Opportunities and Challenges of Model Predictive Control in Food Technologies

Želimir Kurtanjek

University of Zagreb,Faculty of Food Technology and Biotechnology,

Pierotijeva 6, Zagreb, CROATIA

Basic concept of Model Predictive Control (MPC)

Industrial process

Non-manipulative input variables

Output variables

Predictive model

Optimization

y(k)x(k)

)1(ˆ ky x(k+1)

Manipulative input variables

Process flows

Information flows

Control actions

Process flows:

mass, substances

energy, heat

momentum

Information flows:

discrete off-line measurements : HPLC,

continuous on-line measurements: T, p, NIR, IR, …

Control actions:

flow rate, heating/cooling, manipulation, …..

Optimization:

product quality, energy, productivity, profitability

Very recent references on MPC in food technology

Carlos Bordons, Amparo Nunez-Reyes

“Model based predictive control of an olive oil mill”

Journal of Food Engineering 84 (2008) 1-11

Nazru I. Shaikh, Vittal Prabhu

“Model predictive controller for cryogenic tunnel Freezers”

Journal of Food Engineering 80 (2007) 711-718

Review of industrial applications:

Manfred Morrari

“Beyond Process Control”

ETH presentation

Review of modern control theory: MPC and beyond

Model predictivity (prediction horizon)

time

output Y

future past

k k+1 k+2 k+n k-1 k-2 k-m

measured model predicted Y

prediction horizont

OPTIMIZATION

time

input X

future past

k k+1 k+2 k+n k-1 k-2 k-m

measured optimized

X(k+1)

Shift horizon one step

present

present

Challenges for modeling in food processes

Complex substance composition

Time varying composition

Nonhomogeneous

Multiphase

Lack of property data

Challenges for substance modeling Challenges for process modeling

Unsteady (batch) and nonlinear

Large time delays

Unmeasured essential states

Complex and unknown kinetics

Complex transport phenomena

……………… ……………………..

Modeling techniques applied in food engineering

Steady state single input-single output regression

y=f(b,x)x y

n

n xbxbxbby ..2

210

Unsteady state discrete single input single output ARMA

mikuibikyiakyuy N

i

N

i

00

Unsteady state continuous single input single output

0)0())(,( yytxyfdt

dy

x1

Multivariate models

x2xm

y1y2yn

y=f(b,x1,x2··xm)

Steady state linear multivariate model multiple input – single output

nn xbxbxbby 22110

0)0())(,( yytxyfdt

yd

Unsteady state continuous multiple input single output

Partial linear regression (PLR) multiple input single output

nn xbxbxbby 22110 nn xcxcxccy 22110

Modeling by Principal Component Analysis (PCA)

x1

x2

x3

x4

xn

Xn-1

x…

L1

L2

L3

2min

Space of real process variables

Space of latent process variables

Measured variables: x1= temperature, x2=pressure, x3=humidity, x4=composition..

Linear projection

Many inter-correlated variables

Few uncorrelated principal components in latent space

Modeling by principal components

High measurement random error rejection

Robust models, high predictivity

Ž. Kurtanjek, D. Horvat, D. Magdić, G. Drezner,

“Factor Analysis and Modeling for Rapid Quality Assessment of Croatian Wheat Cultivars with Different Gluten Characteristics” , Food Technology and Biotechnology, 2008 (accepted)

P rojec t ion of the variables on the fac tor-plane ( 1 x 2)

A c tive

2

3

4

5

6

7

8

9

10 11

12

13

14

15 16

17

18

19

20

21

22

23

24

25

26

27

28

29 30

31

32

33 34

35

36

37

38 39

40

41

42

43

44

45

-1.0 -0.5 0.0 0.5 1.0

Fac tor 1 : 43.47%

-1.0

-0.5

0.0

0.5

1.0

Fac

tor

2 :

22.1

8%

44

technological and biochemical variables

First 2 principal components account for 86% variance

Example of effective variable reduction by principal component analysis

05

101520253035404550

1 3 5 7 9

11

13

15

17

19

Principal components

% V

ari

an

ce

Scree plot

Nonlinear multivariate models

Neural networks

Fuzzy logic

Highly applicable for process monitoring and control

Schematic representation of a neurone with a sigmoid activation Schematic representation of a neurone with a sigmoid activation functionfunction

O

x1

x3

x2

xi

xN

ACTIVATION

0

0,2

0,4

0,6

0,8

1

1,2

-6 -4 -2 0 2 4 6

INPUTO

UTP

UT

)exp(1

1)(

ssf

x1

x2

x3

xn

y

Schematic diagram of a feedforward multilayer perceptronSchematic diagram of a feedforward multilayer perceptron

Y3

Y2

Y1

X1

X2

X3

X4

I H O

y1

x4

x2

x2

x1

y2

y3

ModelModel equationsequations

k

TtytyE

2

1

)1(

1

)1()1(

1

)1(lN

i

lj

li

lijl

lN

i

lj

li

lij

lj koWnetkoWfko

jiji W

EW

,,

Methods of adaptation:

On-line back propagation of error with use of momentum term

Batch wise use of conjugate gradients ( Ribiere-Pollack, Leveberg-Marquard)

Fuzzy logic modelsFuzzy logic models

In fuzzy logic models input and output spaces are covered or approximated with discourses of fuzzy sets labeled as linguistic variables

For example, if Ai X is an i-th fuzzy set it is defined as an ordered pair:

fAi ttXtxtxtxA ,0,,

where x(t) is a scalar value of an input variable at time t, and A is called a membership function which is a measure of degree of membership of x(t) to Ai expressed as a scalar value between 0 and 1.

Typical membership functions have a form of a bellshaped or Gaussian, triangular, square, truncated ramp and other forms

Gaussian membership functionsGaussian membership functions

e=regulation error

e=0 e = highe = low

Triangle membership functions

X

Input space of physical variables

Input space of linguistic variables

AX

Output space of linguistic variables

AY

Output space of physical variables

Y

Logical rules with linguistic variables

Fuzzy Logic Inference Systems

( Mamdani Model )

Process of mapping scalar between input and output Process of mapping scalar between input and output sets by sets by

Fuzzy Inference System.Fuzzy Inference System.

Fuzzification Fuzzy inference Defuzzification

x(t) y(t)

OPTIMIZATION

Objective function J

J=J(y1, y2, y3,··x1, x2, x3, )

Examples:

J=food quality

J=profit

J=productivity

J=energy consumption

J=environment impact

1)(1)(

)()(min

**

kkkk

kkkkkJ

U

T

Y

T

U XXWXX

YYWYYLinear objective function for process regulation

Methods for optimization

Simplex algorithm

Conjugate gradients

Genetic algorithm

Conjugate gradients

By Wolfram Research “Mathematica”

Simplex algorithm

Down-hill tumbling of a simplex

Genetic algorithm

Tmin

Tmax

pHmin

pHmax

Smin

Smax

K1 K2 Kk KN

GT

GpH

GS

population N chromosons

0 1

Kk

Kj

KjL KjD

KkL KkD

Kk

Kj

KjL

CkL KjD

KkD

"cross over"

r1

r2 mutation

new generation

new generation

A B

Kj

Kk

Ž. Kurtanjek, PBF: Optimization of T, pH and S in a bioreactor

Results of MPC application

In about last 20 years, in literature is reported that MPC has been used in over 5000 industrial applications, most of them in chemical and electrical industry, and less in fermentation and food process industry

For industrial process control practitioners, MPC has the following advantageous properties:

It is a true multivariate control algorithm enabling integration of various plant information into process monitoring and control software

Has ability to naturally and explicitly handle nonlinearities, time delays, and multivariable input and output constraints by direct incorporation into on-line optimization

Enables early detection of process disturbances and prediction of malfunctions in process equipment improve the safety of the process, minimize the time and resources needed for maintenance, and increase the uniform quality of the products

The objective of on-line monitoring is to trace the state of the process and the condition of process equipment in real-time, and to detect faults as early as possible

Available are standard commercial numerical and statistical algorithms needed for MPC

ConclusionsConclusions

Due to expanding global food market food Due to expanding global food market food industry needs to achieve higher levels of industry needs to achieve higher levels of productivity, enhanced safety assurance productivity, enhanced safety assurance and better quality products, which will and better quality products, which will expansion of process automation and expansion of process automation and intelligent on-line control which will intelligent on-line control which will inevitably advance application of MPC inevitably advance application of MPC based control.based control.