Model Predictive Control for Distributed Systems:

Coordination Strategies & Structure

Yi ZHENG, Shaoyuan LI School of Electronic Information and Electrical Engineering

Shanghai Jiao Tong University Aug. 1st, 2015

The 26th Chinese Process Control Conference, 2015

Dynamic Systems Optimization Group -----Institute of Automation, Shanghai Jiao Tong University Team Member

• Pro. Shaoyuan Li • Pro. Ning Li • Associate Pro. Yi Zheng • Associate Pro. Jing Wu • Associate Pro. Dang Huang • PhD: 14, Master: 21

Researching Fields • Predictive Control for Large-Scale

Systems • Plant-wide optimization • Fuzzy system • Application of advance control

CONTENTS

• Background

• Coordination strategies

• System structure

• Applications

• Conclusion

Background

Technology Development large scale complicated Large-scale process industry systems

Characteristics: • More units with inputs and outputs • Wide spatial distribution • Couplings (Energy, mass, information) • Complicated models with constraints and multi-objects

Ethylene catalytic

Chemical process Sewage disposal Power station

Centralized and decentralized control systems DCS，PLC, Sensors、transmitter

.Form H. Kirrmann’s PPT (ABB)

Centralized control

Cable

Cable

Industrial field

Master control room

Background

Field bus, Intelligent instrument, Network convert of control structure and mode

Centralized control

Distributed control Distributed control systems

Information exchange Local control separately

Background

WSN Field bus Smart device Network

Hierarchical structure of the industry process control From Qin’s PPT

FC PC

TC LC

FC PC

TC LC

Global steady optimization

Device1: local optimization (steady or dynamic optimization)

High/low logic

PID Lead/Lag PID

SUM SUM

Device1: Decentralized PID

Model Predictive control —— MPC

Device2: Decentralized PID

Device2: local optimization (steady or dynamic optimization)

Algorithms • PID • MPC • Robust • Optimal • Decoupling

Application • SISO • MIMO • Dynamic

optimization • Steady optimization

Background

Background

Large-scale system theory(1970’s) Decentralized/ Hierarchical control：

Decentralized control Hierarchical control

Background

Hierarchical Decentralized vs Distributed Model Predictive Control

Networked distributed control systems

Time scale

Hierarchical structure Distributed structure

Background

Distributed system

Distributed Control

MPC

*1u

sp1y

MPC

MPC

MPC

MPC

sp2y sp

3y sp1my −

spmy

*2u *

3u *-1mu *

mu1y 2y 3y -1my my

Network

Steady economic optimization

Real time optimization

Optimization Ti

me

scal

e

Flexible

Control problem of distributed large-scale system 90’ Large-scale system theory 2008.09 European FP7 STREP project 《Hierarchical and Distributed Model Predictive Control of Large-Scale Systems》

http://www.ict-hd-mpc.eu IEEE TAC , Automatica, JPC

W. B. Dunbar, IEEE TAC, 2007, 52, 1249-1263; J.B. Rawlings, et. al. JPC,2008,18,839-845; H. Scheu, et.al. JPC,2011. 21.715-728. M. Farina, et.al. Automatica, 2012, 48,1088-1096. E. Camponogara, IEEE TAC, 2012. 57, 804-809. R. Scattolini, JPC , 2009, 19,723-731 , Comp.&ChEng, 2013, 51, 21-41

Applications in different process industry

Reactor/separator system By Al-Gherwi, JPC, 2011

Morosana, Energy &Building, 2011

hydro-power valley J. Zárate Flórez,

Mathem. & Comp., 2012

Focus on DMPC

Background

hot

Background

COORDINATION STRATEGIES FOR

DISTRIBUTED MODEL PREDICTIVE CONTROL

S1 S2

S3

S*

SNa-1

SNa

S*

Problems

• Physically composed by many interacting “small-scaled” plants (Spatially distributed)

• Distributed control structure (communication with network)

E-mail: yizheng@sjtu.edu.cn

Distributed System

Distributed MPC • Good dynamic performance • Constraints • Practical

The performance of entire system under the control of DMPC framework is not as good as that under the control of centralized MPC

Cont

Cont

Cont

Cont

Cont

Cont

Cont

MPC

MPC

MPC

MPC

MPC

MPC

MPC

Existing Strategies of DMPC Cataloged by Cost Function

Local cost optimization

Iterative Nash optimality Stabilized LCO-DMPC

Global cost optimization

Impact-region cost optimization

M. Farina, R. Scattolini, Automatica, 2012 W.B. Dunbar, IEEE TAC, 2007

D. Jia, B.H. Krogh IEEE, TCST, 2001 X. Du, S. Li, Y. Xi, ACC, 2000

Problems

E-mail: yizheng@sjtu.edu.cn

,

,

1

, | , | , |0

min ( )

ˆ ˆmin

∆

−

+ + +∆=

= + +

∑

U

U

i k

i ii k

i

N

i k l k i k l k i k N kQ Pl

J k

x u x

S1 S2

S3

S*

SNa-1

SNa

S*

MPC

MPC

MPC

MPC

MPC

MPC

MPC

S. Li , Y. Zhang, Q. Zhu, Info. Sci. 2005

Existing Strategies of DMPC Cataloged by Cost Function

Local cost optimization

Global cost optimization

Iterative Pareto optimality

Impact-region cost optimization

Problems

E-mail: yizheng@sjtu.edu.cn

S1 S2

S3

S*

SNa-1

SNa

S*

MPC

MPC

MPC

MPC

MPC

MPC

MPC

Venket. A. IEEE TCST, 2008 Y. Zheng, S. Li, et. Al IEEE TCST 2012

,

,

1

, | , | , |0

min ( )

ˆ ˆ min

i k

i ii k

i

N

i k l k i k l k i k N kQ Pl

J k

x u x

∆

−

+ + +∆=

= + +

∑

U

U

( )min ( )

∈∆ ∑Uijj Pk

J k

Existing Strategies of DMPC Cataloged by Cost Function

Local cost optimization

Global cost optimization

Impact-region cost optimization

Stabilizing ICO-DMPC

(A general framework for linear systems)

Problems

E-mail: yizheng@sjtu.edu.cn

S1 S2

S3

S*

SNa-1

SNa

S*

MPC

MPC

MPC

MPC

MPC

MPC

MPC

S. Li, Y. Zheng, Z. Lin, IEEE ASE, 2015

,

,

1

, | , | , |0

min ( )

ˆ ˆ min

i k

i ii k

i

N

i k l k i k l k i k N kQ Pl

J k

x u x

∆

−

+ + +∆=

= + +

∑

U

U

( )min ( )

∈∆ ∑U iijj Pk

J k

ACC Process, BaoSteel Co. Ltd. by: Y. Zheng, S. Li, X. Wang JPC, 2009 Y. Zheng, S. Li, N. Li, CEP, 2011

Problems

With the increasing of coordination degree

• In most cases: Global Performance ↑ √

• Existing Methods: Network connectivity ↑ not expected

Design a DMPC which could increase coordination degree without any increasing of network connectivity ?

See. Al-Gherwi, et.al. JPC, 2010. 20(3): p. 270-284.

Impact-Region Cost Optimization DMPC

Strategies:

downstream neighbors

Impaction to Spdi

Presumed states trajectory of Spd

i Spdi

• Optimizing the performance of impacted-region, increasing coordination degree

• Neighbor to neighbor communication

J i (k)

X

i2 P di

J j (k)

¹J i (k)

Y. Zheng, S. Li. IFAC 2014

Formulation • Local Sub-system Model

• Predictive Model

• Impaction of input to its downstream neighbor

Assumption: There is a static feedback ui=kix, such that the closed-loop linear system is asymptotically stable. (ui=kixi dunbar 2007 IEEE TAC, Farina2012 Automatica)

ICO-DMPC

（*）

Assumption:

Formulation • Performance of each subsystem-based MPC

ICO-DMPC

ATo P Ao + AT

o P Ad + ATd P Ao < bQ=2:

Formulation

Optimization problem

s.t.

ICO-DMPC

m1 = maxi2 P

f number of elements in P ui g

®l = maxi2 V

maxj 2 P i

n¸

12m ax

¡ ¹Ali Ai j )TPj ¹Al

i Ai j¢o

l = 0; 1; ¢¢¢; N ¡ 1

Feasibility constraint

Terminal constraint

CJ2

CJ1

Dual-mode algorithm

ICO-DMPC

Check if

Controller i

Solve MPC

Calculate Predictions

State feedback

ε∈x

Y N

, 1: |

, : 1|

ˆˆ

,

+ +

+ −

∈ ≠

k

i k k N k

j k k N k

xxuj P j i

kx1 2

3 3 5

0

( )i kx

, , : 1ˆ, + −i k i k k Nx u

1, 1, : 1|ˆ, + −j k j k k N kx u

,i kx

, : 1|ˆ + −i k k N ku

2, 2, : 1|ˆ, + −j k j k k N kx u

No local feed-back control is also ok!

Assumptions • There exists an initial feasible control for each subsystem

Analysis

Feasibility

• Theorem 1: suppose that above assumption hold, and all constraint are satisfied. Then the control and state pair

is a feasible solution to ICO-DMPC at every update

∈0( )x k Xf f, : 1| 1: | ,( , )i k k N k k k N k iu x+ − + +

>1k

, 1| 1f, 1| f

, 1|

, 1, , 1

,i k l k

i k l ki i k N k

u l Nu

K x l N+ − −

+ −+ −

= … −= =

lX

s = 1

®l¡ s jjxi ;k + s jk ¡ xi ;k + s jk ¡ 1 jj2 ·»· "

2p mm1

Analysis

Stability • Theorem 2: suppose that above assumption hold,

and all constraints are satisfied, and the following parametric condition hold

Then, by application of ICO-DMPC algorithm, the closed–loop system is asymptotically stabilized to the origin.

Proof: details Please see the paper :

Impacted-Region Optimization for Distributed Model Predictive Control Systems with Constraints

∈0( )x k X

(N ¡ 1)·2

+1¹

¡12

< 0

Simulation Multi-zone Building Temperature Regulation

System

Subsystem models:

Simulation

The evolution of the states under the centralized MPC, LCO-DMPC and ICO-DMPC

Comparison with LCO-DMPC, CDMPC

Simulation

Required network connectivity of each controller

Comparison with LCO-DMPC, CDMPC

State square errors under each controller

ICO-DMPC: 3.04 (28.83%) LCO-DMPC: 71.45 (679.89%)

x CDMPC

CDMPC

e ee−

SYSTEM STRUCTURE OF STABILIZED

DISTRIBUTED MODEL PREDICTIVE CONTROL

Large-scale complicated distributed systems

Global cost optimization • Global information • Stabilizing

Non-global information (LCO, ICO) • Non-global information based • Assumption strictly

Requires: Non global Information based asymptotically stabilized DMPC with constraints !

Internet plus, cyber physics system, Industrial 4.0

Control structure

design

Problem

2001- present difficult

Our Solution:

Mass and energy coupling

System

Steam flow

Burning coal

Main pressure

Load

Different structures for different control purposes

Improve performance through reasonable

structure design

System Structure Design

Structural characteristics of the information layer

X X XX X

XX X

X X X

Structure Adjacency matrix

min ε

Knowledge Casual logic

Ref: Theory of large-scale systems, Yugeng Xi Control for complex system, A. Zeˇcevi´c & D.D. Šiljak.

System Structure Design

• Interaction (Strong, weak); • Controllability; • Observability.

Process network model for large-scale system

Bond-graph of mass and energy balance

Computers and Chemical Engineering 32 (2008) 1120-1134

• Easy performance analysis: closed-loop dissipativity condition • Precondition: system structure design by the coupling relationship

between mass and energy

System Structure Design

Physical network

MPC

MPC

MPC

MPC

MPC MPC

MPC

MPC

MPC MPC

MPC GCO-DMPC

GCO-DMPC GCO-DMPC

MPC

MPC

ICO-DMPC

Information network

Structure of Stabilized DMPC

Global Information is not necessary!

GCO-DMPC

Iterative Communication once

Structure model

1 0 0 1 1 10 1 1 0 0 00 1 1 1 0 01 0 1 1 1 01 0 0 1 1 11 0 0 0 1 1

=

A

1, 0, ij

=

A if i is affected by j

if i is not affected by j

System decomposition

Advantages:

• Qualitative research • Simple expression and easy to get • Logic calculation • Uniform model for nonlinear systems

(Taylor series approximate) Adjacency matrix

( 1) ( )k k+ =x Ax

T T

Ta

=

x u y

x A 0 CA

u B 0 0y 0 0 0

T 1 T 2 T

1 T T 2 T T 3 T

( ) ( )( ) ( )

N N

N N Na

− −

− − −

+ + = + +

A I 0 A I CR I A B A I I B A I C

0 0 I=( )

Dynamic system structural model ( 1) ( ) ( )( ) ( )k k kk k+ = +

=

x Ax Buy Cx

N-step Adjacency Matrix

Adjacency matrix for dynamic system

Input state Input output

State output State state

System decomposition

, 1 ,

, 1 ,

, , 1

a k a k

a k a k

a k a k

+

+

−

=

x A B 0 xu 0 0 0 uy C 0 0 y

System is controllable, if and only if

([ ])gr n=A B

Structure Controllability

Is the maxim rank of numerical matrices related to the structural matrix ( ) max( ( ))gr A rank A=

2gr( )c n=G

0 0 0 0 00 0 0 00 0 0 0 0 0

0 0 0 00 0 0 0

c

− − −

=

−

B IA B I

AG

B IA B

System is controllable, if and only if

1. Input reachable

2.

Condition 1 Condition 2

Controllability of subsystems

APPLICATIONS OF

DISTRIBUTED MODEL PREDICTIVE CONTROL

Manipulated variables • Strip speed • Water fluxes of jet • State of cooling water jet

Control objective • Cooling curve of strip • Final temperature • Average temperature

Laminar Cooling Process

Heavy Plate Mill, Baoshan Irion & Steel Co. Ltd.

Control structure

（Zheng & Li, JPC, 2009）

Applied result • FT qualification rate: 60% 85% • Hit rate of finished strip: 80% 95％ • Production: 180 210 ton/hour

Laminar Cooling Process

Micro-Grid Energy Management System

Distributed generation • Renewable energies

(wind turbine, photovoltaic) • Adjustable energy

(diesel engine, gas turbine)

Storage • Storage battery

Loads • Shift-able loads • Un-adjustable loads

Micro-grid Structure of Wuning Technical Park, Shanghai, China

Wind turbine

Renewable energy

Adjustable energy

Photovoltaic

Gas turbine

Storage battery

Ener

gy st

orag

e

Grid

Dist

ribut

ed G

ener

atio

n

Diesel engine

Un-adjustable loads

Shift able loads

Load

s

Micro-Grid Energy Management System

Control strategy Multi-objective DMPC Economic, pollution, peak value

Initialization

Micro-Grid Energy Management System Numeric results

Reference

E. Camponogara, D. Jia, B.H. Krogh, and S. Talukdar, “Distributed Model Predictive Control,” IEEE Control Systems Magazine, vol. 22, no. 1, pp. 44–52, 2002.

Li, S., Y. Zhang, and Q. Zhu, Nash-optimization enhanced distributed model predictive control applied to the Shell benchmark problem. Information Sciences, 2005. 170(2–4): p. 329-349.

Venkat, A.N., et al., Distributed MPC Strategies With Application to Power System Automatic Generation Control. IEEE Transactions on Control Systems Technology, 2008. 16(6): p. 1192-1206.

W.B. Dunbar, “Distributed Receding Horizon Control of Dynamically Coupled Nonlinear Systems,” IEEE Trans. on Automatic Control, vol. 52, no. 7, pp. 1249–1263, 2007.

M. Farina and R. Scattolini, “Distributed predictive control: A non-cooperative algorithm with neighbor-to-neighbor communication for linear systems,” Automatica, vol. 48, no. 6, pp. 1088–1096, 2012.

Conclusion & Future Work Conclusion

• DMPC algorithm which could increase coordination degree without any increasing of network connectivity

• Structure decomposition which provide an implementation framework for large scale coupling systems

Future work Non global communication based constraint DMPC with guaranteeing of stabilization?

Thanks for your attention!