advanced process control: an overview · automation lab iit bombay 12 model predictive control...

1

Advanced Process Control: An Overview

Sachin C. PatwardhanDept. of Chemical Engineering

I.I.T. Bombay Email: [email protected]

Automation LabIIT Bombay

2

Long Term Scheduling and Planning

On-line Optimization

Multivariable / Nonlinear Control

Regulatory (PID) Control

Plant

Slow Parameter drifts

MarketDemands /Raw materialavailability

MV Fast Load Disturbances

PV

Advanced

Control

Setpoints PV, MV

Plant Wide Control Framework


3

Hierarchy of control system functions


4

Why On-line Optimization ?

Shift if operational priorities Example: FCC Unit operated under Maximization of Gasoline / LPG production Maximization of ATF production Maximization of profits Minimization of energy consumption

Changes in operating conditions Changes in feed quality (refinery: change in crude blend) Changes in operating parameters

Catalyst degradation Heat-exchanger fouling Changes in separation efficiency


5

On-line Optimization

PLANT

Inputs

Outputs

Steady State Data Reconciliation

Steady State Model Parameter Estimation

Cleaned input Output Data On-line Steady

State Optimization

Updated SteadyState Model

Operational Goals

Updated

Set Points


6

Why Advanced Control ?

Why advanced control? Complex multi-variable interactions Operating constraints

Safety limits Input saturation constraints Product quality constraints

Control over wide operating range Process nonlinearities Changing process parameters / conditions

Conventional approach Multi-loop PI: difficult to tune Ad-hoc constraint handling using logic programming

(PLCs): lack of coordination Nonlinearity handling by gain scheduling


7

Example: Quadruple Tank System

21

21

h and h :Outputs Measuredv and v :Inputs dManipulate

14

114

4

44

23

223

3

33

22

224

2

42

2

22

11

113

1

31

1

11

)1(2

)1(2

22

22

vA

kghAa

dtdh

vA

kghAa

dtdh

vAkgh

Aagh

Aa

dtdh

vAkgh

Aagh

Aa

dtdh

Pump 2V2

Pump1V1

Tank3

Tank 2

Tank 1

Tank 4


8

Multi-loop Control

Industrial Processes: multivariable (multiple inputs influence same output) and exhibit strong interaction among the variables

Conventional Control scheme: Multiple Single Input Single Output PID controllers used for controlling plant (Multi-Loop Control)

Consequences: Loop Interactions Lack of coordination between different PID

loops Neighboring PID loops can co-operate with

each other or end up opposing / disturbing each other


9

Tennessee Eastman Problem

Primary controlled variables: Product concentration of GProduct Flow rate


10

TE Problem: Objective Function


11

TE Problem: Operating Constraints


12

Model Predictive Control

Multivariable Control based on On-line use of Dynamic Model

Most widely used multivariable control scheme in process industries over last 25 years Dynamic Matrix Control (DMC) developed by Shell in

U.S.A. (Cutler and Ramaker, 1979) Model Algorithmic Control developed by Richalet et. al.

(1978) in France Used for controlling critical unit operations (such

as FCC / crude column) in refineries world over Mature technology Can be used for controlling complex large dimensional

systems


13

Advantages of MPC

Modified form of classical optimal control problem

Can systematically and optimally handle Multivariable interactions Operating input and output constraints Process nonlinearities

Basic IdeaGiven a model for plant dynamics, possible consequences of the current input moves on the future plant behavior (such as possible constraint violations in future etc.) can be forecasted on-line and used while deciding the input moves


14

MPC: Schematic Diagram

Set point Trajectory

Disturbances

Dynamic Model: used for on-line forecasting over a moving time horizon (window)

Process

Dynamic Model

Dynamic Prediction

Model

Optimization

MPCPlant-model mismatch

Inputs Outputs


15

),,,,,(

),,,,,(

02

01

cinAcA

cinAcAA

TCFFTCfdtdT

TCFFTCfdt

dC

cinm

A

Tc

TA

TDC

FFUTYTCX

)( esDisturbancMeasured)(D esDisturbancUnmeasured

][)(Inputs dManipulate)( OutputMeasured)( States

u 0

CSTR ExampleConsider non-isothermal CSTR dynamics

If model is known, can we estimate CA from measurements of T ?

feed flow rate

coolant flow rate

Feed conc.

Cooling waterTemp.


16

CSTR: Multi-Loop PI Performance

Linear Plant

Simulation

PID PairingCA - Fc

T - F

3.00028.0

2.034.6

2,

2,

1,

1

I

c

I

c

k

k

0 5 10 15 20 250.2

0.25

0.3

0.35

0.4

Time (min)

Con

c.(m

ol/m

3)Controlled Outputs

0 5 10 15 20 25385

390

395

400

Time (min)

Tem

p.(K

)


17

CSTR: Multi-Loop PI Performance

Linear Plant

Simulation

0 5 10 15 20 2510

20

30

Time (min)

Coo

lent

Flo

w (

m3/

min

) Manipulated Inputs and Disturbance

0 5 10 15 20 250.5

1

1.5

Time (min)

Infl

ow (

m3/

min

)

0 5 10 15 20 251.5

2

2.5

Time (min)

Inle

t Con

c. (

mol

/m3)


18

CSTR: LQG Performance

Linear Plant

Simulation(No Plant

ModelMismatch

Case)

0 5 10 15 20 250.2

0.25

0.3

0.35

0.4

0.45

Time (min)

Con

c.(m

ol/m

3)Controlled Outputs

0 5 10 15 20 25388

390

392

394

396

398

Time (min)

Tem

p.(K

)


19

CSTR: LQG Performance

Linear Plant

Simulation(No Plant

ModelMismatch

Case)

0 5 10 15 20 2510

20

30

Time (min)

Coo

lent

Flo

w (

m3/

min

)

Manipulated Inputs and Disturbance

0 5 10 15 20 250

1

2

3

Time (min)

Infl

ow (

m3/

min

)

0 5 10 15 20 251.5

2

2.5

Time (min)

Inle

t Con

c. (

mol

/m3)


20

Linear MPC Applications (2003)


21

Industrial Application: Ammonia Plant


22

State Feedback Controller Design

Step 1 (Model Development) : Develop a discrete time dynamic model for process under consideration

Step 2 (Soft Sensing) : Design a state estimator (soft sensor) using dynamic model and measurements

Step 3 (Controller Design): Assume the states are measurable and design a state feedback controller

Step 3: Implement state feedback controller using estimated states


23

Models for Plant-wide Control

Aggregate Production Rate Models

Steady State / Dynamic First Principles Models

Dynamic Multivariable Time Series Models

SISO Time Series Models, ANN/PLS/Kalman Filters

(Soft Sensing)

Layer 4

Layer 3

Layer 2

Layer 1


24

Mathematical ModelsQualitativeQualitative Differential Equation Qualitative signed and directed graphs Expert Systems

QuantitativeDifferential Algebraic systems Mixed Logical and Dynamical Systems Linear and Nonlinear time series modelsStatistical correlation based (PCA/PLS)

MixedFuzzy Logic based models


25

White Box Models

First Principles / Phenomenological/ Mechanistic Based on

energy and material balances physical laws, constitutive relationships Kinetic and thermodynamic models heat and mass transfer models

Valid over wide operating range Provide insight in the internal working of systems Development and validation process:

difficult and time consuming


26

Example: Quadruple Tank System

Pump 2V2

Pump1V1

Tank3

Tank 2

Tank 1

Tank 4

21

21

h and h :Outputs Measuredv and v :Inputs dManipulate

14

114

4

44

23

223

3

33

22

224

2

42

2

22

11

113

1

31

1

11

)1(2

)1(2

22

22

vA

kghAa

dtdh

vA

kghAa

dtdh

vAkgh

Aagh

Aa

dtdh

vAkgh

Aagh

Aa

dtdh


27

Data Driven ModelsDevelopment of linear state space/transfermodels starting from first principles/gray box models is impractical proposition. Practical Approach• Conduct experiments by perturbing process

around operating point • Collect input-output data • Fit a differential equation or difference

equation model Difficulties • Measurements are inaccurate • Process is influenced by unknown disturbances• Models are approximate


28

Discrete Model Development

0 2 4 6 8 10 12 14 16 18 202

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

Sampling Instant

Man

ipu

late

d In

pu

t

Excite plant around the desired operating point by injecting input perturbations

Process

0 5 10 15 201.8

2

2.2

2.4

2.6

2.8

3

3.2

Sampling Instant

Mea

sure

d O

utp

ut

Input excitation for model identification

Unmeasured Disturbances Measured output

response

Measurement Noise

Automation LabIIT Bombay4 Tank Experimental Setup

29

Quadruple Tanks Setup


30

Identification Experiments on 4 Tank Setup

Input 1 Input 2

Output 1Output 2


31

4 Tank Setup: Input Excitations

0 200 400 600 800 1000 1200

-1

0

1In

put 1

(m

A)

Manipulated Input Sequence

0 200 400 600 800 1000 1200

-1

0

1

Inpu

t 2 (

mA

)

Time (sec)


32

Splitting Data for Identification and Validation

0 500 1000-5

0

5

y1

Input and output signals

0 500 1000

-0.50

0.51

Samples

u1

Identification Data Validation data


33

x(k+1) = x(k) + u(k) + e(k)Y(k) = C x(k) + e(k) = [0.6236 1 0 0

0.8596 0 1 00.0758 0 0 1-0.5680 0 0 0 ]

= [ 0.0832 0.0040 = [ 0.15410.0276 0.0326 0.05790.0268 -0.0184 -0.0307

-0.1214 0.0201 ] -0.0826 ] ;C = [ 1 0 0 0 ]

ARMAX:State Realization

L

L


34

OE Model: Validation

1100 1150 1200 1250 1300 1350 1400

-3

-2

-1

0

1

2

3

Time

y1

Measured and simulated model output

oe221 Fits 87.07%Validation data


35

State Estimation (Soft Sensing)

Quality variables : product concentration, average molecular weight, melt viscosity etc. Costly to measure on-line Measured through lab assays: sampled at irregular

intervals

Measurements available from wireless sensors are at irregular intervals due to packet losses

For satisfactory control of such processes: Quality variable / efficiency parameters should be estimated at a higher frequency

Remedy: Soft Sensing and State Estimation


36

Inferential Measurement: Basic Idea

Since fast sampled (primary) variables (temperatures, pressures, levels, pH) are correlated with the quality variable, can we infer values of quality

variables from measurements of primary variables?

On line state estimation:Feasible after availability of fast Computers


37

Model Based Soft Sensing

Fast-rate Low-cost measurements from

Plant (Temperature / Pressure / Speed)

Dynamic Model

(ODEs/ PDEs)

Irregularly / Slowly sampled Quality variables

from Lab assays

On-line Fast Rate Estimates of Quality variables

Soft Sensing: Cost Effective Solution


38

Soft Sensing Approaches

Soft Sensing Techniques

Static / Algebraic

Correlations

Dynamic Model based State Estimation

Deterministic (e.g. Luenberger

Observers)

Stochastic (e.g. Kalman filters)

Principle Components

AnalysisNeural

Networks


39

),,,,,(

),,,,,(

02

01

cinAcA

cinAcAA

TCFFTCfdtdT

TCFFTCfdt

dC

cinm

A

Tc

TA

TDC

FFUTYTCX

)( esDisturbancMeasured)(D esDisturbancUnmeasured

][)(Inputs dManipulate)( OutputMeasured)( States

u 0

CSTR ExampleConsider non-isothermal CSTR dynamics

If model is known, can we estimate CA from measurements of T ?

feed flow rate

coolant flow rate

Feed conc.

Cooling waterTemp.


40

“Closed Loop” State Observer

Use of output prediction error to 1. Stabilize estimator for unstable processes 2. Improve rate of convergence for stable systems

Open Loop Observer: Difficulties1. Not applicable to unstable systems 2. Rate of convergence governed by spectral

radius of

u(k)

)(ˆ ky

Process

Model

Y(k) +

-)(ke


41

Case Study-2 : Plug Flow Reactor (PFR)

A B C

Steam, Tjo

Tj(0,t)

CAo, TRo

CA(1,t), CB(1,t)

CC(1,t), TR(1,t)

(Endothermic Reaction)

T T T

Tj-1, TR-1 Tj-2, TR-2

Tj-5, TR-5

(Shang et al., 2002)


42

Material Balances (Distributed Parameter System)

Energy Balances

1 rE / RTA Al 10 A

C Cv k e Ct z

1 r 2 rE / RT E / RTB Bl 10 A 20 B

C Cv k e C k e Ct z

1 r

2 r

r1 E / RTr rl 10 A

m pm

r2 E / RT w20 B j r

m pm m pm r

HT Tv k e Ct z C

H U k e C T TC C V

j j wjr j

mj pmj j

T T Uu T T

t z C V

……..Reactant A

……..Product B

……..Reactor Temp.

……..Jacket Temp.

Fixed Bed Reactor


43

Simulation Result: Concentration profiles of product B at different time instants


44

Experiment: Combined State and Parameter Estimation on Heater-Mixer Setup

CV-1

Cold Water Flow

Tank - 1

LT

CV-2

ThyristerControl Unit

Tank - 2

4-20 mA Input Signal

3-15 psiInput

Cold Water Flow

TT

TT


45

Example: Stirred Tank Heater-Mixer

)(;/5.139

0093.071.0279.3)(0073.0989.0979.7)(

)()()(1

)(1

)()(

202

32

22222

31

2111

2222211

22

2

2212

2

1

111

1

11

hhkhFKsmJU

IIIIFIIIIQ

CTTUATTFTTF

AhdtdT

FIFFAdt

dhCVIQTT

VF

dtdT

p

atmi

pi

valve control to input current%:Icontroller power thyrister to input current % :

2

1I


46

Experimental result: Tank 1 temperature and heat loss parameter estimates

Automation LabIIT BombayController Design

State Feedback Controller Design: Assuming state are measurable, design a state feedback controller such as LQG or MPC

Advantage: Multi-variable systems can be controlled relatively easily

Separation principle ensures nominal closed loop stability with state estimator-controller pair

47


48

Course Outline

System Identification: Development of On-line Model Based Control Relevant Models from Input-Output Data Time series model development Discrete State Realization

State Estimation (soft sensing) : Estimation of unmeasured states (variables) by fusing Input-Output data with dynamic model predictions Luenberger observer design by pole placement Kalman filtering


49

Course Outline

Online Model Based Control Introduction to Classical Linear Quadratic Optimal

Control Linear Model Predictive Control

Evaluation Scheme Mid-semester exam (20 %) End-semester exam (40 %) Programming assignments and Project (20 %, tentative) Quizzes (20 %, tentative)

advanced process control: an overview · automation lab iit bombay 12 model predictive control...

Documents