATLAB representation and open-loop response or

29. PID D ESIGN METHOD FOR THE P ITCH C ONTROLLER The design requirements : 29

30. PID D ESIGN METHOD FOR THE P ITCH C ONTROLLER 30

31. R OOT -L OCUS D ESIGN METHOD FOR THE P ITCH C ONTROLLER The acceptable region of the locus 31 - Original root-locus plot

32. R OOT -L OCUS D ESIGN METHOD FOR THE P ITCH C ONTROLLER Adding Lead compensator 32

33. F REQUENCY R ESPONSE D ESIGN METHOD FOR THE P ITCH C ONTROLLER Closed Loop System Bode plot 33 bandwidth frequency and the phase margin must be greater than 0.9 and 52 degrees we have a bandwidth frequency of 1 rad/sec and a phase margin of 80 degrees!

34. F REQUENCY R ESPONSE D ESIGN METHOD FOR THE P ITCH C ONTROLLER 34 Adding Lead-Lag compensator

35. D ESIGNING P ITCH C ONTROLLER USING S TATE -S PACE METHOD Discrete state-space 35

36. D ESIGNING P ITCH C ONTROLLER USING S TATE -S PACE METHOD Controllability and observability 36

37. D ESIGNING P ITCH C ONTROLLER USING S TATE -S PACE METHOD Control design via pole placement 37

38. DESIGN GUI S sisotool opens the SISO design toll with Root Locus view and Bode diagram. rltool opens the SISO design tool with only Root Locus view on. 38

39. S ISO TOOL DESIGN MATLAB GUI Example: 39

40. L OAD A M ODEL FROM M ATLAB W ORK S PACE >>sisotool 40

41. I MPORT SYSTEM DATA 41

42. H OW TO DESIGN A CONTROLLER 42

43. H OW TO DESIGN A CONTROLLER Auto tuning 43

44. R OOT L OCUS AND B ODE DIAGRAMS 44

45. S TEP RESPONSE AND OTHER TIME SPECIFICATIONS 45

46. R OOT L OCUS DESIGN MATLAB GUI >>rltool 46 A Single Input Single Output (SISO) Design window will appear This GUI is exactly like “sisotool” but without frequency response design facilities!

47. R OOT L OCUS DESIGN MATLAB GUI import a pre-defined open-loop transfer function 47

48. R OOT L OCUS DESIGN MATLAB GUI Enter design parameters 48

49. R EFERENCE 49 [1]http://www.engin.umich.edu/class/ctms/exampl es

50. T HANK Y OU 50