cont 123456789

7/25/2019 Cont 123456789

1/58

Control Systems Lab - SC4070

Organization, Modeling Recap and Lab Overview

Dr. Manuel Mazo Jr.Delft Center for Systems and Control (TU Delft)[email protected].:015-2788131

TU Delft, February 10, 2014(slides modified from the original drafted by Robert Babuska)

M. Mazo Jr. (DCSC/TUD) Dynamics 1 / 48
http://find/http://goback/

7/25/2019 Cont 123456789

2/58

Outline

1 Course Organization and Content

2 Short Recap on System Modeling, Identification andPractical Control Synthesis

3 Overview of Laboratory Setups

http://find/

7/25/2019 Cont 123456789

3/58

Outline




http://goforward/http://find/http://goback/

7/25/2019 Cont 123456789

4/58

Control Systems Lab SC4070

Lecturer: Manuel Mazo Jr.Lab Assistants: Yiming Wan

Harsh Shukla

Questions on theory, class organization Lecturer

Questions on models, implementation Lab Assistants

http://find/

7/25/2019 Cont 123456789

5/58

Control Systems Lab SC4070

4 lecturesMonday 10-02 2014, 3mE-CZ F, 15:45-17:30Friday 14-02 2014, 3mE-CZ D, 15:45-17:30Friday 21-02 2014, 3mE-CZ D, 15:45-17:30

(TBC) Monday 24-02 2014, 3mE-CZ F, 10:45-12:30

1 lab demoMonday 17-02 2014, 3mE 34 F-0-420, 15:45-17:30

home preparation, laboratory sessions


7/25/2019 Cont 123456789

6/58

Control Systems Design Lab

Lab: Room 3mE 34 F-0-420


7/25/2019 Cont 123456789

7/58

Groups and Setups

Group Names Lab Setup Schedule of Lab

A

B

C

D

E

...

Lab groups are formed by three students. Send via email:

1. names, 2. student numbers, 3. emails of the three members


7/25/2019 Cont 123456789

8/58

Course Objectives

Recall control system design techniques

Applymethodologies to a real process:

first in simulations then on the actual experimental setup

Understandtheory,develophands-on experience

Prerequisites and background

Introduction to Modeling and Control Basics of Classical Control Engineering

Basics of Control Systems Design Experience with MATLAB and Simulink


7/25/2019 Cont 123456789

9/58

Outline of the lectures

(I). Logistics, introduction, modeling

(II). Dynamical systems, modeling and identification

(III). Control design methods

(III and IV). Matlab & Simulink, implementation

http://find/

7/25/2019 Cont 123456789

10/58

Home work and Laboratory sessions

follow lectures and lab demo (first two weeks)

form group, choose laboratory setup (first week)

implement a Simulink model (home)

calibrate model (estimate parameters) to match process (lab)

identify a black-box model (lab), compare with above (home)

design a controller for the simulation model (home)

test and tune the controller on the process (lab)

Discuss with the lecturer / lab assistants your plans along the way, and the

possible theory / lab problems you may encounter.

http://find/

7/25/2019 Cont 123456789

11/58

Assesment

Work is done in groups of three students.

Participation to lab sessions.

Presentation of results.(Week 12 (week of March 17th))

Written report.(Deadline: Friday morning, 28-03-2014) max 10 pages clear and complete stating exact contributions of each group member


7/25/2019 Cont 123456789

12/58

Tips for presentations and reports

Include Table of content, Introduction and Conclusions

Motivate all choices made (e.g., sampling, design parameters)

Compare simulation and real-time results, evaluate critically

Plots:

label axes (variables and units), provide figure captions use the Matlab function plot, do not paste Simulink scopes

Write concisely, do not include much theoretical background

Stress own experience, inventions, lessons learnt

Presentations: do not explain mathematical models in detail, doexplain what is measured and actuated


7/25/2019 Cont 123456789

13/58

Course Material

Book (background on control theory):Franklin, Powell, and Emami-Naeini.Feedback Control of Dynamic Systems.

Fifth Edition, Prentice Hall, 2006.

Slides and handouts:available on the WEBhttp://www.dcsc.tudelft.nl/sc4070

http://find/

7/25/2019 Cont 123456789

14/58

Course Material

Book (elements of digital control):Astrom K.J. and Wittenmark B.:Computer Controlled Systems 3ed.

Prentice Hall, 1997.(Chapters 1 9)

Matlab/Simulink Software


C

7/25/2019 Cont 123456789

15/58

Course information on the Web

Public website: www.dcsc.tudelft.nl/sc4070

Course information

Material, files

Important dates, notifications sent via BlackBoard


S h d l
http://find/

7/25/2019 Cont 123456789

16/58

Schedule

"##$ %&' ) * + , /. // /0 /( /- /1 /)

"##$ %&'# + ( ( ( ( () ( ( (* (*) )

,#-./012 3##$ D'@012

H@#-$ 754 756 757 758 759 75: 75; 75< 75= 754>

"#$%&' 7 4> 4; 68 7 4> 4; 68 74 ; 48

01*2%&' 8 44 4< 69 8 44 4< 69 4 < 49

3*%$*2%&' 9 46 4= 6: 9 46 4= 6: 6 = 4:

041/2%&' : 47 6> 6; : 47 6> 6; 7 4> 4;

5/+%&' ; 48 64 6< ; 48 64 6< 8 44 LJJF

*@0F-&

D-%E@F-& 6 49G>6 66G>6 4G>7 7 49G>7 66G>7 6=G>7 9G>8 46G>8 4=G>8

DE1F-& =G>6 4:G>6 67G>6 6G>7 =G>7 4:G>7 67G>7 7>G>7 :G>8 47G>8 6>G>8


St d L d
http://find/

7/25/2019 Cont 123456789

17/58

Study Load

Week 7 8 9 10 11 12 13 Total

Lectures 4 4 8Home prep. 10 10 10 10 6 46

Laboratory 5 5 5 15Presentation 8 3 11Report 8 12 20

Total 14 14 15 15 19 11 12 100


S i t t t t f h
http://find/

7/25/2019 Cont 123456789

18/58

Some important concepts to refresh

Frequency IO models, transfer functions

State-space models

Linearization of nonlinear models

State feedback

Observers, output feedback

Digital control


M tl b d Si li k

7/25/2019 Cont 123456789

19/58

Matlab and Simulink

software is available via BlackBoard and on faculty desktops

Matlab basics (plot, load, save, M-files, etc.)

Control toolbox:

LTI class (ss, tf, zpk) time-domain and frequency analysis (step, bode) control design tools (place, acker)

Simulink (interface between computer and experimental device)


O tli
http://find/

7/25/2019 Cont 123456789

20/58

Outline


2

Short Recap on System Modeling, Identification andPractical Control Synthesis



S bje t f the e feedb k t l
http://find/

7/25/2019 Cont 123456789

21/58

Subject of the course: feedback control

outputs

Process

inputs

disturbances

reference

Controller

feedback


Digital implementation
http://find/

7/25/2019 Cont 123456789

22/58

Digital implementation

design + implementation of computer-controlled systems

y(t)u(t)

Computer

ProcessAlgorithm

Clock

{ ( )}u t{ ( )}y tk kA-D D-A


How to obtain a process model?
http://find/

7/25/2019 Cont 123456789

23/58

How to obtain a process model?

1 physical, mechanistic modeling

1 use first principles differential equations (possibly

nonlinear)2 linearize around an operating point3 discretize to interface with controller


How to obtain process model?
http://find/

7/25/2019 Cont 123456789

24/58

How to obtain process model?

1 physical, mechanistic modeling

1 use first principles differential equations (possiblynonlinear)

2 linearize around an operating point3

discretize/digitalize to interface with controller2 from data, system identification

1 measure inputoutput data (around single operating point)2 define model structure (order), mostly linear3 estimate model parameters from data (e.g., via least

squares)


Example: Physical Modeling of a DC

7/25/2019 Cont 123456789

25/58

Example: Physical Modeling of a DCMotor

V

T

J

,

R L

+

V = Kb

b

-

+

-



7/25/2019 Cont 123456789

26/58


V

T

J

,

R L

+

V = Kb

b

-

+

-

L didt

+Ri=V Vb , Vb=K=K d

dt


http://find/

7/25/2019 Cont 123456789

27/58


V

T

J

,

R L

+

V = Kb

b

-

+

-

L didt

+Ri=V Vb , Vb=K=K d

dt

Jd2

dt2 bd

dt =T , T =Ki


Modeling: Euler-Lagrange equation
http://find/

7/25/2019 Cont 123456789

28/58

Modeling: Euler-Lagrange equation

Let T and Vbe the kinetic and potential energy of a system, then one can

use the following equations to obtain the dynamics equations of the system:

L(x) =T(x) V(x)

d

dt

L

x

=

L

x

Example: mass-spring system

T(x) = mx2

2

V(x) = kx2

2

Applying the Euler-Lagrange equation results into:

mx= kx


Example: System Identification

7/25/2019 Cont 123456789

29/58


y

Process

u


http://find/

7/25/2019 Cont 123456789

30/58


Input data

u

t

y

Process

u


http://find/

7/25/2019 Cont 123456789

31/58


y

Output data

t

Input data

u

t

y

Processu

u(1), u(2), . . . , u(N) y(1), y(2), . . . , y(N)

y(t) =G(s)u(t)


Controller Design in
http://find/

7/25/2019 Cont 123456789

32/58

Controller Design inIndustrial Practice

Order the controller.

Unpack and connect.

Turn the knobs (e.g. PID) until it works.

This is of course slightly exaggerated, notable exceptions exist:aerospace, mechatronics, automotive, process/chemical . . .


http://find/

7/25/2019 Cont 123456789

33/58



Unpack and connect.




http://find/

7/25/2019 Cont 123456789

34/58



Unpack and connect.




http://find/

7/25/2019 Cont 123456789

35/58



Unpack and connect.




In-Class Controller design procedure

7/25/2019 Cont 123456789

36/58

g p

Develop a mathematical model of the process.

Implement the model for simulation purposes, estimate parameters.

Analyze dynamic properties of the system.

Determine the specifications (objective) for the controller.

Design a controller to comply with specs.

Test controller in simulations, redesign (if necessary).

Implement on the process, test, evaluate.

At least, this is the desired situation . . .


http://find/

7/25/2019 Cont 123456789

37/58

g p










http://find/

7/25/2019 Cont 123456789

38/58










http://find/

7/25/2019 Cont 123456789

39/58










http://find/

7/25/2019 Cont 123456789

40/58










http://find/

7/25/2019 Cont 123456789

41/58










http://find/

7/25/2019 Cont 123456789

42/58










http://find/

7/25/2019 Cont 123456789

43/58










Outline
http://find/

7/25/2019 Cont 123456789

44/58





Inverted pendulum / wedge setup

7/25/2019 Cont 123456789

45/58


Inverted wedge

7/25/2019 Cont 123456789

46/58

ac M, J

m

b

g

ukm

d

d = 1

m

kmu ma bd+md

2 +mgsin()

= 1

J+ma2 +md2 mad 2 mdd+mga sin()

+mgdcos() +Mgcsin()


Parameters for inverted wedge

7/25/2019 Cont 123456789

47/58

Symbol Parameter Value

g acceleration due to gravity 9.81 ms2

a height of track 0.11 mc distance from COG to axis 0.045 mm mass of cart 0.49 kgM mass of balance 3.3 kgJ inertia of balance 0.42 kgm2

km input-to-force gain 5.0 Nb damping coefficient 4 to 10 kgs1


Inverted pendulum
http://find/

7/25/2019 Cont 123456789

48/58

m, l, J

d

b

M

g

uk

m

= 1J+ml2

mglsin() mldcos()

d = 1

M+m

kmu+ ml

2 sin() bd ml cos()


Parameters for inverted pendulum
http://find/

7/25/2019 Cont 123456789

49/58

Symbol Parameter Value

g acceleration due to gravity 9.81 ms2

l half length of pendulum 0.30 mm mass of pendulum 85 or 210 g

J inertia of pendulum 1

3 ml

2

M mass of cart 0.49 kgkm input-to-force gain 5.0 Nb damping coefficient 4 to 10 kgs1


Helicopter setup
http://find/

7/25/2019 Cont 123456789

50/58


Helicopter
http://find/

7/25/2019 Cont 123456789

51/58

u

+ = K1u

+b+K2sin = f() ( approximation . . .= K3)


Propeller nonlinearity
http://find/

7/25/2019 Cont 123456789

52/58

u

y


Gantry crane
http://find/

7/25/2019 Cont 123456789

53/58


Gantry crane
http://find/

7/25/2019 Cont 123456789

54/58


Gantry crane
http://find/

7/25/2019 Cont 123456789

55/58


Rotational pendulum
http://find/

7/25/2019 Cont 123456789

56/58


Rotational Pendulum
http://find/

7/25/2019 Cont 123456789

57/58

m1

m2

l2

l1

m2g

m1g

motor

M()+C(, )+G() = kmu

0


Rotational Pendulum: matrices
http://find/

7/25/2019 Cont 123456789

58/58

M() =

P1+ P2+ 2P3cos 2 P2+ P3cos 2

P2+ P3cos 2 P2

C(, ) = b1 P32sin 2 P3(1+ 2)sin 2

P31sin 2 b2

G() =

g1sin 1 g2sin(1+ 2)

g2sin(1+ 2)

http://find/

cont 123456789

Documents