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

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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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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C REATING A NEW MODEL 6

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

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

C HANGING THE STEP SIZE 9

S AVING A MODEL 10

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

C REATING A SUBSYSTEMS 12

B LOCK HELP 13

M ODELING 14

M ODELING A SYSTEM OF TRANSFER FUNCTIONS 15

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

F EEDBACK CONTROL 17

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

EXAMPLE 19 State variable and output equation Transfer Function

EXAMPLE State-Space 20

EXAMPLE Simulink Model 21

Running the model: 22 - Defining the input: EXAMPLE

23 - Simulating the model for 1000 seconds EXAMPLE

Obtaining the MATLAB Model 24

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

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

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

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

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

PID D ESIGN METHOD FOR THE P ITCH C ONTROLLER 30

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

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

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!

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

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

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

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

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

S ISO TOOL DESIGN MATLAB GUI Example: 39

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

I MPORT SYSTEM DATA 41

H OW TO DESIGN A CONTROLLER 42

H OW TO DESIGN A CONTROLLER Auto tuning 43

R OOT L OCUS AND B ODE DIAGRAMS 44

S TEP RESPONSE AND OTHER TIME SPECIFICATIONS 45

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!

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

R OOT L OCUS DESIGN MATLAB GUI Enter design parameters 48

R EFERENCE 49 [1] es

T HANK Y OU 50