Advanced Process Control: An Overview Sachin C. Patwardhan Dept. - - PowerPoint PPT Presentation

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Advanced Process Control: An Overview

Sachin C. Patwardhan

• Dept. of Chemical Engineering

I.I.T. Bombay Email: sachinp@iitb.ac.in

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Long Term Scheduling and Planning On-line Optimization Multivariable / Nonlinear Control

Regulatory (PID) Control

Plant

Slow Parameter drifts Market Demands / Raw material availability

MV

Fast Load Disturbances

PV

Advanced Control

Setpoints PV, MV

Plant Wide Control Framework

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Hierarchy of control system functions

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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

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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 Steady State Model

Operational Goals

Updated Set Points

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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

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Example: Quadruple Tank System

2 1 2 1 2 4 2 2 4 4 4 4 1 3 1 1 3 3 3 3 2 2 2 2 4 2 4 2 2 2 2 1 1 1 1 3 1 3 1 1 1 1

h and h : Outputs Measured v and v : Inputs d Manipulate ) 1 ( 2 ) 1 ( 2 2 2 2 2 v A k gh A a dt dh v A k gh A a dt dh v A k gh A a gh A a dt dh v A k gh A a gh A a dt dh γ γ γ γ − + − = − + − = + + − = + + − =

Pump 2 V2 Pump1 V1 Tank3 Tank 2 Tank 1 Tank 4

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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

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Tennessee Eastman Problem

Primary controlled variables: Product concentration of G Product Flow rate

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TE Problem: Objective Function

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TE Problem: Operating Constraints

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Model Predictive Control

Multivariable Control based on On-line use

• f 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

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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 Idea

Given 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

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MPC: Schematic Diagram

Set point Trajectory Disturbances

Dynamic Model: used for on-line forecasting

• ver a moving time horizon (window)

Process Dynamic Model

Dynamic Prediction Model

Optimization MPC

Plant-model mismatch Inputs Outputs

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) , , , , , ( ) , , , , , (

2 1 cin A c A cin A c A A

T C F F T C f dt dT T C F F T C f dt dC = =

[ ]

[ ] [ ] [ ]

cin m A T c T A

T D C F F U T Y T C X ≡ ≡ ≡ ≡ ≡ ) ( es Disturbanc Measured ) (D es Disturbanc Unmeasured ] [ ) ( Inputs d Manipulate ) ( Output Measured ) ( States

u

CSTR Example

Consider 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 water Temp.

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CSTR: Multi-Loop PI Performance

Linear Plant Simulation PID Pairing CA - Fc T - F

3 . 0028 . 2 . 34 . 6

2 , 2 , 1 , 1

= = = =

I c I c

k k τ τ

5 10 15 20 25 0.2 0.25 0.3 0.35 0.4

Time (min) Conc.(mol/m3) Controlled Outputs

5 10 15 20 25 385 390 395 400

Time (min) Temp.(K)

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CSTR: Multi-Loop PI Performance

Linear Plant Simulation

5 10 15 20 25 10 20 30

Time (min)

Coolent Flow (m3/min)

Manipulated Inputs and Disturbance

5 10 15 20 25 0.5 1 1.5

Time (min)

Inflow (m3/min) 5 10 15 20 25 1.5 2 2.5

Time (min)

Inlet Conc. (mol/m3)

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CSTR: LQG Performance

Linear Plant Simulation (No Plant Model Mismatch Case)

5 10 15 20 25 0.2 0.25 0.3 0.35 0.4 0.45

Time (min)

Conc.(mol/m3)

Controlled Outputs

5 10 15 20 25 388 390 392 394 396 398

Time (min)

Temp.(K)

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CSTR: LQG Performance

Linear Plant Simulation (No Plant Model Mismatch Case)

5 10 15 20 25 10 20 30

Time (min)

Coolent Flow (m3/min)

Manipulated Inputs and Disturbance

5 10 15 20 25 1 2 3

Time (min)

Inflow (m3/min) 5 10 15 20 25 1.5 2 2.5

Time (min)

Inlet Conc. (mol/m3)

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Linear MPC Applications (2003)

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Industrial Application: Ammonia Plant

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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

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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

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Mathematical Models

Qualitative Qualitative Differential Equation Qualitative signed and directed graphs Expert Systems Quantitative Differential Algebraic systems Mixed Logical and Dynamical Systems Linear and Nonlinear time series models Statistical correlation based (PCA/PLS) Mixed Fuzzy Logic based models

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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

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Example: Quadruple Tank System

2 1 2 1 1 4 2 2 4 4 4 4 2 3 1 1 3 3 3 3 2 2 2 2 4 2 4 2 2 2 2 1 1 1 1 3 1 3 1 1 1 1

h and h : Outputs Measured v and v : Inputs d Manipulate 1 2 1 2 2 2 2 2 v A k gh A a dt dh v A k gh A a dt dh v A k gh A a gh A a dt dh v A k gh A a gh A a dt dh ) ( ) ( γ γ γ γ − + − = − + − = + + − = + + − =

Pump 2 V2 Pump1 V1 Tank3 Tank 2 Tank 1 Tank 4

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Data Driven Models

Development of linear state space/transfer models 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

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Discrete Model Development

2 4 6 8 10 12 14 16 18 20 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 Sampling Instant Manipulated Input

Excite plant around the desired operating point by injecting input perturbations Process

5 10 15 20 1.8 2 2.2 2.4 2.6 2.8 3 3.2

Sampling Instant Measured Output

Input excitation for model identification Unmeasured Disturbances Measured output response Measurement Noise

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4 Tank Experimental Setup

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Quadruple Tanks Setup

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Identification Experiments

• n 4 Tank Setup

Input 1 Input 2 Output 1 Output 2

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4 Tank Setup: Input Excitations

200 400 600 800 1000 1200

• 1

1 Input 1 (mA) Manipulated Input Sequence 200 400 600 800 1000 1200

• 1

1 Input 2 (mA) Time (sec)

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Splitting Data for Identification and Validation

500 1000

• 5

5 y1 Input and output signals 500 1000

• 0.5

0.5 1 Samples u1

Identification Data Validation data

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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 0 0.0758 0 0 1

• 0.5680 0 0 0 ]

= [ 0.0832 0.0040 = [ 0.1541 0.0276 0.0326 0.0579 0.0268 -0.0184 -0.0307

• 0.1214 0.0201 ] -0.0826 ] ;

C = [ 1 0 0 0 ]

ARMAX:State Realization

Φ Γ

∞

L Φ Γ

∞

L

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OE Model: Validation

1100 1150 1200 1250 1300 1350 1400

• 3
• 2
• 1

1 2 3 Time y1 Measured and simulated model output

• e221 Fits 87.07%

Validation data

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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

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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

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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

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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 Analysis Neural Networks

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) , , , , , ( ) , , , , , (

2 1 cin A c A cin A c A A

T C F F T C f dt dT T C F F T C f dt dC = =

[ ]

[ ] [ ] [ ]

cin m A T c T A

T D C F F U T Y T C X ≡ ≡ ≡ ≡ ≡ ) ( es Disturbanc Measured ) (D es Disturbanc Unmeasured ] [ ) ( Inputs d Manipulate ) ( Output Measured ) ( States

u

CSTR Example

Consider 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 water Temp.

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“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: Difficulties 1. Not applicable to unstable systems 2. Rate of convergence governed by spectral radius of

u(k)

) ( ˆ k y

Process Model Y(k) +

• )

(k e

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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)

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• Material Balances (Distributed Parameter System)
• Energy Balances

1 r

E /RT A A l 10 A

C C v k e C t z

−

∂ ∂ = − − ∂ ∂

1 r 2 r

E /RT E /RT B B l 10 A 20 B

C C v k e C k e C t z

− −

∂ ∂ = − + − ∂ ∂

( ) ( )

( )

1 r 2 r

r1 E / RT r r l 10 A m pm r2 E / RT w 20 B j r m pm m pm r

H T T v k e C t z C H U k e C T T C C V

− −

−Δ ∂ ∂ = − + ∂ ∂ ρ −Δ + + − ρ ρ

( )

j j wj r j mj pmj j

T T U u T T t z C V ∂ ∂ = + − ∂ ∂ ρ

……..Reactant A ……..Product B

……..Reactor Temp. ……..Jacket Temp.

Fixed Bed Reactor

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

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

CV-1

Cold Water Flow Tank - 1 LT

CV-2

Thyrister Control Unit

Tank - 2

4-20 mA Input Signal 3-15 psi Input

Cold Water Flow TT TT

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Example: Stirred Tank Heater-Mixer

[ ]

) ( ; / 5 . 139 0093 . 71 . 27 9 . 3 ) ( 0073 . 989 . 979 . 7 ) ( ) ( ) ( ) ( 1 ) ( 1 ) ( ) (

2 2 3 2 2 2 2 2 2 3 1 2 1 1 1 2 2 2 2 2 1 1 2 2 2 2 2 1 2 2 1 1 1 1 1 1 1

h h k h F Ks m J U I I I I F I I I I Q C T T UA T T F T T F A h dt dT F I F F A dt dh C V I Q T T V F dt dT

p atm i p i

− = = + − + = − + = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − − − + − = − + = + − = ρ ρ

valve control to input current % : I controller power thyrister to input current % :

2 1

I

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Experimental result: Tank 1 temperature and heat loss parameter estimates

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Controller 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

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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

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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)