Decentralized and distributed control - Introduction - EECI · 2014-06-10 · Decentralized and distributed control Introduction ... challenging for systems deployed over a wide area

Decentralized and distributed controlIntroduction

M. Farina1 G. Ferrari Trecate2

1Dipartimento di Elettronica e Informazione (DEI)Politecnico di Milano, [email protected]

2Dipartimento di Informatica e Sistemistica (DIS)Universita degli Studi di Pavia, Italy

[email protected]

EECI-HYCON2 Graduate School on Control 2012Supelec, France

Farina, Ferrari Trecate () Decentralized and distributed control EECI-HYCON2 School 2012 1 / 29

[email protected]

[email protected]

Outline

1 Course information and scheduling

2 Control of large-scale systems

3 Decentralized and distributed control: motivating examples

4 Course description


Outline






Outline






Outline






Course information

European Embedded Control Institute

Lightweight association based on volunteer work created in 2006 inthe framework of the HYCON network of excellence. Currentlysupported by the network of excellence HYCON2 ”Highly-complexand networked control systems”

Mission: ”to become a long-term world-wide renowned focal point bystimulating new collaborative research on networked and embeddedcontrol”

Members: about 20 european universities and research centers

Education: since 2007 EECI organizes each year the Graduate Schoolon Control

I Several modules (18 this year) on many different topics in controltheory


Course information

Course on decentralized and distributed control

Module M4 of the European Embedded Control Institute(EECI-HYCON2) Graduate School on Control 2012

Eligible for 2nd Year Master Degree credits and Scientific Thesismodules

I

Exam for getting 3 ECTS

The exam will take pace on Friday at 13:00 How it works:

A set of papers has been distributed to students that will take theexam

Each student chooses 1 paper and presents it in 20 min. Noconstraints on the presentation style and no need of professionalpresentations !


Schedule of the course


Course information

Entry requirements

State-space approach to system and control theory for linear systems.

Course material

Recommended books:I J. Lunze. Feedback control of large scale systems. Upper Saddle River,

NJ, USA: Prentice Hall, Systems and Control Engineering, 1992.I D.D. Siljak. Decentralized control of complex systems. Mathematics in

Science and engineering, vol. 184, Academic Press, 1991.I J. B. Rawlings and D. Q. Mayne. Model predictive control: theory and

design. Nob Hill Pub., Madison, WI, USA, 2009.

Detailed references to specific papers will be provided during thecourse.

An updated version of the slides will be available at the webpagehttp://sisdin.unipv.it/lab/personale/pers_hp/ferrari/

EECI_DEDICO.php


http://sisdin.unipv.it/lab/personale/pers_hp/ferrari/EECI_DEDICO.php

http://sisdin.unipv.it/lab/personale/pers_hp/ferrari/EECI_DEDICO.php

Control of large-scale systems


Centralized control

Feedback control of Multi Input Multi Output (MIMO) systems

System

Cu y u: control variables

y : outputs

possible external setpoints


Centralized control


System


y : outputs


Pros

Simple conceptual framework: one system one controller

Studied for decades. Many controller design procedures available forlinear systems


Centralized control


System


y : outputs


Cons

Pitfalls for large-scale systems (many inputs, states and outputs)

Offline design: model-based controller synthesis can be prohibitive ifthe system model is huge and system structure is not exploited

Real-Time (RT) operations: in a sampling intervalI Transmission of system measurements to an unique controller might be

challenging for systems deployed over a wide areaI computation of the control variables might become unfeasible

Centralized control might be also unappealing for economical, political orsocietal reasons


Decentralized control

Decentralized regulators for MIMO systems

C1 C2 C3

u1 u2 u3

System

y3y2y1

Controllers attached toinput/output channels




C1 C2 C3

u1 u2 u3

System

y3y2y1


Pros

Advantages in RT operations:

Parallel computation of control variables

Easier communication if controllers, sensors and acutators arecollocated




C1 C2 C3

u1 u2 u3

System

y3y2y1


Cons

Absence of communication between controllers limits the achievableperformance


Distributed control

Distributed regulators for MIMO systems

C1 C2 C3

u1 u2 u3

System

y3y2y1

Controllers attached toinput/output channels (as indecentralized schemes)

Controllers can communicate


Distributed control


C1 C2 C3

u1 u2 u3

System

y3y2y1



Pros

Advantages in RT operations:

Parallel computation of control variables

One can tune the trade-off between communication burden andperformance


Distributed control


C1 C2 C3

u1 u2 u3

System

y3y2y1



Remarks on distributed control

Middle ground between centralized and decentralized schemes

Communication network can be part of the design problem

Challenges due to network non idealties (delays, packet drops etc ...)


Decentralized and distributed control

De/Di regulators

C1 C2 C3

u1 u2 u3

System

y3y2y1 C1 C2 C3

u1 u2 u3

System

y3y2y1


Decentralized and distributed control

De/Di regulators

C1 C2 C3

u1 u2 u3

System

y3y2y1 C1 C2 C3

u1 u2 u3

System

y3y2y1

Remarks

Decentralized control has been studied since the 70’s, mainly forlinear and unconstrained systems

Recent renowned interest triggered by advances in technology andtelecommunications

I sensor networks that enable the monitoring and control of processesspread over large geographical areas

I smart actuators with onboard communication and computationcapabilities


Exploiting system structure

Graph of N dynamically coupled systems

x1u1 ⌃1

⌃2

x2u2

u3 x3⌃3

Subsystems with their owninputs ui , states xi andoutputs

Bold arrows representphysical coupling and definethe coupling graph

I edge (j , i) iffxj influences Σi

Set of neighbors to subsystem Σi

𝒩i = {j : (i , j) is an arc of the coupling graph}In the example: 𝒩3 = {1, 2}




x1u1 ⌃1

⌃2

x2u2

u3 x3⌃3

Sometimes subsystems arenaturally defined

Temperature control in buildings

subsystems: rooms orthermal zones

coupling: heat transfer

actuators: radiators/chillers




x1u1 ⌃1

⌃2

x2u2

u3 x3⌃3

More often there are degreesof freedom in decomposing alarge-scale MIMO systeminto a set of physicallycoupled subsystems

Remarks on decomposition

Guideline: define subsystems that are loosely coupled

Ideal case for controller design: totally decoupled subsystems



De/Di regulators

x1⌃1

⌃2

x2

x3⌃3

C1

C2

C3

u1

u2

u3

x1⌃1

⌃2

x2

x3⌃3

C1

C2

C3

u1

u2

u3



Decentralized synthesis of De/Di regulators

x1⌃1

⌃2

x2

x3⌃3

C1

C2

C3

u1

u2

u3

How difficult is the offline designof a single controller ?

Centralized synthesis: somedesign step requires themodel of the whole plant

Decentralized synthesis:controllers can be designedindependently using a partialmodel of the system

Pure decentralized synthesis guaranteeling stability is available only forspecial system structures (e.g. cascade of subsystems)


Decentralized and distributed control:motivating examples


Frequency control in power network

Power network model

⌃1

⌃2

⌃3

�Pref,1

�Pref,2

�Pref,3

�!1

�!2

�!3

�PL,3

�PL,1

�PL,2



Power network model

⌃1

⌃2

⌃3

�Pref,1

�Pref,2

�Pref,3

�!1

�!2

�!3

�PL,3

�PL,1

�PL,2

Σi : power generation area equipped with primary load frequencycontrol. Linearized model with

I input ΔPref ,i : deviation of reference power from the nominal valueI output Δ𝜔i : deviation of frequency from the nominal valueI disturbance ΔPL,i : deviations from nominal load

Arrows: tie lines



Power network model

⌃1

⌃2

⌃3

�Pref,1

�Pref,2

�Pref,3

�!1

�!2

�!3

�PL,3

�PL,1

�PL,2

Goal

Design the Automatic Generation Control (AGC) layer for computingΔPref ,i , i = 1 : 3 using states of the whole network in order to guaranteethat Δ𝜔i → 0 as t → +∞ for step loads ΔPL,i .



Power network model

⌃1

⌃2

⌃3

�Pref,1

�Pref,2

�Pref,3

�!1

�!2

�!3

�PL,3

�PL,1

�PL,2

Pitfalls of a centralized controller

Not scalable with the number of areas

Not compatible with different regulation authorities

A fault in the controller might compromise the whole network stability



Case study: 4-area network

⌃1�Pref,1 �!1

�PL,1

�Pref,2

�PL,2

⌃2�!2

�PL,3

�Pref,3 �!3⌃3

�PL,4

�Pref,4⌃4

�!4

Realistic parameter valuesfrom (Saadat, 2002)

Σi is a 4-th order LTI model



5

Case study - Decentralized control

⌃1�Pref,1 �!1

�PL,1

�Pref,2

�PL,2

⌃2�!2

�PL,3

�Pref,3 �!3⌃3

�PL,4

�Pref,4⌃4

�!4C1

C2 C3

C4



Case study - Decentralized control

⌃1�Pref,1 �!1

�PL,1

�Pref,2

�PL,2

⌃2�!2

�PL,3

�Pref,3 �!3⌃3

�PL,4

�Pref,4⌃4

�!4C1

C2 C3

C4

Simulation results

0 50 100−4

−2

0

2 x 10−3 Area 1

6t

1

0 50 100−2

0

2

4 x 10−3 Area 2

6t

2

0 50 100−4

−2

0

2

4 x 10−3 Area 3

t [s]

6t

3

0 50 100−10

−5

0

5 x 10−3 Area 4

t [s]

6t

4

0 50 1000

0.05

0.1

0.15

0.2Area 1

6P re

f 1

0 50 100−0.2

−0.1

0

0.1

0.2Area 2

6P re

f 2

0 50 100−0.2

−0.1

0

0.1

0.2Area 3

t [s]

6P re

f 3

0 50 100−0.2

0

0.2

0.4Area 4

t [s]

6P re

f 4

�Pref,i for centralized and decentralized control �!i for centralized and decentralized control


Ramp metering in motorways

Intelligent transportation systems

Goal: advanced trafficmanagement for

improving driver satisfactionand safety

minimize time spent inqueues, congestion andpollution



Intelligent transportation systems

Goal: advanced trafficmanagement for

improving driver satisfactionand safety

minimize time spent inqueues, congestion andpollution

Various types of sensors, e.g. wireless magnetometers, for measuringvehicle density

Actuators: traffic lights (urban roads) variable speed limits, rampmetering



Motorway scheme

u2

u3

u1

Motorway model

Σi : blocks of cells with atleast an access point

inputs: ui ∈ [0, 1] meteringrates

state: density of vehicles

Goal:

minimize total time spent byall vehicles in the motorwayor in queues at access points



Motorway scheme

u2

u3

u1

Pitfalls of centralized control

For large number of blocks

High computational burdenfor small sampling times (10s.)

Difficult to transmit allmeasurements to a singlelocation

Lack of robustness tocontroller failure



Motorway scheme

u2

u3

u1

Current research

Development of distributedcontrollers in the EU-FP7 projectHYCON 2


Course description


Course description

The course will cover basics on1 Modelling of large-scale systems

2 Stability analysis for large-scale systems

3 Design of decentralized and distributed controllers for

3.1 unconstrained systems3.2 constrained systems

Goal

Provide the necessary background for starting research in the field ofDe/Di control

Remarks

To keep it simple, most results will be developed for LinearTime-Invariant (LTI) systems

Before starting there will be a short review of mutivariable centralizedcontrol


Course description

1. Modelling of large-scale systems

Focus on:

Different equivalent representations of large-scale systems

Decomposition of a model into subsystemsI input/output pairsI subsystems with local states


Course description

2. Stability analysis for large-scale systems

Classic tools for checking stability of LTI systems become computationallyprohibitive when applied to large-scale models. As an alternative,approaches based on the analysis of subsystems and the way they areinterconnected will be presented.


Course description

3.1 De/Di controllers for large-scale unconstrained systems

A summary of classic results developed in the 70’s and 80’s on systemstabilizability and pole placement using decentralized controllers

Some methods for the synthesis of De/Di controllersI Techniques based on LMIs (Linear Matrix Inequalities)I Pole placement through a specific channelI Recent approaches to the design of De/Di output feedback controllers


Course description

3.2 De/Di controllers for large-scale constrained systems

Methods based on Model Predictive Control (MPC).

Introduction to MPC and dynamic noncooperative games

Some De/Di MPC schemes with stability analysis (2 systems setting)


Documents

Decentralized and distributed control - Introduction - EECI · 2014-06-10 · Decentralized and distributed control Introduction ... challenging for systems deployed over a wide area