From Multi-Parametric Programming Theory to MPC-on-a-chip...

From Multi-Parametric

Programming Theory to

MPC-on-a-chip Multi-scale

Systems Applications

Stratos Pistikopoulos

FOCAPO 2012 / CPC VIII

Acknowledgements Funding

EPSRC - GR/T02560/01, EP/E047017, EP/E054285/1

EU - MOBILE, PRISM, PROMATCH, DIAMANTE, HY2SEPS

CPSE Industrial Consortium, KAUST

Air Products

People J. Acevedo, V. Dua, V. Sakizlis, P. Dua, N. Bozinis, N. Faisca

Kostas Kouramas, Christos Panos, Luis Dominguez, Anna Vöelker, Harish Khajuria, Pedro Rivotti, Alexandra Krieger, Romain Lambert, Eleni Pefani, Matina Zavitsanou, Martina Wittmann-Hoghlbein

John Perkins, Manfred Morari, Frank Doyle, Berc Rustem, Michael Georgiadis

Imperial & ParOS R&D Teams

http://www.brandsoftheworld.com/download/?id=32298

Outline

Key concepts & historical overview

Recent developments in multi-parametric

programming and mp-MPC

MPC-on-a-chip applications

Concluding remarks & future outlook

What is On-line Optimization?

MODEL/OPTIMIZER

SYSTEM

Data -

Measurements

Control

Actions

What is Multi-parametric Programming?

Given: a performance criterion to minimize/maximize

a vector of constraints

a vector of parameters

s

n

u

u

x

xug

xufxz

R

R

0),( s.t.

),(min)(

What is Multi-parametric Programming?

Given: a performance criterion to minimize/maximize

a vector of constraints

a vector of parameters

Obtain: the performance criterion and the optimization

variables as a function of the parameters

the regions in the space of parameters where these functions remain valid

s

n

u

u

x

xug

xufxz

R

R

0),( s.t.

),(min)(

Multi-parametric programming

s

n

u

u

x

xug

xufxz

R

R

0),( s.t.

),(min)(

)(xu

(2) Critical Regions

(1) Optimal look-up function

Obtain optimal solution u(x) as a

function of the parameters x


1001001010

0

0

0

0

8

121

20

13

00

10

00

01

14

228

45

11

.

83min21 ,

21

2

1

2

1

21uu

xx

x

x

u

u

uu

st

Problem Formulation

Multi-parametric programmingCritical Regions

-10 -8 -6 -4 -2 0 2 4 6 8 10-100

-80

-60

-40

-20

0

20

40

60

80

100

x1

x2

4 Feasible Region Fragments

CR001

CR002

CR003

CR004

x2

x1

Multi-parametric programmingMulti-parametric Solution

100

10

65.8

10

01

11.01

8.9

8.11

06.00

05.00

100

5

5.7

10

01

045.01

13

0

01

00

100

100

10

5.7

71.6

65.8

10

10

01

045.01

031.01

115.01

5.7

5.5

03.026.0

03.073.0

100

100

10

5

71.6

10

10

01

01

031.01

67.14

67.1

033.1

033.0

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

x

xif

x

x

x

x

ifx

x

x

x

ifx

x

x

x

ifx

x

U


Only 4 optimization problems solved!

100100,1010

0

0

0

0

8

121

20

13

00

10

00

01

14

228

45

11

.

83min

21

2

1

2

1

21

xx

x

x

u

u

st

uuu

-10 -8 -6 -4 -2 0 2 4 6 8 10-100

-80

-60

-40

-20

0

20

40

60

80

100

x1

x2

4 Feasible Region Fragments

CR001

CR002

CR003

CR004

100

10

65385.8

10

01

115385.01

80769.9

8462.11

0641.00

05128.00

100

5

5.7

10

01

0454545.01

13

0

01

00

100

100

10

5.7

71875.6

65385.8

10

10

01

0454545.01

03125.01

115385.01

5.7

5.5

03333.026667.0

0333.07333.0

100

100

10

5

71875.6

10

10

01

01

03125.01

6667.14

6667.1

0333.1

0333.0

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

U

if

if

if

if

On-line Optimization via off-line

Optimization

System

State

Control

Actions

OPTIMIZER

SYSTEM

POP

PARAMETRIC PROFILE

SYSTEM

System

State

Control

Actions

Function Evaluation!

Multi-parametric/Explicit Model

Predictive Control

Compute the optimal sequence of manipulated inputs which minimizes

On-line re-planning: Receding Horizon Control

tracking error = output – reference

subject to constraints on inputs and outputs

Compute the optimal sequence of manipulated inputs which minimizes

On-line re-planning: Receding Horizon Control

Multi-parametric/Explicit Model

Predictive Control

Solve a QP at each time interval

Multi-parametric Programming Approach

State variables Parameters

Control variables Optimization variables

MPC Multi-Parametric Programming

problem

Control variables F(State variables)

Multi-parametric Quadratic Program

Explicit Control Law

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

-1.5

-1

-0.5

0

0.5

1

1.5

2

x1

x2

CR0

CR1

CR2

2065.07083.07059.02

2065.07083.07059.02

2065.0

2065.0

7083.07059.0

7083.07059.08585.68355.6

t

t

tt

t

xif

xif

xifx

u

)( 1,2j 22

0064.0

0609.0

9909.01722.0

0861.07326.0s.t

01.0min))((

||

|||1

|2|2

1

0

2

|||, |1|

t

PtxJ

tttjt

tjttjttjt

tt

T

tt

j

tjttjt

T

tjtuu tttt

xxu

uxx

xxuxx

Multi-parametric Controllers

SYSTEM

Parametric Controller

Optimization Model



MeasurementsControl Action

Input Disturbances

System Outputs

Explicit Control Law

Eliminate expensive, on-line computations

Valuable insights !

MPC-on-a-chip!

Key milestones-Historical Overview

Number of publications

2002 Automatica paper ~ 580 citations

Multi-parametric programming – until 1992 mostly

analysis & linear models

Multi-parametric/explicit MPC – post-2002 much

wider attention

Multi-Parametric

Programming

Multi-Parametric

MPC &

applications

Pre-1999 >100 0

Post-1999 ~70 250+

AIChE J.,Perspective (2009)

Patented Technology

Improved Process Control

European Patent No EP1399784, 2004

Process Control Using Co-ordinate Space

United States Patent No US7433743, 2008

Outline



programming and mp-MPCModel reduction/approximation

mp-NLP & explicit nonlinear mp-MPC

mp-MILP

Robust explicit mp-MPC

State estimation and mp-MPC

Framework for mp-MPC

A framework for multi-parametric

programming & MPC (Pistikopoulos 2008, 2009)

‘High-Fidelity’ Dynamic Model

Model Reduction Techniques

System Identification

Modelling/ Simulation

Identification/ Approximation

Model-Based Control & Validation

Closed-Loop

Control System Validation

Extraction of Parametric Controllers

u = u ( x(θ) )

‘Approximate Model’

Multi-Parametric Programming (POP)

Model Reduction/Approximation

Replace discrete dynamical

System with a set

of affine algebraic models

N-step ahead prediction-enables use of Linear MPC routines

Model Reduction/Approximation

N-step-ahead approximation based on initial conditions

(measurements) and sequence of controls (constant

control vector parameterization). Set of affine algebraic

models

For all j point over the time horizon - approximations are

constructed as follows

t

y

Direct ApproachStrategy:

Discretize state and controls via Orthogonal Collocation Techniques

Multi-parametric Nonlinear Programming Problem (mp-NLP)

Quadratic Approximation Based

Solve sequence of mp-QP‟s

Nonlinear Sensitivity based

Solve sequence of NLP‟s

Partition state space recursively

Approximate

Multi-parametric Nonlinear Dynamic Optimization Problem

mp-NLP Algorithms for Explicit NMPC

Key features:

• Characterizes the parameter space using NLP sensitivity information and linearization of the constraints.

NLP Sensitivity Based (NMPC mp-NLP)

Quadratic Approximation based (General mp-NLP)

Two implementations for the characterization of the Parameter space

v(x) v0

(x) = 0 (M0)1 N0 + (x x0)+(||x | |)

(x) 0

• Characterizes the parameter space by sub-partitioning CRs where the QA approximation provides “poor” solutions.

x0 v* x0 v*

Validity of approximation:

(x) = O(||x||) (x)/||x|| → 0 as x → 0.


Key Advantage: Fast implementation of the control laws

• State-of-the art multi-parametric solvers (e.g. mp-QP)

• Straightforward characterization of critical regions

• Complexity reduction through region merging

• Extension to address hybrid systems


Decompose mp-MINLP into two sub-problemsStrategy:

Multiparametric Mixed-Integer Nonlinear Programming

Primal sub-problem (mp-NLP)

Master sub-problem (MINLP)

y = y*x = f()

Iterate until master sub-problem is infeasible

Approximate

via mp-QPs

Characterize feasible regionPre-processing Simplicial

Approximation

Step 1

Step 2 mp-MILP

Applications

• Pro-active Scheduling under price, demand and processing time uncertainty (seee poster & paper)

• Explicit Model Predictive Control of Hybrid Systems: Control actions as optimization variables, states as parameters, input and model disturbances as parameters

• Integration of scheduling & MPC

Explicit Solution of the general mp-MILP Problem

Hybrid Approach - Two-Stage Method for

mp-MILP1

1 Wittmann-Hohlbein, Pistikopoulos (2011)

Stage 1 – Reformulation

Partially robust RIM-mp-MILP* model;

Solutions are immunized against all immeasurable parameters and complicating

constraint matrix uncertainty

Stage 2 – Solution

Suitable multi-parametric programming algorithms (e.g. Faisca et al. (2009))

Optimal partially robust solution; Upper bound on optimal objective function value

*objective function coefficient and

right hand side vector uncertainty

Global Optimization of mp-MILP1

Challenges in Global Optimization of mp-MILP Problems:

• Comparison of parametric profiles, not scalar values

• High computational requirements

Multi-Parametric Global Optimization:

• Adaptation of strategies from the deterministic case to multi-parametric framework: Parametric B&B procedure

• Globally optimal solution is a piecewise affine function over polyhedral convex critical regions

Can we find “good solutions” of an mp-MILP problem with less effort?

1 Wittmann-Hohlbein, Pistikopoulos; JOGO, submitted , 2011

Constraint matrix uncertainty poses major challenge mp-MINLP

33

Robust Explicit mp-MPC Famous control problem: Dynamic Systems with Model Uncertainties

(Mayne, Rawlings, Rao & Scokaert, 2000)

10

inputs control :

states system :

NuuU

u

x

:

:

,

0,0,

0,0,

ijijijijij

ijijijijij

mnij

nnij

bbbbb

aaaaa

bBaA

RR

Parametric Uncertain System

Uncertainty due to modelling, identification errors,

measurement errors etc.

Constraints represent safety, operational constraints

It is very critical that the system does not violate them

Immunize against uncertainty

xx

uuu

Mx

dDuCx

Bu + WθkAxx

PxxRuuQxxxV

N

kk

kkk

N

k

NNkkkkU

0

maxmin

1

1

0

)(min)(

maxmin

Exogenous Disturbance

Robust Explicit mp-MPC

Robustification – robust reformulation step (Ben-Tal &

Nemirovski, 2000; Floudas& Co-workers, 2004-2007)

Dynamic Programming framework to Robust MPC

Novel Multi-parametric Programming algorithm to constrained Dynamic Programming (Faísca, Kouramas,

Saraiva, Rustem & Pistikopoulos, 2008) Small mp-QP at each stage

No need for global optimization

Main idea:

Step 1. Formulate the dynamics that govern the estimation error

Step 2. Use these dynamics to find the set that bounds the estimation error

Step 3. Incorporate the bounding set into the controller to „robustify‟ against the estimation error

MHE & mp-MPC

Te S

1 1,T T Te f e w

0

12 2 2

,0 0

1

1

* * *0 0 0

1

0

min

s.t. (actual system),

(

ˆ ˆ (estimated system step 1.3),

nominal system),

ˆ , ,

MPC MPC

MPC MPC MPCMPCk

MPC

k k k

N N

N k kQ RPx uk k

k k k k

k k k

N f

k

x x u

x Ax Bu Gw

x Ax Bu

u u K x x

x Ax Bu t

u K x

x

,U X=

X=

S

0 0

1 1

ˆ, 1... 1, , ,

ˆ ˆis mRPI of .

XMPC

k k k k t

k N x x

x x A BK x x

X

S

S S Ex S S

Moving Horizon Estimation (MHE)

Model-based state estimator

Obtains current state estimate xT

Main advantage: incorporates system constraints

MHE is dual to MPC: backwards MPC

1 11 1

| |

122 2 21 2

| | |ˆˆ ,

1

* *

| 1| 1 1| 1 1| 1

ˆ ˆ ˆ ˆmin

ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆs.t. , , ,

ˆ ˆ (

,

T N T T N T

T TT T

T N T T N T T N T N T T N k kQ RPx Wk T N k T N

k k k k k k k k k k

T N T T N T T N T T N T

x x Y x cbU w v

x Ax Bu Gw y Cx v x w v

x Ax Bu Gw

X W W

WO

smoothed update of arrival cost)


programming & MPC (Pistikopoulos 2008, 2009)







Closed-Loop



u = u ( x(θ) )


Multi-Parametric Programming (POP)







Closed-Loop



u = u ( x(θ) )


Multi-Parametric Programming

(POP)

REAL SYSTEM EMBEDDED CONTROLLEROn-line Embedded

Control:

Off-line Robust Explicit Control Design:


programming and MPC (Pistikopoulos 2010)

Outline




MPC-on-a-chip applications PSA system

Fuel Cell system

Biomedical systems

PSA system and the cycle

Impurities

BED 1 FEED DEP 1 DEP 2 DEP 3 Bd Pu PE 1 PE 2 REPRES

BED 2 PE 2 REPRES FEED DEP 1 DEP 2 DEP 3 Bd Pu PE 1

BED 3 Bd Pu PE 1 PE 2 REPRES FEED DEP 1 DEP 2 DEP 3

BED 4 DEP 1 DEP 2 DEP 3 Bd Pu PE 1 PE 2 REPRES FEED

Time

FeedOff gas

Pure product

REPRES

DEP 1

DEP 2

DEP 3


programming and mp-MPC for PSA

‘High Fidelity’ PSA Model (PDAE)

Extraction of explicit MPC controllers u = u(x(θ))


‘Approximate’ Model


In-silico closed loop controller validation

Modeling & Simulation

Model Based Control & Validation

MATLABPOP Toolbox

Modelling - internal Bed

Mass balance

2

2

)1())1((Z

iC

DZibt

iQ

bpZ

iUC

t

iC

pbb

Radial effects neglected

Transport properties independent of state variables

Axial mass dispersion (Wakao and Funazkri, 1978), velocity dependent

neglected

Species Accumulation

Bulk fluid convection

Mass transfer with adsorbent

Dispersion in axial direction

Energy balance

Energy accumulation in gas phase Energy accumulation in solid phase

Energy convection Heat of adsorption Heat dispersion

Lumped energy balance on gas and solid phase

Radial effects neglected

Specific heat, transport properties independent of state variables

Axial mass dispersion (Wakao et.al., 1978), velocity dependent

neglected

2

2

)()1())1((

)1()1())1((

111

11

Z

T

iH

t

iQ

pbt

iC

RTpbbZ

TU

t

T

pC spbt

T

iQpbt

T

pbb

NCOMP

i

NCOMP

i

NCOMP

i

ip

NCOMP

i

v

NCOMP

i

iv

CC

CCC

i

ii

Energy accumulation in adsorbed phase

Momentum balance & adsorption

characteristics

UU

pd

ii

MWi

C

U

pdZ

P

NCOMP

31

175.1

23

21150

iiLDFi QQK

t

Qi

*

RT

HKK i

i iexp

ia

ii

Q

iQ

RTiCiKia

iQ

iQ NCOMP

1max

*

1max

* Nitta et.al. (1984), Ribeiro et.al. (2008), multisite Langmuir adsorption isotherm (multi-component mixture)

LDF Rate expression

Ergun‟s equation, steady

state pressure drop

Valve Equation (for boundary

conditions)

v

p

critical

High

V

critical

High

LowLowHigh

V

C

CP

OtherwiseP

PC

PP

Pif

P

PPC

U

1

2

1

2

1

P = PHigh if gas leaving the bed

= PLow if gas entering the bed

Chou and Huang (1994), Nilchan and Pantelides (1998)

•Prictical constant since Cp

and Cv are assumed constant

•For REPRES and DEP Cp

and Cv calculated

at yH2= 0.7, yCH4

= 0.3

•For blowdown and purge

(off gas) Cp and Cv calculated

at yH2= 0.5, yCH4

= 0.5

Constraints - Boundary conditionsZ = 0 Z = L

),( Q FEEDTFEEDPSLPMUA PRODUCTPP

RT

iFeedPY

iC 0

Z

iC

FeedTT 0

Z

TZ = 0

Z = L

Z = 0 Z = L

i iC

CODEPi iCUU

PURGEVCCODEPPPURGEPValvefU ,,

iiCODEPCRT

iCODEPPC

iC

CODEPTT

0

Z

iC

0

Z

T

Z = 0

Z = L

Feed

Step

Purge

Step

A boundary condition for each process step

Base case system

BED 1 FEED DEP 1 DEP 2 DEP 3 Bd Pu PE 1 PE 2 REPRES

BED 2 PE 2 REPRES FEED DEP 1 DEP 2 DEP 3 Bd Pu PE 1

BED 3 Bd Pu PE 1 PE 2 REPRES FEED DEP 1 DEP 2 DEP 3

BED 4 DEP 1 DEP 2 DEP 3 Bd Pu PE 1 PE 2 REPRES FEED

FeedOff gas

99.99 % H2

REPRES

DEP 1

DEP 2

DEP 3

Number of Beds 4 AdsorbentActivated

Carbon

Feed pressure 7 bars Bed length 1 m

Blowdown

pressure

1.01325

barsBed diameter 0.12 m

Bed Porosity 0.4Feed

temperature303.15 K

Feed

Composition

70 % H2,

30 %CH4

Feed flow rate 8.0 SLPM

REPRESPEPEPuBdDEPDEPDEPFEED ttttttttt 21321 Adsorption time

Objective and process variables Changes in adsorption time effects purity the

most

Adsorption time – Manipulated variable

Purity – Controlled variable

Fast tracking of H2 purity to the set point

99.99%

Regulate changes in adsorption time

Avoid bed saturation

Avoid high fluid inlet velocities as it causes

mechanical damage

Hard constraints on adsorption time has to be

satisfied for safe and economical operation


programming and MPC









MATLABPOP Toolbox

System Identification - Approximation

PDAE model not suitable for current model

based control approaches

Process model approximations are

needed

Input – Adsorption time

Output – H2 purity

Sampling time – 1 PSA cycle

Input signal design for system perturbation

Random pulse employed for persistent

excitation

Maximum amplitude decided by hit and

trial studies

Pulse duration (constant) calculation

based on closed loop response

System identification

Model fit to the input

output data above by an

8th order state space system

kk

kkk

Cxy

BuAxx

1


programming and MPC









MATLABPOP Toolbox

MPC Formulation for PSA

1

..

min

1

1

0

'1

1

'

k

highklow

mismatchkk

kkk

k

M

kk

R

kk

N

k

R

kku

y

uuu

yCxy

BuAxx

ts

uRuyyQyyZ y = hydrogen purity at the end of adsorption stage

u = adsorption time, sec

N = 4, M = 2 Q = 1

2 optimization variables u0, u1

Optimal R based on the closed loop response

Constraints on u

Low u: low adsorption time/cycle time, fast PSA cycles

More ON/OFFs of the switch valves per unit time

Extra wear and tear of manipulative variable hardware

Fast loading-unloading of adsorbent leading to its degradation

High u: high adsorption time/cycle time, long PSA cycles

Risk of over saturation, or irreversible adsorption of adsorbent

(1) Critical Regions(2) Optimal Look-up Function

Measurements

Control Action

Input Disturbances

System Outputs

EXPLICIT/MULTI-PARAMETRIC MPC CONTROLLER

MPC on a chip

Explicit Control Law Eliminate expensive, on-line computations

Valuable insights!

mp-MPC for PSA control

Explicit/Multi-Parametric MPC Design

Critical Regions from POP software

Solve the mp-optimization problem for all values of the parameters to obtain the

explicit control laws (u = D1x + u0) and the corresponding critical region

maps (D2x.≤ q).


programming and MPC









MATLABPOP Toolbox

MPC Vs PID

Step Disturbance in PSA feed rate – 10 % of Design

ControllerResponse time

(Cycles)

Average ∆U

(Seconds)Maximum ∆U (Seconds)

mp-MPC 13 0.74 1.8

PID 25 0.84 5.09

Impulse Disturbance in PSA feed rate – 35 % of Design

mp-MPC 7 0.75 1.6

PID 5 4.72 12.12

Open Loop 9

Impulse Disturbance in PSA feed rate – 54 % of Design

mp-MPC 7 1.77 4.18

PID1 4 17.11 32.29

PID2 5 9.44 21.16

Open Loop 10

MPC Vs PID

Outline





Fuel Cell system

Biomedical systems

PEM Fuel Cell System

PI

PI

PI

H2O

Water

MassFlow

MassFlow

MassFlow

TE

TE

TE

PT

A

K

PDT

PTTE

TE PT

TE PT

M

TE TE

PT

VENT

VENT

Hydrator

Hydrator

RadiatorFilter

Electronic

Load

N2

H2

Air


Develop 1kW PEM fuel cell system

Collect data for the PEM fuel cell, fan, hydrogen storage

Design controller for the integrated system

mair

Vfan

mcool


Tst

λO2

Tamb

Ist

u: mair,Vfan, mcool

d: Tamb,Ist

y: Tst ,λO2

θ: xt , Tamb,Ist , Tst ,Tst,sp

PEM Fuel Cell System - Controller Design

Nominal MPC Controller

1

0

1

1,,

)()()()()()(minM

k

R

kk

TR

k

R

NN

R

NN

N

k

R

kkk

TR

kkuyx

uuRuuyyPyyyyQRyyJ

Subject to: 1

1

t t t

t t

x Ax Bu

y Cx

Optimized PID Controller

Robust MPC Controller Include in the controller design the model error

u: mair,Vfan, mcool

d: Tamb,Ist

y: Tst ,λO2

θ: xt , Tamb,Ist , Tst ,Tst,sp

PEM fuel cell system

Dynamic model

Ideal and uniformly distributed gases

The fuel and the oxidant are humidified

No liquid can go into the membrane because it is waterproof

Uniform temperature in the fuel cell stack

Simplified mathematical models for humidifier, radiator and pump

Controller evaluation (closed-loop simulation)

Incorporate controller into high fidelity model and perform computational

studies

MATLAB+

POP Software

yt

ut+1ut+1

yt

Incorporate controller into the PEM Fuel Cell System - perform experiments

mair

mcool


Tst

λO2

Tamb

Ist

Unit Specifications

Fuel Cell : 1.2kW

Anode Flow : 5..10 lt/min

Cathode Flow : 8..16 lt/min

Operating Temperature : 65 – 75 °C

Ambient Pressure

Control Strategy

Start-up Operation

Heat-up Stage : Control of coolant loop

Nominal Operation

Control Variables :

Mass Flow Rate of Hydrogen & Air

Humidity via Hydrators temperature

Cooling system via pump regulation

Known Disturbance : Current




mH2

mAir

mcool

TYHydrators

Vfan

Tst

HTst


Outline





Fuel Cell system

Biomedical systems

Type 1 diabetesMaintain blood glucose concentration within the normal range

by optimising insulin delivery

Model predictive control problem

Hyper

Normal

Hypo

AnaesthesiaProvide hypnosis, analgesia and muscle relaxation while

maintaining the vital functions

Multiple input multiple output model predictive control

Acute Myeloid LeukaemiaProvide optimal chemotherapy dose to minimise the cancer cells

While keeping normal cells above a minimum level

Scheduling Problem

Muscle Relaxation

ERC MOBILEDevelopment of models and model based control and optimisation algorithms for biomedical systems

Individual Patient

High Fidelity Model

Model Reduction

Set points

Individual constraints

Patient

Measurement

device/ State Estimation

OPTIMAL DRUG DELIVERY/DOSAGE

MEASUREMENTS/

STATES

Disturbances

Model Development

mp-MPC

Model Predictive Control/ Optimisation

-37 -36 -35 -34 -3313.5

14

14.5

15

15.5

16

16.5

x1

x 2

Optimal control

law/ trajectory

Optimal Scheduling

mp-MPC on a Chip

Optimal dose

1st Cycle 2nd Cycle 3rd Cycle 4th Cycle

Cancer cells

Normal cells

drug 1

drug 2

Framework towards optimal drug delivery systems

Mathematical Modelling

Model Development

Individual Patient

High Fidelity Model

Ve

in

Arte

ry

Skin

Lung

Brain

Heart

Muscle

Skeleton

Liver

Kidney

Adipose

Gut

Spleen

Pancreas

Pharmacokinetics

Cell Cycle

Pharmacodynamics

Effe

ct

Efficacy

Individual variability

Potency

Concentration

C50

E0

Emax

E50

0 10 20 30 40 50 60 7040

60

80

100

120

140

160

180

200

220

240

gluc

ose(

mg/

dl)

time(hr)

day2 day3

35g 100g 35g 40g 90g 50g 50g 80g 20g

day1

Diabetes Type I

Anaesthesia

Leukaemia

Glucose Profile

Anaesthetic concentrations

Cell population profiles

Step 1: The sensor measures the glucose concentration from

the patient

Step 2: The sensor then inputs the data to the controller which analyses it and implements the

algorithm

Step 3: After analyzing the data the controller then signals

the pump to carry out the required action

Step 4: The Insulin Pump delivers the required dose to

the patient intravenously

Controller

Sensor

Patient

Insulin Pump

12

3 4

ERC MOBILE

Outline




MPC-on-a-chip applications

Concluding remarks & future outlook

MPC-on-a-chip technology –

Reflections (10 years since 2002 Automatica paper appeared .. )

Scientific/academic impact ?

Application/industrial impact ?

MPC-on-a-chip technology –

Reflections (10 years since 2002 Automatica paper appeared .. )

Scientific/academic impact ? HIGH – many

un-resolved issues ..

Application/industrial impact ? Limited –

not panacea to all MPC solutions ..

MPC-on-a-chip – Perspectives

Application types for Multi-parametric

Programming & MPC

Type 1 - Large scale and expensive industrial

processes with slow/medium dynamics

Type 2 - Medium scale and cost industrial

processes with medium/fast dynamics

Type 3 - Small scale and inexpensive

processes/equipment with medium/fast dynamics


Type 1 – Large scale and expensive

industrial processes with slow/medium

dynamics


Type 1 - Large scale and expensive

industrial processes with slow/medium

dynamics

Control hardware/software availability

MPC implementation mainly via online

optimization

Explicit MPC can play a role for low level

process control

Hybrid (on-line + off-line) approach possible –accelerate on-line dynamic optimization step


Type 2 – medium scale and cost

industrial processes with medium/fast

dynamics

HEX

Column

LIN

Air

Product - GAN

Waste

Reboiler/condenser


Type 2 – medium scale and cost

industrial processes with medium/fast

dynamics

Limited Control hardware/software availability

Online optimization/MPC usually prohibitive

Multi-parametric MPC ideal – proved in

previous applications (Air Separation,

Automotive)


Type 3 – small scale and inexpensive

processes/equipment with medium/fast

dynamics

Patient

MPC-on-a-ChipMechanical Pump

Glucose Sensor


Type 3 – small scale and inexpensive

processes/equipment with medium/fast

dynamics

Available control hardware/software limited -

not suitable for online MPC

Multi-parametric MPC technology ideal/

essential

MPC-on-a-Chip part of embedded (all-in-one)

system

Suitable for new technologies (FPGA, wireless)

From Multi-Parametric

Programming Theory to

MPC-on-a-chip Multi-scale

Systems Applications

Stratos Pistikopoulos

FOCAPO 2012 / CPC VIII

From Multi-Parametric Programming Theory to MPC-on-a-chip...

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