system identification in dynamic networks · system identification g + v u y •use of models, for...

System Identification:from open-loop and closed-loop systems

to dynamic networks

Paul M.J. Van den Hof

Inauguration speech,

Hungarian Academy of Sciences, October 2, 2017, Budapest, Hungary

System identification

• Estimating dynamic models on the

basis of noisy observations over time

G +

v

u y

• Dynamic cause-effect relationships described by

(linear) ordinary differential equations (ODE’s)

• Models in physical structure or “black-box”


G +

v

u y

• Omnipresent/ubiquitous in many branches of

science and technology

• from econometrics to mechatronics, and

• from medicine / disease treatment to robotics

• from automotive systems to industrial processes


G +

v

u y

• Use of models, for

• understanding

• prediction of future behaviour

• simulation

• indirect measurement / monitoring

• control

• Model-based control and optimization is the leading

paradigm for the optimal operation of dynamical

systems

• Model = knowledge base,

stored structured information from the past

+ G +

v

C- u yr

A “man-on-the-moon” example

• Moving mass 90 kg

• Scan a wafer in 13 sec,

0.13 sec per chip.

• Overlay of around 2 nm.

https://youtu.be/jH6Urfqt_d4?t=2m29s

ASML Wafer scanner

https://youtu.be/jH6Urfqt_d4?t=2m29s

System identification – the birth

Proc. IFAC Symp. Self-Adaptive Control Systems,

Teddington, England, 1965Karl J. Åström Torsten Bohlin

Rudolf KalmanEffective construction of linear state-variable models from

input-output functions.

Regelungstechnik, Vol. 14 (1966), 545-548.


1974Pieter Eykhoff

Goodwin and Payne (1977)Graham Goodwin

System identification – Prediction Error Approach

Lennart Ljung

(1987) (1999)


Rik Pintelon and Johan Schoukens

(2000,2012), Frequency domain approach

My own entrance into the field

Tibor Vamos Janos Gertler Laszlo Keviczky

Contents

• Introduction

• Developments and some highlights

• From SISO to MIMO

• Orthogonal basis funcitons

• Closed-loop identification

• Identification for control

• The role in future technology

• Towards dynamic network identification

Developments and some highlights

• From SISO to MIMO (multi-input multi-output)

Gu y

Just technicalities and added complexity?

How to parsemoneously and uniquely parametrize models through

a real-valued vector to be estimated from data?

For number of outputs p > 1 this is a nontrivial problem

For black-box models:

From SISO to MIMO

Options:

State space models:

For p>1, there exists no continuous parametrization that covers all models,

with a predefined order (state space dimension) [Hazewinkel and Kalman, 1976]

Matrix fractions / Vector difference equations:

with matrix polynomials in the forward and backward shift operators

Focus of many contributions in the 1980s, on the construction of canonical and

pseudo-canonical (overlapping) forms.

From SISO to MIMO

Focus of many contributions in the 1980s, among which Gevers, Wertz, Guidorzi,

Bokor and Keviczky, Correa and Glover, Rissanen, ....

After 1990s in identification

• succeeded by subspace and other techniques,

• less sensitive to lack of uniqueness of the parameters – models mapping

Important insights into the structural properties of linear MIMO systems

Set of all models with order n

Orthogonal basis functions (OBFs)

0 10 20 30 40-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Pulse response representation:

As a parametrized model set:

with complete set of orthogonal basis functions

of the function space (all stable models)

with possibly large values of

Are there appropriate generalizations of the set of basis functions

that allow a fast convergence of the series?


0 10 20 30 40-0.2

0

0.2

0.4

0.6

0.8

Consider

where the functions have dynamics

(prior info)

Examples:

Laguerre:

Orthogonalized version of

Takenake/Malmquist:

Orthogonalized version of

GOBF’s: use repeated set of poles


Generalization of tapped delay line:

With all-pass functions

Analysis and completeness:

Built on the clasic work of a.o. Otto Sász (1955) and Gábor Szegő (1939,1958)


GOBFs: very effective model structure for identification:

• identification properties fully analyzed (VdH, Heuberger, Bokor, 1995)

• simple (linear regression) algorithms

• appropriate handling of prior info

• fit for large scale problems

• used for uncertainty quantification

• for nonlinear (LPV) modeling

• and in system (realization) theory


GOBFs: very effective model structure for identification:

Hambo Transform

Closed-loop identification

+ G +

v

C

- u yr

• Many systems operate under the

presence of feedback (control)

• Intrinsic problem that input and

disturbances are correlated

• Plant input u is only partly under control of

a designed experiment rr, u and y are measured

Classical approach:

• Direct parametric method, based on u,y, (Swedish school, 1970s)

• Consistent and minimum variance (CRLB), under perfect conditions

No well-interpretable results in case of approximations


Plant representation

white noise

and uncorrelated

+ G0 +

v

C

- u yr

H0

eProjection/two-stage/IV method

Use measured excitation signal ,

to generate ,

the signal projected onto

[Van den Hof & Schrama, 1993]

Estimate the dynamics between and


Plant representation

white noise

and uncorrelated

+ G0 +

v

C

- u yr

H0

e1. Direct method

Consistent estimate of

provided that u is sufficiently exciting

2. Projection/two-stage/IV method

Consistent estimate of

provided that is sufficiently exciting

[Van den Hof & Schrama, 1993]

[Ljung, 1987]

Estimate achieves minimum variance

(CRLB)

No minimum variance properties

Implicit approximation properties

Tunable approximation properties

Identification for control

Feedback control systemIdentification

processprocessoutputinput

disturbance

1 0- 2

1 0- 1

1 00

1 0- 4

1 0- 2

1 00

1 02

10-2

10-1

100

-600

-400

-200

0

amplitude

fase

frequency

Data Model

Model Controller

Feedback control systemFeedback control system

controllercontroller processprocess+

-

outputreferenceinput

disturbance

Model-based control


controllercontroller processprocess+

-

outputreferenceinput

disturbance

• High interest from control community in 1990sGevers, Bitmead, Anderson, Schrama, de Callafon, Keviczky, Banyasz, Lee,

Skelton, Kosut, Hansen, Mareels, Bombois

• Primal result:

Optimal models for control are identified under

closed-loop conditions, with the to-be-designed

controller in the loop


ImplementatieImplementatieImplementation

RegelaarontwerpControl design

controller

IdentificatieIdentification

model

Experiment

data

ExperimentExperiment

evaluation

experiment design

Modelling for control is

learning(Gevers, 1993; Schrama, 1992;

Lee, Anderson et al, 1992,1993)

Solution through iterative

procedure

Modern version of

adaptive control


• In process control, experiments are typically expensive

Reaching the highest performance for an

expensive experiment

Designing the most economic experiment that

reaches the performance requirements

Least-costly experiment design (Bombois et al., 2006)

EU-STREP 2010-2013 – 2.5M€ www.fp7-autoprofit.eu

Goal of the project:

Advanced Autonomous Model-Based

Operation of Industrial Process Systems

Improved lifetime performance of model-based (MPC)

controllers by autonomous cost efficient maintenance.

Identification for control - Autoprofit

Autonomous maintenance for linear

model-based operation

Developments focused on:

• Performance monitoring and

diagnostics

• Autonomous testing:

• Autonomous MPC tuning:

• Extension to non-linear systems

• LPV modeling

Prototype testing on industrial

FT depropanizor (Sasol)

eco

no

mic

cri

teri

on

ba

se

d d

ecis

ion

s

least-costly

re-identification

Model structure

assessment

Retuning of

model-based

application

Performance

monitoring & diagnosis

selection of appropriate action

Degradation detected

Identification for control - Autoprofit

Contents

• Introduction








Industry 4.0 – process operations aspects

• integrated chains/networks of production units,

• fully automated, high level of sensing/actuation,

• data and product flows across classical

(company) borders (suppliers,customers,

energy grid)

• modular build-up

• continuously monitored for control,

optimization, (predictive) maintenance,

analysis, ......

• adapting to changing circumstances (process

and market conditons), and learning

• economically optimized

• supervised by new-generation HMI technology

and operators

From isolated (statically) optimized units to

[Boston Consulting Group report: “Industry

4.0, The Future of Production & Growth in

Manufacturing Industries“, 2015]

Cyber-physical systems of systems

Proposal of a European Research and Innovation Agenda on Cyber-Physical Systems of Systems, 2016-2025

Similar developments in other domains of technology

Role in future technology

Future requirements on engineering systems:

Handling of highly complex

interacting

distributed systems that

operate autonomously

with variable objectives

in a ``learning’’ mode

adapting to changing circumstances

and maintain a verifiable high performance

Role in future technology

Some required capabilities of models

1. Accuracy assessmenton-line assessment of model validity

2. Adaptabilityflexible on-line updating of models (dynamics and

interconnection structure)

3. Active data-driven learningdemands on accuracy, autonomy, robustness

active probing for information

all relating to phenomena of data-driven modeling

Data-driven modeling becomes an integral part in

virtually all complex engineering systems

Information-driven operations

From model-based control to information-driven operations

Models

Process data

Optimal proces operations

First principles

• Monitoring

• Indirect measurements

• Control

• (Predictive) maintenance

• Optimization

• Scheduling

Networked and distributed systems:

• collection of dynamical subsystems

• local control capability,

• physically interacting

Examples: smart power grids, intelligent traffic

networks, sensor networks & process plants

and their supply chain.

From single loops to interconnected systems

Contents

• Introduction








Dynamic network identification

C1

C2

G1

G2

G21

+

+

+

+ +

++

-

-

y1

y2

r1

r2

u1

u2

v1

v2

G10

G12

Gudi, R. D. and Rawlings, J. B. (2006). Identification for decentralized model predictive control.

AIChE Journal, 52(6):2198-2210.

Example decentralized MPC; 2 interconnected MPC loops

Target:

Identify interaction dynamics

Addressed by

Gudi & Rawlings (2006)

for the situation

(no cycles)


C1

C2

G1

G2

G21

+

+

+

+ +

++

-

-

y1

y2

r1

r2

u1

u2

v1

v2

G10

G12

Example decentralized MPC; 2 interconnected MPC loops

Target:

Identify interaction dynamics

Structural aspects

need to be addressed.


Some modules may be known (e.g. controllers)

ri external excitation

vi process noise

wi node signal


Relevant identification questions that appear:

How to perform local identification?

which signals to measure?



Where to optimally locate sensors and actuators?



How to identify a subnetwork?

which signals to measure?



How can we benefit from known (orange) modules?



Can we (on-line) identify the topology?

(notion of identifiability)



• Fault detection and isolation?

• Detect/identify/handle nonlinear elements


• Attractive and rich domain

of research

• Many challenges ahead

• Relation to distributed

control / optimization

(multi-agent systems)

• Relate to developments in

machine learning / data

analytics

G1

C1

G2

C2

Gr

Cr

An exciting area with lots of new questions to be explored

Acknowledgements

• My teachers and supervisors:

Ad Damen, Pieter Eykhoff, Okko Bosgra and Jan Willems

• My co-authors, PhD students and postdocs, and

colleagues from TU Delft and TU Eindhoven

• My Hungarian colleagues and co-authors from SZTAKI,

Jozsef Bokor, Laszlo Keviczky, Szoltan Szabo

• International colleagues in the control community

• My sponsors, among which EU (FP7, ERC).

Acknowledgements

Köszönöm nagyrabecsülésüket és a megtiszteltetést, amit e rangos cím jelent számomra!

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