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### Identification for industrial model-based control

### NOT IN ORIGINAL PRESENTATION!

Vidar Alstad

Department of Chemical Engineering

NTNU

June 8, 2005

Title: "Identification for industrial model-based control. "

Deatils: The committee would like a survey of what kind of models (soft/hard) are used by industry for model predictive control (MPC), how the models are identified, and the expected future direction. The candidate should also address the following question: "Why does industry today use almost exclusively black-box (soft) models?"

Outline

- Scope of presentation
- Introduction & brief history of MPC
- Model identification
- Linear models used in industrial MPC
- Non-linear models in industrial MPC
- Future directions
- Why still black-box models?
- Concluding remarks

Model based control (Brosilow and Joseph, 2001 )

Examples:

Internal model control (Morari and Zafiriou, 1989)

Model predictive control (Richalet et al, 1976, Cutler and Ramaker, 1979)

Black-box and first principles

Scope of presentation”Control systems that explicitely embed a process model in the control algorithm”

Based on the current measured variables and the current and future inputs, the model must predict the future outputs (Rossitier, 2003)

- Steady-state models

Often steady-version of the above dynamic model or a separate comprehensive model (Qin and Badgwell, 2003)

Scope of presentation- Types of models formulations used in MPC

- Continuous processes

Model predictive control (Gorinevsky, 2005)

control horizon

- At each time step, compute the optimal control inputs over the control horizon by solving an open loop optimization problem over the prediction horizon taking constraints into account

- Apply the first value of the computed control input into the process

- At the next time step, redo the calculation

Brief history of industrial MPC

- LQR (Kalman, 1964)
- Little impact in process industries due to lack of constraint handling (Richalet et al., 1976, Garcia et al. 1989)
- IDCOM and DMC (Richalet et al., 1976, Cutler and Ramaker, 1979)
- Input/output representation
- Ad hoc constraint handling
- QDMC (Cutler et al., 1983)
- Explicit constraint handling (improved DMC)
- IDCOM-M, HIECON, SMCA and SMOC (late 1980-1990s)
- State space representation
- Hard constraints and priorities
- DMC-plus and RMPCT (2000+)
- Improved identification technology
- Non-linear MPC (Aspen, DOT-products)

Industrial usage of MPC

- Factors for widespread usage in process industries (Piche, et al. 2000)
- Open-loop settling time minutes or hours
- Well suited for multivariable control (MIMO)
- Explicit constraint handling
- Empirical modelling tools
- Standard in refining, chemical, petrochemical, pulp and paper and food processing.
- Many industrial commercial vendors.

Non-exhaustive MPC Vendor List (Allgöwer, 2004)

- ABB
- ACT
- Adaptics
- Adaptive Resources
- Adersa
- Aspen Technology
- Aurel Systems Inc.
- Batch CAD
- Bonner and Moore
- Brainwave
- C.F. Picou and Associates
- Chemstations
- Comdale Technologies
- Control Arts Inc.
- Control Consulting Inc.
- Control Dynamics
- Controlsoft Incorporated
- Cybosoft
- Cybernetica
- DOT Products

Objectspace

Optimal Control Research

Pavilion Technologies

Predictive Control Ltd.

Predictor

Process System Consultants

RSI

Simulation and Advanced

Simtech

Texas Controls Inc.

Trieber Controls

Yokogawa APC

US Process Control L.L.C.

Eldridge Engineering Inc.

Elsag Bailey

Envision Systems Inc.

Gensym

Enterprise Control Technologies

Fantoft Process Group

MATHWORKS

Honeywell

Inferential Control Company

IntellOpt

Knowledgescape

MDC Technology

Neuralware

Nexus Engineering

- Introduce a sequence of inputs ujk
- yjk contain the process information
- By treating the time series of yk with uk , a model can be estimated.
- Near all model types need experiments

PROSESS

Identification

method

Model

Identification for MPC”In a typical commissioning project, modeling efforts can take up to 90% of the cost and time” (Andersen and Kummel, 1992).

”Model identification is clearly the ”Achilles heel” of MPC (or any other model-based controller design technique)” (Ogunnaike and Ray, 1994)

Instrument verification

Time to steady-state (TSS)

Data for initial identification

Steps in industrial identification(Söderström and Stoica, 1989)Pre-test

- Sequential
- Simultanious
- Signal type (PRBS or step)

Test protocol

Model

- Model formulation to use

Model identification

- Model parameter estimation
- Equation error
- Output error

Model validation

Model validation: Measure goodness of model

No

Accept?

Pre-test and test protocol

Pre-test

- Pre-testing (Seborg et al., 2004)
- Estimate process gains
- Time constants
- Time delays
- Plant instrumentation verification

Test protocol

Model

- Test protocol
- Signal type
- Sequential vs. simultaneous
- Closed loop or open loop

Model identification

Model validation

Accept?

MPC relevant signal design (McLellan, 2004)

Require good estimate on steady-state gain and slower dynamics

power

Higher frequencies handled by the regulatory control layer.

frequency

Test signals for MPC identification- Data from tests should be informative, e.g. contain information on sufficient distinct frequencies. (Ljung, 1999).

- Industrial test signals (McLellan, 2004)
- Step signals
- Pseudo-Random Binary signals (PRBS)

power

frequency

frequency

Test signals for MPC identificationPRBS

y

u

y

u

STEP

t

t

t

t

Provides good information on steady-state gain and higher frequencies.

Provides very good information on steady-state gain

Limited information on higher frequencies

- Input magnitude
- Duriation

- Input magnitude
- Duration
- Minimum switching time
- Desired frequency content

Test signals and identification( Qin and Badgwell, 2003; Conner and Seborg, 2004; Morari and Lee, 1999; Li and Lee, 1996)

- Open loop and sequential
- Step
- Easy to administer and easier to interpret data
- Long test time

- SISO identification
- Easy identify model structure
- No information on directionality
- Good individual SISO match (either step or frequency response), poor MIMO model.
- MISO identification
- Simultanious excitation signals
- Output models fit one-by-one
- Better disturbance model
- No information on directionality

- Process upset
- Open loop and simultanious

Model formulation in industrial MPC (Qin and Badgwell, 2003)

Non-linear

Pre-test

- Input/Output models
- Nonlinear neural net (NNN) + auto-regressive with exogenous inputs (ARX)
- State space
- Nonlinear state space model (LSS) (NNN)

- Nonlinear state space
- Hybrid models

Test protocol

Model

Empirical

First principles

Model identification

- Input/Output models
- Finite impulse response (FIR)
- Finite step response (FSR)
- Laplace transfer function (TF)
- Auto-regressive with exogenous inputs (ARX)
- State space
- Linear state space model (LSS)

Model validation

Accept?

Linear

Linear models

Empirical

- Majority of industrial MPC applications use linear empirical models (Qin and Badgewell, 2003)

Linear

- Input/Output models
- Finite impulse response (FIR)
- Finite step response (FSR)
- Laplace transfer function (TF)
- Auto-regressive with exogenous inputs (ARX)
- State space
- Linear state space model (LSS)

Parameters si is the sampled output after a unit step input

Non-linear

Input/output modelsFIR and FSREmpirical

First principles

Nonparametric models

- Finite Impulse Response

Linear

- Parameters hi are the sampled output after a unit impulse input

Input/output modelsFIR and FSR (Qin and Badgwell, 2003; Ljung, 1999)

Empirical

First principles

- General Finite Impulse Response (FIR)

Linear

- General Finite Step Response (FSR)

Input/output modelsFIR and FSR (Zhu et al., 2000, Ljung, 1999; Qin and Badgwell, 2003)

Empirical

First principles

- Finite impulse response (FIR) and Finite step response (FSR) model
- Can handle complex dynamics
- Time delays, inverse response
- Little prior process knowledge needed
- Time to steady state (TTSS)
- Nu,Nd,Nv
- Model identification
- No bias in parameters due to measurement noise
- Bias due to truncation
- Over-parametrized
- Sample time selected so 30-120 coefficients describe the full open loop response
- Cannot handle unstable or integrating processes
- Output feedback

Linear

Polynomial matrices, e.g.

Non-linear

Input/output modelsARX (Zhu et al., 2000; Ljung, 1999; Qin and Badgwell, 2003)Empirical

First principles

Parametric models

Linear

Autoregressive model with exogenous inputs (ARX)

Example

Non-linear

Input/output modelsARX (Zhu et al., 2000; Ljung, 1999; Qin and Badgwell, 2003)Empirical

First principles

Same autoregressive part for inputs and disturbances

Disturbances enter near input of process (same denominator term)

Handles stable, unstable and integrating dynamics

Model order

Linear

v

Ev

u

B

S

S

A-1

y

- Other parametric models used
- Box-Jenkins
- Transfer function (converted to discrete time)

Ed

d

Empirical

First principles

Linear

State space models (Qin and Badgwell, 2003)- Discrete state space

- Handles stable, unstable and integrating processes
- Systematic output feedback (Kalman filter)
- Distinction between controlled and feedback variables
- Unmeasured disturbance models
- Linearized first principle model
- Used in research literature

Linear model identification (Qin and Badgwell, 2003)

Pre-test

- Prediction error methods
- Minimize a least square criterion

Test protocol

using either

Model

- Equation error approach (one step ahead prediction)
- Output error approach (multi step ahead prediction)

Model identification

- Finite impulse and step response (FIR and FSR) yield linear least square.

Model validation

Accept?

- Predictor

Equation error identification approach

Linear least square

Output error identification approach

Nonlinear parameter estimation

Linear model identification ARX (Qin and Badgwell, 2003)Prediction error

- Past measurements fed back in model
- Preferred industrial implementation
- Parameter estimates biased given white measurement noise
- One-step ahead prediction

- Past estimates fed back in model
- Numerically more challenging
- Gauss-Newton methods
- Gradient descent methods
- Global methods
- Parameter estimates unbiased
- Multi-step ahead prediction

Linear model identification state space models

- Based on subspace model identification (Van Overschee, 1996)
- Efficient method for estimating MIMO models as compared to existing PEM methods (Favoreel, et al, 2000)

- Two step procedure
- Estimate the state sequence from input/output data
- Linear regression to find the system matrices

- Can yield suboptimal estimates as compared to existing PEM methods (Van Overschee, 1996)

Nonparametric models

(FIR and FSR)

Bias error due to truncation

Poor with fast/slow dynamics

Non-compact.

Unable to model unstable and integrating processes

Ad hoc bias sceeme output feedback

Linear least square for parameter estimation

Little process knowledge needed

Parametric models

(ARX and state space)

Order selection (ARX)

Ad hoc bias sceeme output feedback (ARX)

No bias (if sufficient order) (ARX)

Compact

Handles unstable and integrating processes

MIMO identification (state space)

Output feedback (state space)

Linear models – Summary(Qin and Badgwell,2003; Zhu and Butoyi, 2002; Ljung, 1999)Model formulation in industrial MPC (Qin and Badgwell, 2003)

Non-linear

Pre-test

- Input/Output models
- Nonlinear neural net (NNN) + auto-regressive with exogenous inputs (ARX)
- State space
- Nonlinear state space model (LSS) (NNN)

- Nonlinear state space
- Hybrid models

Test protocol

Model

Empirical

First principles

Model identification

- Input/Output models
- Finite impulse response (FIR)
- Finite step response (FSR)
- Laplace transfer function (TF)
- Auto-regressive with exogenous inputs (ARX)
- State space
- Linear state space model (LSS)

Model validation

Accept?

Linear

Non-linear empirical models

Empirical

First principles

Linear

- Input/Output models
- Nonlinear neural net (NNN) + auto-regressive with exogenous inputs (ARX)
- State space
- Nonlinear state space model (LSS) (NNN)

Input/output (Piche et al., 2000, Qin and Badgwell, 2003)

Empirical

First principles

- Pavilion
- Steady-state nonlinear model superimposed on a linear dynamic model

Linear

- Second order linear model for dynamics
- Open loop step response for identification

- Steady state nonlinear part modeled as a bounded derivative neural net.
- Trained using historical closed loop data

State space( Zhao et al. ,1998;2001)

Empirical

First principles

- Aspen Apollo™

Linear

- Claimed that above model can approximate any discrete time nonlinear process with fading memory (Sentoni et al., 1998)
- Bounded derivative network (Turner and Guiver, 2005)
- Calculated bounds (max/min) on the gains
- Globaly constrained, i.e. smooth transition to a linear approximation (constant gain) in regions of extrapolation.
- Identification
- MISO identification of linear state space model using Principal Component Analysis and Partial least squares methods
- Neural net trained on prediction error for the linear model

Non-linear first principle models

Empirical

First principles

- Mass, energy and impulse conservation equations (Kouvaritakis and Cannon, 2001)

Linear

- Empirical data needed
- Plant data not sufficient

- Uncertain parameters estimated using least square (Young, et al. 2001)
- Robustness and reliablility of identification algorithm
- “Art” in estimation of the parameters. (Young, et al. 2001)
- Nonlinear test signal design
- Open topic (Morari et al., 1999)

Future directions

Linear models

- Parametric models (Qin, 2005)
- State space representation (Qin and Badgwell, 2003)
- Subspace identification methods
- Output feedback

Non-linear models

- Non-linear empirical models (Piche et al., 2000)
- Extensive testing
- First principle models
- Modeling and identification
- Servo control problem with changes in operating point

Identification

- MIMO identification

Why does industry still use black-box models?

- Why not first principle nonlinear models?
- Modeling and maintenance cost (Pische, 2000)
- Justification criteria
- Often process and operation specific
- Test signal and identification (Morari and Lee, 1999)
- Modeling tools
- Non-convex online optimization, computationally expensive (Morari and Lee, 1999)

- Historical reasons
- Regulator problem
- Sufficient performance using a linear models (Keep it simple!)
- Non-linearities handled by variable transformations
- Easy to identify
- Linear least square (ARX, FIR/FSR)
- Subspace methods
- Efficient online optimization
- Empircal nonlinear models
- “… next step beyond linear modeling of chemical processes.’’ (Henson and Seborg, 1997)

Concluding remarks

- Predictive models for MPC
- Linear empirical models
- Sequential and open loop testing
- Non-linearity addressed using empirical models (e.g. neural net)
- First principle models not widely used due to cost of design and maintenance
- Improvements in identification technology would have an positive impact on MPC technology

Acknowledgements:

Bjørn Glemmestad, Vinay Kariwala, Audun Faanes, Tor Steinar Schei, Stig Strand, Kjetil Fjaalestad, Svein Olav Hauge and Olav Slupphaug

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