Eindhoven WIDE Meeting WP3 Apr, 2009 Pavel Trnka Honeywell Prague Laboratory.

Eindhoven WIDE MeetingWP3

Apr, 2009

Pavel Trnka

Honeywell Prague Laboratory

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Topics

WP3 goals alignment with industrial needsComments and ideas resulting from the discussions with Honeywell industrial application specialists and developers of Experion (Honeywell flag ship (complex) solution for process control).

Results / Ideas:

• Consistent identification of structured systems

• Experiment Design

• Hierarchical model management

• Greybox subspace ID for large scale

• Distributed Kalman Filtering (Luboš Baramov)

• Distributed MPC (Jaroslav Pekař)

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WP3 & Industrial needs

Important tasks aligned with industrial business objectives:

Consistent sub-models merging

• Merging of possibly overlapping sub-models with given inter connection structure into single model while respecting different model qualities and interconnections.

• Identification simplification, allowing to merge models from small ID experiments / improved estimates.

Experiment design

• Big issue (time/costs saving) especially for large systems

• Grey-box (non-linear) models

• Practical solutions are missing – subopt. solution Profit StepperHierarchical model management

• Consistent update and changes propagation to models on different hierarchical levels (lower models are seen as Closed Loops from upper layers point of view)

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WP3 - Model Management

Prior information incorporation

• model improvement / reduced number of parameters

• reduction of application engineering work

• template solutions – mistakes elimination

WP3 is well aligned with industrial needs.WP3 is well aligned with industrial needs.

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WP3 – Consistent Models Identificaton in Structure

• Sub-models in a priori given structure

• Measurements:

• In each sampling period only some measurements may be available.

• Noisy measurements.

Goal: Consistent identification / update of submodels in structure.

S1

y3

S4

S5

S2

S3

u1

u2

u3

S6

S7

S8

y1

y2

y4

y5

y6

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First approach / Simplified problem:Consistent identification of cascade systems (Bo Wahlberg)

S1,S2 : FIR models S1 S2u

v1

y1 y2

v2+ +1 20 0

( ) , ( )a bn n

i ii i

i i

S d a d S d b d

1 1 1 2 2 1 2,y S u e y S S u e

Problem: second measurement is bilinear function in parameters

First order approximation estimates fail or are biased.

0 02 0 1 1 0 2( ) ( ) ( 1)a b a by t u t b u t ea

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Further simplification:

ML estimation of parameters in product

1 1 1

2 1 2 2

y u e

y u e

Multiplied likelihoodscan be far fromlikelihoods of linear systems -> higher orderestimators needed

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Example:

Measured: u(t),y1(t),y2(t)

ML estimation – non linear problem for measurement y2.

Approximations:1) v1=0 assumption

-> offset error2) 1st order LMS -> offset error3) 2nd order LMS correct estimate

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( ) 0.91 0.18 0.8

( ) 0.56 0.62 0.13

S d d d

S d d d

S1 S2u

v1

y1 y2

v2+ +

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• Same ideas for FIRs can be directly extended to models with orthogonal basis functions and later to certain class of subspace identification methods

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WP3 – Hierarchical models

Practical application example of change propagation in hierarchical model:Configuration changes in boilers and turbines connection to common header in power plant.

Problem: consistent change (header valve on/off) propagation to all hierarchical levels without complete model recomputation (reidentification)

Industrial testing data available.

Boiler 1 Turbine 1

Ste

am H

eade

r

Boiler nb Turbine nt

... ...

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WP3 – Experiment Design

• Optimal experiment design for identification is difficult non-convex problem

• It needs to be simplified in order to become tractable

Our simplification approach:

• From parameters uncertainty p.d.f. select in each sampling period two models, such that discriminating between these two models would bring the largest improvement in model quality (improvement in parameters variance or control oriented model quality criterion)

• Design the input with limited energy to cause the largest difference on the outputs of selected models to efficiently distinguish between them

• Base the algorithm on modification of LQ / MPC to be able to identify in closed loop (open loop ID impossible for many industrial processes)

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• Based on relaxed LQ controller (LQID) – allows limited deviation from LQ optimal control

• Degree of freedom used for perturbation causing the largest output difference between selected models

1) parameters. uncertainty p.d.f. -> selection of two models to differentiate2) two models -> sorted basis of input signal ordered in differentiation

efficiency3) Ordered basis -> negative definite quadratic criterion minimization

LQID -> quadratic constraints4) non-convex QPQC (easy to solve) -> input trajectory (diminishing

horizon)

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Differentiation of two models example

• Assume two 4th order models different only in damping on two resonance frequencies

• The task is to design additional perturbation to LQ tracking controller to identify which model is closer to real system

10-2

10-1

100

101

-15

-10

-5

0

5

10

15

20

25

Mag

nitu

de (

dB)

Selected models for differentiation

Frequency (rad/sec)

M1

M2

• LQID computes perturbation close to the sum of harmonics with resonance frequencies

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LQID used for identification

• Two models selected in each sampling period from the direction of the largest parameters variance.

• LQID starts with model obtained from insufficient excitation ID

• Perturbation energy reduced in t=160, before that the system is excited to reveal directions with the largest uncertainty.

• Note the quality of step reference tracking in t=200

• Can be used for closed loop identification, where model quality monitoring (predictions monitoring) initiates reidentification.

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Subspace Greybox ID for Large Scale

• HPL developed subspace based method for prior information incorporation into Subspace identification of state space models

• We would like to extend its possibilities for large scale systems, where grey box approach should be important.

• There is no tool available for systematic use of such prior information in systematic way for systems with multiple inputs and multiple outputs

ExperimentalLow Quality Data

PriorInformation

Gre

ybox I

denti

fica

tion

Linear StateSpace Model

First Principles

Analysis of Long Time Data Log

...

Process Operator Knowledge

Possible types of prior information

• Stable/integrating/unstable channel

• Static gain

• Dominant time constant

• Settling time

• Time delay

• Direct Feed Through h(0)

• Step response smoothness (limitinghigh frequencies)

• Relative static gain

All types can be specified with accuracy.

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Distributed Estimation

• Developed an algorithm for distributed Kalman filtering- Fully optimal

- Distributed, parallelized, but communication overhead

- Heavy communication: Information need to be passed across the network

- Local estimators need to know models of other subsystems

- Can be simplified for special structures

• Advantageous for subsystems with far more states than measurements- E.g. finite approximations of PDE systems

• Ongoing work on simplifications/ suboptimal strategies

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Framework – Interconnected system

Sub-system models

1u 2u 3u1y 3y2y

1v

12i 13o12o

21o

23o31o

21i

23i

31i

32i1S 2S 3S

(( ) ( ) ) )( ) (i

i i i ui i vi ij ijj C

ix k A x k B u k B v B ik k

( ) ( ) ( )i yi i yv iy k C x k D v k

) ( )( oik iik C xo k k

Interconnections

,) ( ) ,(ij ji ii jk ko i Ck

Strictly no feed-through from iij to oik

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Distributed Estimator

• Local Kalman Filter- Interconnections modeled as

random variables with given means and covariances

- Needs measurement data from other subsystems

- Local state mean and covariance: ‘Standard KF’ with

noise/state cross-correlation

- Cross-correlation of local state with other subsystems statesNeeds injection gains from

other subsystems passed across the network

Needs models of other subsystems

iS

1iji

miji

1iji

miji

i

i

Ny

Ne

Ny

iy

1y 1y

Ne

• Simplifications:- Using measurements from a

certain network neighborhood (e.g., local and neighboring)

- Neglecting cross-covariances with states of large network distance

- Sub-optimal strategies – work OK, but need rigorous performance, robustness measures

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Distributed Estimator cntd

• Ongoing work – Suboptimal strategies- Stability conditions

- Consistency of estimations: local KFs estimate combinations of interconnected inputs; may not be consistent with estimates of the neighbors

- Exploring consensus-like strategies for estimate reconciliations.

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Task 3.2.1 Distributed MPC –Plan

1. Assess algorithms for cooperative distributed control and hierarchical coordinated control for standard (linear-quadratic) case and select one prospective for further improvements.

• Consider structural improvements as a hybrid strategy to overcome basic difficulties (e.g. horizontal communication in the coordination strategy to reduce load in the primal task/ some coordination in the cooperative scheme to handle coupled constraints/ speed-up convergence).

2. Explore suboptimal strategies trading performance for speed/computational resources, guarantee stability.

• Develop design methods. • Propose tuning techniques.

3. Develop methods for robustness analysis and design, uncertainty handling

• Extend robust MPC techniques to the distributed framework.• Cautious optimization in distributed framework

4. Propose the extension of proposed design methods to asynchronous communication.

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T3.2.2 Distributed Estimation – Plan

• Propose algorithms for distributed KF - that are consistent with the centralized KF

- compatible with distributed MPC

• Explore suboptimal strategies - trading performance for speed/computational resources,

guarantee stability. Design methods and propose tuning techniques.

• Robustness analysis / design for both distributed state estimation and distributed output feedback MPC.

• Extend design techniques to time varying systems and some classes of nonlinear systems.

• Including network delay in the estimator design - integration with T4.1-T4.2

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T3.3.2 Real-time optimization/coordinating subordinate MPCs – Plan

• Case studies – identifying industrial processes that require dynamic RTO, determining benchmark cases.

• Modelling issues– integration of results of T3.1.: - decomposition of the overall process between layers based on time-

scale and degree of non-linearity. - Safe model adaptation/scheduling based on on-line sysID in the

multilayer environment.- Interlayer model consistency.- Reduced-order control-model co-design: model for an upper layer

considers a controller in the lower one, with possible uncertainties.• Stability and robustness issues of the interlayer integration

considering feedback spanning several layers.• Uncertainty handling

- ‘Cautious optimization’ in the hierarchical framework and worst case control.

- Uncertainty decomposition: global uncertainty arising from interconnections, demands, coupled objectives versus uncertainties at the unit level; localization/propagation of uncertainties.

- Failure detection and isolation: represent failures as a class of high magnitude uncertainty; resolving failures optimally by (hybrid) optimization.

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Hierarchical decomposition of QP

• The QP Hierarchical decomposition algorithms are useful when the number of constraints of the problem is large and have a special block diagonal form.

• Properties:- Non-separable cost function

- Special structure of constraints

• Two versions- Primal decomposition – feasible solution at

each iteration

- Dual decomposition – optimal solution at each iteration, dual feasible

1

2

1 1 2 2 0

1 1 1

2 2 2

min ;

.

T T

x

xx Qx x F x

x

s t A x A x b

B x b

B x b

• The structure is suitable for MPC control with local constraints

• ‘Iterations spread in time’ approach

• Feasibility is ensured at each iteration

• Further extensions

- Extension for parametric programs

- Extension for nonlinear programs (SQP ?)

Eindhoven WIDE Meeting WP3 Apr, 2009 Pavel Trnka Honeywell Prague Laboratory.

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