Introduction StochasticAdaptiveControl(02421)

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Stochastic Adaptive Control (02421)

www.imm.dtu.dk/courses/02421

Niels Kjølstad Poulsen

Build. 303B, room 016 Section for Dynamical Systems

Dept. of Applied Mathematics and Computer Science The Technical University of Denmark

Email: nkpo@dtu.dk phone: +45 4525 3356 mobile: +45 2890 3797

2018-01-29 19:17

Introduction

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Objective (L1)

What is in the course

Dynamic systems

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Course Contents

Stochastic process and systems Filter and Control design (SS and trf) System identification

Adaptive control

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Course title

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The paper machine

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The paper machine

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Wind turbine

demand Drive

train

Generator Rotor

Wind speed

Power demand

Grid Power

Controller Pitch

angle Actuator Pitch

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Wind turbine

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Wind turbine

0 10 20 30 40 50 60 70 80 90 100

200 400 600

power [KW]

0 10 20 30 40 50 60 70 80 90 100

10 15 20

wind [m/s]

0 10 20 30 40 50 60 70 80 90 100

8 10 12 14

time [s]

pitch [deg]

Stochastic caused by weather

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Control of Marine Vessels

Surface Vessel

From: C. Holden, Roberto Galeazzi, C. Rodrguez, T. Perez, T. I. Fossen, M. Blanke, M. A. S.

Neves. Nonlinear Container Ship Model for the Study of Parametric Roll Resonance Modeling,

Identification and Control, 28, pp. 87-113, 2007.

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Control of Marine Vessels

Surface Vessel

Stochastic caused by weather

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Cruise Control

Follow that car - but don’t hit it

zt ¯ v0

1.8 1.1

Stochastics caused by human activity

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Active suspension

(a)

k b

F

mb xb

xg mb

k b

F

kt

xt mw

(b)

20 22 24 26 28 30 32 34 36 38

-15 -10 -5 0 5 10 15

Road surface

z

x

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Modelling and analysis of Stochastic Processes

Disturbance

v H v

20 22 24 26 28 30 32 34 36 38

-15 -10 -5 0 5 10 15

Road surface

z

x

d dt c

x t = Ax t + v t y t = H ( d dt c

)e t

y t = Cx t + e t

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Modelling of Stochastic Systems

Output Output

Stochastic

Control action Control action

System System

Disturbance

40 42 44 46 48 50 52 54 56 58

-15 -10 -5 0 5 10 15

Road surface

z

x

d dt c

x t = Ax t + Bu t + v t y t = G( d dt c

)u t + H( d dt c

)e t

y t = Cx t + e t

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Control design

w y

e

u System and disturbances

Model of

Objectives Constraints

System Controller

Design

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Pitch control of WT

50 60 70 80 90 100 110 120 130 140 150

100 200 300 400 500 600 700

Time [s]

Pe [KW]

50 60 70 80 90 100 110 120 130 140 150

5 10 15 20

Time [s]

Pitch angle [deg]

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State estimation (Kalman filtering)

0 20 40 60 80 100 120 140 160 180 200

-8 -6 -4 -2 0 2 4 6

x

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Kalman filtering

0 20 40 60 80 100 120 140 160 180 200

6 6.5 7 7.5 8 8.5 9

Time [s]

Wind speed [m/s]

0 20 40 60 80 100 120 140 160 180 200

-0.4 -0.2 0 0.2

Time [s]

Estimation error [m/s]

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System identification

Controller for stochastic systems do require information on the system and the stochastic disturbances.

Model

y e

u

ID Uncertainty

Knowledge Objective

System

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Wind turbine

0 10 20 30 40 50 60 70 80 90 100

200 400 600

power [KW]

0 10 20 30 40 50 60 70 80 90 100

10 15 20

wind [m/s]

0 10 20 30 40 50 60 70 80 90 100

8 10 12 14

time [s]

pitch [deg]

d dt c

x t = Ax t + Bu t + v t y t = G( d dt c

)u ^t + H( d dt c

)e ^t y t = Cx t + e t

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System identification

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System identification

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System identification

Experimental Design

Validate model Estimate parameters − Calculate model Data

Choose

Model set Choose

Criterion

Prior knowledge

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System identification

0 10 20 30 40 50 60 70 80 90

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

θ

t in sec

θ

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Adaptive Control

Time variation, nonlinearities

w

Controller System

Design

e u

y

ID

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Adaptive Control

0 10 20 30 40 50 60 70 80 90

-1 -0.5 0 0.5 1

Y, W

t in sec

y t w t

0 10 20 30 40 50 60 70 80 90

-1 -0.5 0 0.5 1

U

t in sec u t

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02421: Stochastic Adaptive Control.

Spring 2011:

The purpose of 02421 Stochastic Adaptive Control (former 04332 and 0414) is to give the students

knowledge of methods for modelling and control of Dynamic Stochastic Systems. In more details the focus is on:

Modelling and analysis of stochastic systems (ie. dynamic systems which are influenced by stochastic disturbances).

Control of stochastic systems.

Identification of stochastic systems (i.e. estimation of unknown parameters) and, finally Adaptive control of stochastic systems (i.e. simultaneous identification and control).

The Lectures will take place in F3 (Tuesdays 8-12 and Friday 12-17) in room 205, build 305 and the exercises in the G-bar (room 115 and 221, building 305).

Lecture: Niels Kjølstad Poulsen (nkp), DTU Informatics.

Teaching assistant: Mahmood Mirzaei (mmir), DTU Informatics.

Further information:

Introduction

Course description (in english) and in danish Course schedule (Timetable)

Lectured material in english and danish . This list will develop during term.

Course material Foils and slides Exercises and projects

Toolbox as zip file. (Last updated 2.12.2009) Information from an earlier version of the course:

Exercises (and solutions from E00) Not part of the course any longer.

Further information available at: Niels Kjølstad Poulsen ,IMM Bldg. 321, DTU Tel.: 4525 3356/ Fax: 4588 2673, E-mail: nkp@imm.dtu.dk

Last update Jan 29 2010

Page 1 of 1 Stochastic Adaptive Control, E2010

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1:Topi:Introdution,Systemtheory

DanishLitt.:5-8(Introdution),46-52(LTIsystems).

EnglishLitt.: Å+W:Chapter2

Exerise:1.

2:Topi:Systemtheory

DanishLitt.:52-72(Statetransformations,Polesandzeroes).

V:487-488(Z-transform)

Exerise:2.

3:Topi:Systemtheory

DanishLitt.:71-72(Stability),73-86(Control-andobservability).

502(denitematries)

EnglishLitt.: Å+W:Chapter3,p.77-79(Stability),

93-103(ontrolabilityandobservability).

Exerise:3

4:Topi:StohastiProessesI

DanishLitt.:124-135(Stohastivariable).Nottheorem3.4.

135-146mid(Stohastivetors)

EnglishLitt.: Jz:8-42.Goeasyonpage37-38and

onharateristifuntions

Exerise:4

5:Topi:StohastiProessesII

DanishLitt.: 176-240(stohastiproesses),

209-216(Internalproessmodels).

EnglishLitt.: Jz:p.47-56(stohastiproesses),

p.85-90(Internalproessmodels).

Exerise:5

6:Topi:StohastiSystemsandStateEstimation

DanishLitt.: 229-240(StohastiSystems),

146-153(ProjetionTheorem)[notproofofTheorem3.19,3.20℄,

249-260(StateEstimationandKalmanlter)[notproofof

Theorem7.7,7.8℄

265-273(EstimationerrorandStationarity)

EnglishLitt.: Å70:210-215(Filtering)[notproofoftheorem2.1℄,

218-221(ProjetionTheorem)[notproofsandnotTheorem3.3℄,

225-233(Kalmanlter)[notalgebraiproofoftheorem4.2℄.

Exerise:6

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2008

1:(30.1.2007):Topi:Introdution,Systemtheory

DanishLitt.:5-8(Introdution),46-52(LTIsystems).

Exerise:1.

ÅW:K.J.ÅströmandB.Wittenmark(1984):ComputerControlledSystems

Å+W:K.J.ÅströmandB.Wittenmark(1997):ComputerControlledSystems,

Theoryanddesign

T-bookK.J.ÅströmandB.Wittenmark(1995):AdaptiveControl

DV:M.H.A.DavisandR.B.Vinter(1985):StohastiModellingandControl

Jz: A.H.Jazwinsky(1970):StohastiProessesandFilteringTheory.

TS:TorstenSöderströmandPetreStoia(1989):SystemIdentiation

Å70: K.J.Åström(1970):IntrodutiontoStohastiControlTheory.

LL:LennartLjung(1999):SystemIdentiation-Theoryfortheuser

xreg:NielsKjølstadPoulsen(2004):StohastiControl,Externalmodels

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Course Textbooks http://www2.imm.dtu.dk/courses/02421/textbooks.html

Course material for Stochastic Adaptive Control (02421)

In danish:

Lærebog: Stokastisk adaptiv regulering af Niels Kjølstad Poulsen, Lyngby 2007.

In B5 format in ps and in pdf. Notice page references are given with respect to the B5 version.

In A4 format in ps and in pdf.

The book (in B5 format) can be bought at the IMM book store (300 kr) or be downloaded (for free).

Check opening hours for the IMM book store

In english:

Stochastic control theory, External System description (B5, pdf), (B5, ps), (A4, pdf), (A4, ps), Chapters from the Litteratur (will be announced at the lectures)

Suplementary material:

Mark Gockenback: A Practical Introduction to MATLAB (as ps) or (as html)

For further information contact, Niels Kjølstad Poulsen, IMM Build. 321, DTU Phone: +45 4588 3356 / Fax: +45 4588 2673, E-mail: nkp@imm.dtu.dk

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Foils and overhead http://www2.imm.dtu.dk/courses/02421/foils.html

Stochastic Adaptive Control

You can downlaod foils and slides from the following (developing) list. Please notice, not all foils are here and not all foils here are a part of the curriculum. The slides are in pdf as slideshow or in ps (2 by 2) for printing.

Introduction (pdf, ps) 1.

Dynamic systems (pdf ps) 2.

Stochastic vetors and variable (pdf ps) 3.

Internal process models and systems (pdf ps) 4.

State estimation and Kalman filtering (pdf ps) 5.

Control of systems (internal or state space models) (pdf ps) 6.

External process models and systems (pdf ps) 7.

Control of systems (external or transfer function models) (pdf ps) 8.

System identification (pdf ps) 9.

Model validation (pdf ps) 10.

Recursive estimation (pdf ps) 11.

Adaptive control (pdf ps) 12.

Closed loop identification (pdf ps) 13.

Experimental design (pdf ps) 14.

The total slidesshow collected in one file (pdf ps)

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Exercises in F2004 http://www2.imm.dtu.dk/courses/02421/projects.html

Stochastic Adaptive Control

02421 - Exercises and Projects in F2006.

For each exercise (or project) there exists a problem formulation, some m-files in a distribution (ie. a zipped directory) and in most cases a solution (in terms of a set of m-files). A total collection of m files and solutions can be found below.

A practicel notice in connection to the solutions: Have the distribution (where you work with the exercise) and the solution in separate directories. When examining the solutions (be in that directory and) include the distribution with the path command. For a automatic view of the solutions, just type solution (in Matlab and in the directory containing the downloaded solutions).