This presentation looks into how (large-scale) first-principles models of chemical process plants can be embedded in a framework for advanced process control based on real-time dynamic optimisation. It goes beyond the conventional MPC/RTO architecture and looks into the challenges of i) control problem formulation and interpretation and ii) appropriate handling of soft constraints in an industrial real-time setting. Several simulations of a realistic industrial case study are shows, where the performance of the original (nonlinear) model and a linear-time invariant approximation is compared in terms of i) quality of the solution and ii) computation time. We demonstrate that with state-of-the-art modelling tools it is possible to apply rigorous real-time dynamic optimisation based on sound first-principles models to drive the efficiency of industrial-scale process operations.

1. © 2010 Process Systems Enterprise Limited
Real-time Dynamic Optimisation
Dr Pablo A Rolandi – Head of Development, PSE Ltd
CPSE Spring Consortium Meeting
Imperial College, London – April 23, 2010

2. © 2010 Process Systems Enterprise Limited
Outline
 Motivation
 Online operations and real-time decision-making
 Model-based control and optimisation
− Innovation space
− Engine prototype
 Case study
 Summary and outlook

3. © 2010 Process Systems Enterprise Limited
Motivation
 Real-time Process Optimisation and Training:
− advanced process control (APC)
− on-line optimisation
− training simulation and control validation software
− market: $1 billion in 2008; >$1.5 billion in 2013
− 9%/year x5 years
 Process Industries
− Spare capacity
− New capacity and processes
− CAPEX and OPEX considerations

4. © 2010 Process Systems Enterprise Limited
Motivation
 Novel plant designs: e.g. pulp & paper mills
− CAPEX and OPEX trade-off
− Reduced buffer capacity
− Elimination of redundant (back-up) equipment
− Larger equipment interactions and faster dynamics
 Economic and environmental drivers
− Maximum profit
− Improved management of utilities
− Steam (evaporators train) and water (pulp washing)
 Process operation scenario
− Management of production rate transitions
− Paper machine grade changes

5. © 2010 Process Systems Enterprise Limited
Example: Pulp and Paper Industry
Industrial continuous pulping
Wood chips
Wood pulp
Paper
Reactor
(Continuous
cooking
digester)
Pulp and Paper Mill

6. © 2010 Process Systems Enterprise Limited
Example: Industrial continuous pulping
Digester section
Heterogeneous solid-liquid reaction
Multicomponent mixture
Primary KPIs: selectivity and yield
Secondary KPI: washing efficiency

7. © 2010 Process Systems Enterprise Limited
Industrial continuous pulping
Production rate change: “open-loop” response
+0.6rpm

8. © 2010 Process Systems Enterprise Limited
Industrial continuous pulping
Production rate change: “open-loop” response
+1°C

9. © 2010 Process Systems Enterprise Limited
Industrial continuous pulping
Production rate change: “open-loop” response
+1°C

10. © 2010 Process Systems Enterprise Limited
Industrial continuous pulping
Production rate change: “open-loop” response
Minimise variability of selectivity (quality)
and maximise yield (throughput)

11. © 2010 Process Systems Enterprise Limited
Industrial continuous pulping
Production rate change: “closed-loop” response
Process and reactor design:
Enough degrees-of-freedom for advanced control and optimisation
Operator transition (2 DOF) Rigorous optimisations (1 DOF)

12. © 2010 Process Systems Enterprise Limited
Process operations
Control and optimisation
 Traditional approach:
− Regulatory process control (feedback PID loops)
− Recipes and procedures
− Off-line: idealised scenarios, sub-optimal solutions
Avoiding complexity at the expense of
economic and environmental performance
Timescale
Frequency

13. © 2010 Process Systems Enterprise Limited
Process operations
Real-time decision making support
 Link between the complexity of the plant and the
complexity of the market
 Advanced process control
− Few discrete decisions
− Large nonlinearities
− Minutes to hours
 Planning and scheduling
− Many discrete decisions
− Small nonlinearities
− Days to months
Timescale
Frequency
Timescale
Frequency

14. © 2010 Process Systems Enterprise Limited
Model-based Process Control
Model Predictive Control (MPC)
Timescale
Frequency
Plant
MPC
y
y
yss
uss
u
d
m
PID
min
U , v
t f 
t f =∫t f
∥e
y
t∥Qt
۲
∥e
u
t ∥Rt
۲
∥ut∥S t
۲
dt∥e
y
t f ∥Qf
۲
∥e
u
t f ∥R f
۲
s.t. F  ˙xt, xt, yt,ut,v ,=۰
x۰=x۰
uminut=U umax

15. © 2010 Process Systems Enterprise Limited
Model Predictive Control (MPC)
Characteristics
 Multi-variable control
 Constraint (CVs) violations and controls (MVs) saturation
 Process model
− Linear: computational cost and solution algorithms
− Empirical: model identification
− Intrusive, expensive and limited predictive capacity
 Reference trajectories
− Steady-state economic optimisation (unit or plant)
− Off-line recipes (e.g. batch)
 Optimal transition: quadratic penalty
 LMPC: proven, well-established commercial APC technology

16. © 2010 Process Systems Enterprise Limited
Model-based Process Optimisation
Real-time Optimisation (RTO)
Timescale
Frequency
Plant
MPC
RTO
y
y
wss
obj
yss
uss
u
d
m
PID
min
u

=x , y ,u ,
s.t. Fx , y ,u ,=۰
uminuumax
wminwwmax

17. © 2010 Process Systems Enterprise Limited
Model-based Process Optimisation
Real-time Dynamic Optimisation (RTDO)
Plant
MPC
RTDO
y
y
w(t)
obj
yref
(t)uref
(t)
u
d
m
PID
Timescale
Frequency
min
U , v
t f 
t f = ˙xt , xt , yt ,ut ,v ,
s.t. F ˙xt, xt, yt ,ut, v ,=۰
x۰=x۰
uminut=U umax
wmin
ee
w
ee
wmax
ee
wmin
ei
t f w
ei
t f wmax
ei
t f 
wmin
ii
t w
ii
twmax
ii
t

18. © 2010 Process Systems Enterprise Limited
Real-time (Dynamic) Optimisation
Characteristics
 Multi-variable optimisation
 Process model
− “First-principles”
− Parameter re-estimation
− Nonlinear: computational cost
 Equipment and conservation-law constraints
 Economic objective function
− No stability guarantees (dynamic)
 RTO: proven commercial APC technology

19. © 2010 Process Systems Enterprise Limited
Model-based Control and Optimisation
The space of innovation
Empirical First-principles
Nonlinear
Linear
1) Constrained
objective function
2) Continuous time
3) SP (PID)
1) Unconstrained quadratic
objective function
2) Discrete time
3) MV (MAN/OUT)/SP (PID)
RTO
MPC
Solution methods
and numerical
algorithms?
Advanced process
modelling tools?

20. © 2010 Process Systems Enterprise Limited
Model-based Control and Optimisation
The space of innovation revisited
Discrete time
Continuous time
Constrained
Unconstrained
Nonlinear
Linear
Empirical Solution algorithms
Models
Control problem
formulation
RTDO
MPC
First-principles
Simultaneous
Sequential

21. © 2010 Process Systems Enterprise Limited
“With the availability of much more powerful computers,
should not the basic approaches
to control systems application
be reconsidered?”
Richalet, Rault, Testud & Papon (1978)

22. © 2010 Process Systems Enterprise Limited
Process operations
Real-time decision making support revisited
 New possibilities...
Model-based Control and Optimisation (MB-C&O)
Timescale
Frequency
Timescale
Frequency
Model-based
Control & Optimisation

23. © 2010 Process Systems Enterprise Limited
First-principles models for RTDO

24. © 2010 Process Systems Enterprise Limited
First-principles models
 Source:
− Model repository
− Corporate R&D departments
− Modelling/consulting centres (e.g. PSE Consulting)
− Academia
 Applications (PSE Ltd)
− Fixed-bed catalytic reactors (AML:FBCR)
− Gas-liquid contactors (AML:GTL)
− Particulate/solid systems (gPROMS:Solids)
− Pressure-relief systems (gPROMS:Flares)
 Sectors (selection)
− Pulp & paper
− Consumer products
− Food & beverages
Solution algorithms
Models
Control problem
formulation

25. © 2010 Process Systems Enterprise Limited
First-principles models: an example
C.C. Pantelides, Z.E. Urban, Š. Špatenka (PSE Ltd)
 Distributed with respect to
− Axial, radial, intra-pellet
spatial position
− Time
 A mixed set of partial
differential & algebraic
equations (PDAEs)
− ~120,000 time-varying
quantities per tube
 Well within scope and
capabilities of current process
modelling technology

26. © 2010 Process Systems Enterprise Limited
RTDO problem formulation

27. © 2010 Process Systems Enterprise Limited
Real-time Dynamic Optimisation
Problem formulation
Control &
optimisation
problem
formulation
Mathematical
problem
statement
Not straightforward!!!
Models
Control problem
formulation
Solution
algorithms
min
U , v
t f 
t f = ˙xt , xt , yt ,ut ,v ,
s.t. F ˙xt, xt, yt ,ut, v ,=۰
x۰=x۰
uminut=Uumax
wmin
ee
wee
wmax
ee
wmin
ei
t f wei
t f wmax
ei
t f 
wmin
ii
t w
ii
twmax
ii
t

28. © 2010 Process Systems Enterprise Limited
Problem formulation
Characteristics
 Control & optimisation problems change continuously:
− Structure:
− Instrumentation signal failure (MVs, DVs, CVs)
− Saturation/exclusion (“loss”) of control variables (MVs)
− Inclusion/exclusion of operative constraints (CVs)
− Change of objective function
− Numerical values:
− Change of feasible region (MVs, CVs)
− Constraint enforcements
 Control & optimisation problems combine
discrete and continuous features:
− Point (discrete), path and zone (continuous) constraints

29. © 2010 Process Systems Enterprise Limited
Problem formulation
Analysis
EVENT
log_time := 0;
event_time := 0;
event_type := Prediction_Horizon_Change;
value := 1800.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Window_Change;
value := 600.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Objective_Function_Change;
process_variable_name := T101.LT002A.SV;
extremisation_type := minimise;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Change;
process_variable_name := T101.FC001B.SP;
value := 0.0;
lower_bound := 0.0;
upper_bound := 40.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Horizon_Point_Constraint_Change;
process_variable_name := T101.LT001A.MV;
lower_bound := 1.99;
upper_bound := 2.01;
event_rank := 3;
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue
Control &
optimisation
problem
formulation
Mathematical
problem
statement
Not straightforward!!!
min
U , v
t f 
t f = ˙xt , xt , yt ,ut ,v ,
s.t. F ˙xt, xt, yt ,ut, v ,=۰
x۰=x۰
uminut=U umax
wmin
ee
w
ee
wmax
ee
wmin
ei
t f w
ei
t f wmax
ei
t f 
wmin
ii
t w
ii
twmax
ii
t

30. © 2010 Process Systems Enterprise Limited
EVENT
log_time := 0;
event_time := 0;
event_type := Prediction_Horizon_Change;
value := 1800.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Window_Change;
value := 600.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Objective_Function_Change;
process_variable_name := T101.LT002A.SV;
extremisation_type := minimise;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Change;
process_variable_name := T101.FC001B.SP;
value := 0.0;
lower_bound := 0.0;
upper_bound := 40.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Horizon_Point_Constraint_Change;
process_variable_name := T101.LT001A.MV;
lower_bound := 1.99;
upper_bound := 2.01;
event_rank := 3;
Problem formulation
Approach
 Event types:
− Prediction horizon
− Control horizon & window
− Objective function
− Control variable
− Initial-point constraint /
Horizon-point constraint
− Fixed-point constraint /
Interior-point constraint
− Path /zone constraints
− Optimisation / event
tolerances
− Constraint relaxation (scaling)
− etc...
Control and optimisation events:
domain-specific high-level declarative specification
C&O
language

31. © 2010 Process Systems Enterprise Limited
EVENT
log_time := 0;
event_time := 0;
event_type := Prediction_Horizon_Change;
value := 1800.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Window_Change;
value := 600.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Objective_Function_Change;
process_variable_name := T101.LT002A.SV;
extremisation_type := minimise;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Change;
process_variable_name := T101.FC001B.SP;
value := 0.0;
lower_bound := 0.0;
upper_bound := 40.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Horizon_Point_Constraint_Change;
process_variable_name := T101.LT001A.MV;
lower_bound := 1.99;
upper_bound := 2.01;
event_rank := 3;
Problem formulation
Overall strategy
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue
User events
Implemented in the RTDO engine (ReTO)
???
gPROMS
language
C&O
language
Interpreted events

32. © 2010 Process Systems Enterprise Limited
Problem formulation strategy
Example
EVENT
log_time := 0;
event_time := 0;
event_type := Prediction_Horizon_Change;
value := 1800.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Window_Change;
value := 600.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Objective_Function_Change;
process_variable_name := T101.LT002A.SV;
extremisation_type := minimise;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Change;
process_variable_name := T101.FC001B.SP;
value := 0.0;
lower_bound := 0.0;
upper_bound := 40.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Horizon_Point_Constraint_Change;
process_variable_name := T101.LT001A.MV;
lower_bound := 1.99;
upper_bound := 2.01;
event_rank := 3;
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue

33. © 2010 Process Systems Enterprise Limited
Problem formulation strategy
Example
EVENT
log_time := 0;
event_time := 0;
event_type := Prediction_Horizon_Change;
value := 1800.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Window_Change;
value := 600.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Objective_Function_Change;
process_variable_name := T101.LT002A.SV;
extremisation_type := minimise;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Change;
process_variable_name := T101.FC001B.SP;
value := 0.0;
lower_bound := 0.0;
upper_bound := 40.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Horizon_Point_Constraint_Change;
process_variable_name := T101.LT001A.MV;
lower_bound := 1.99;
upper_bound := 2.01;
event_rank := 3;
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue

34. © 2010 Process Systems Enterprise Limited
Problem formulation strategy
Example
EVENT
log_time := 0;
event_time := 0;
event_type := Prediction_Horizon_Change;
value := 1800.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Window_Change;
value := 600.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Objective_Function_Change;
process_variable_name := T101.LT002A.SV;
extremisation_type := minimise;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Change;
process_variable_name := T101.FC001B.SP;
value := 0.0;
lower_bound := 0.0;
upper_bound := 40.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Horizon_Point_Constraint_Change;
process_variable_name := T101.LT001A.MV;
lower_bound := 1.99;
upper_bound := 2.01;
event_rank := 3;
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue

35. © 2010 Process Systems Enterprise Limited
Problem formulation strategy
Example
EVENT
log_time := 0;
event_time := 0;
event_type := Prediction_Horizon_Change;
value := 1800.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Window_Change;
value := 600.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Objective_Function_Change;
process_variable_name := T101.LT002A.SV;
extremisation_type := minimise;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Change;
process_variable_name := T101.FC001B.SP;
value := 0.0;
lower_bound := 0.0;
upper_bound := 40.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Horizon_Point_Constraint_Change;
process_variable_name := T101.LT001A.MV;
lower_bound := 1.99;
upper_bound := 2.01;
event_rank := 3;
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue

36. © 2010 Process Systems Enterprise Limited
Problem formulation strategy
Example
EVENT
log_time := 0;
event_time := 0;
event_type := Prediction_Horizon_Change;
value := 1800.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Window_Change;
value := 600.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Objective_Function_Change;
process_variable_name := T101.LT002A.SV;
extremisation_type := minimise;
EVENT
log_time := 0;
event_time := 0;
event_type := Control_Change;
process_variable_name := T101.FC001B.SP;
value := 0.0;
lower_bound := 0.0;
upper_bound := 40.0;
EVENT
log_time := 0;
event_time := 0;
event_type := Horizon_Point_Constraint_Change;
process_variable_name := T101.LT001A.MV;
lower_bound := 1.99;
upper_bound := 2.01;
event_rank := 3;
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue
Scaling of constraints
(also objective)

37. © 2010 Process Systems Enterprise Limited
RTDO problem solution

38. © 2010 Process Systems Enterprise Limited
Real-time Dynamic Optimisation
Problem solution
Explicit handling of
constraints >>
valuable control and
optimisation
technique
Models
Control problem
formulation
Solution
algorithms
Constraints
(point, path, zone)
(hard, soft)
min
U , v
t f 
t f = ˙xt , xt , yt ,ut ,v ,
s.t. F ˙xt, xt, yt ,ut, v ,=۰
x۰=x۰
uminut=Uumax
wmin
ee
w
ee
wmax
ee
wmin
ei
t f w
ei
t f wmax
ei
t f 
wmin
ii
t w
ii
twmax
ii
t
Infeasibilities

39. © 2010 Process Systems Enterprise Limited
Problem solution
Infeasibility scenarios
 Infeasibilities in constrained control and optimisation:
− Incorrect control problem specification
− Structure, numerical values
− Inconsistent constraints
− Correct but (truly) infeasible control problem specification
− Consistent but tight targets/specifications
 Recovery schemes:

40. © 2010 Process Systems Enterprise Limited
Problem solution
Infeasibility recovery schemes
Constraint ranking and
elimination
Constraint identification and
relaxation
strategy Ranking of constraints by priority
levels
“All constraints are created
equal”
algorithm eliminate constraints at current
level
identify problematic constraints
relax by a user-defined factor
re-attempt re-attempt
failure if critical priority level is reached
(hard constraints)
if attempted maximum number of
recoveries
advantages Straightforward concept and
simple to implement
Ranking and elimination as a
special case
More rigorous and optimal
(within relaxation)
disadvantages Elimination of feasible, important
constraints:
More difficult to implement
Sub-optimal User-interaction is required

41. © 2010 Process Systems Enterprise Limited
Constraint ranking and
elimination
Constraint identification and
relaxation
strategy Ranking of constraints by priority
levels
“All constraints are created
equal”
algorithm eliminate constraints at current
level
identify problematic constraints
relax by a user-defined factor
re-attempt re-attempt
failure if critical priority level is reached
(hard constraints)
if attempted maximum number of
recoveries
advantages Straightforward concept and
simple to implement
Ranking and elimination as a
special case
More rigorous and optimal
(within relaxation)
disadvantages Elimination of feasible, important
constraints:
More difficult to implement
Sub-optimal User-interaction is required
Infeasibility recovery schemes
Constraint ranking and elimination

42. © 2010 Process Systems Enterprise Limited
Infeasibility recovery schemes
Constraint ranking and elimination: example
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue
<snip>
Objective function: 0.7262
Current Values of Constrained Variables
([*] denotes violation of constraint)
Constrained Variable Name | Type | Time | Value | Lower Bound | Upper Bound
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue | Endpoint | 1800 | 3.0000 | 1.9900 | 2.0100[*]
No. of No. of Step Objective Current Constraint
Iterations Functions Length Function Accuracy Violations
0 1 0.7262 0.9900
<snip>

43. © 2010 Process Systems Enterprise Limited
Infeasibility recovery schemes
Constraint ranking and elimination: example
<snip>
EVENT
log_time := 0;
event_time := 0;
event_type := Horizon_Point_Constraint_Change;
process_variable_name := T101.LT001A.MV;
lower_bound := 1.99;
upper_bound := 2.01;
event_rank := 3;
<snip>
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue
<snip>
Objective function: 0.7262
Current Values of Constrained Variables
([*] denotes violation of constraint)
Constrained Variable Name | Type | Time | Value | Lower Bound | Upper Bound
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue | Endpoint | 1800 | 3.0000 | 1.9900 | 2.0100[*]
No. of No. of Step Objective Current Constraint
Iterations Functions Length Function Accuracy Violations
0 1 0.7262 0.9900
<snip>

44. © 2010 Process Systems Enterprise Limited
Infeasibility recovery schemes
Constraint ranking and elimination: example
<snip>
EVENT
log_time := 0;
event_time := 0;
event_type := Horizon_Point_Constraint_Change;
process_variable_name := T101.LT001A.MV;
lower_bound := 1.99;
upper_bound := 2.01;
event_rank := 3;
<snip>
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue
<snip>
Objective function: 0.7262
Current Values of Constrained Variables
([*] denotes violation of constraint)
Constrained Variable Name | Type | Time | Value | Lower Bound | Upper Bound
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue | Endpoint | 1800 | 3.0000 | 1.9900 | 2.0100[*]
No. of No. of Step Objective Current Constraint
Iterations Functions Length Function Accuracy Violations
0 1 0.7262 0.9900
<snip>

45. © 2010 Process Systems Enterprise Limited
Infeasibility recovery schemes
Constraint ranking and elimination: example
<snip>
EVENT
log_time := 0;
event_time := 0;
event_type := Horizon_Point_Constraint_Change;
process_variable_name := T101.LT001A.MV;
lower_bound := 1.99;
upper_bound := 2.01;
event_rank := 3;
<snip>
<snip>
Objective function: 0.7262
Current Values of Constrained Variables
([*] denotes violation of constraint)
Constrained Variable Name | Type | Time | Value | Lower Bound | Upper Bound
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue | Endpoint | 1800 | 3.0000 | 1.9900 | 2.0100[*]
No. of No. of Step Objective Current Constraint
Iterations Functions Length Function Accuracy Violations
0 1 0.7262 0.9900
<snip>
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue
Implemented in the RTDO engine (ReTO)

46. © 2010 Process Systems Enterprise Limited
Infeasibility recovery schemes
Constraint identification and relaxation
Constraint ranking and
elimination
Constraint identification and
relaxation
strategy Ranking of constraints by priority
levels
“All constraints are created
equal”
algorithm eliminate constraints at current
level
identify problematic constraints
relax by a user-defined factor
re-attempt re-attempt
failure if critical priority level is reached
(hard constraints)
if attempted maximum number of
recoveries
advantages Straightforward concept and
simple to implement
Ranking and elimination as a
special case
More rigorous and optimal
(within relaxation)
disadvantages Elimination of feasible, important
constraints:
More difficult to implement
Sub-optimal User-interaction is required

47. © 2010 Process Systems Enterprise Limited
Infeasibility recovery schemes
Constraint identification and relaxation: example
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue
<snip>
Objective function: 0.7262
Current Values of Constrained Variables
([*] denotes violation of constraint)
Constrained Variable Name | Type | Time | Value | Lower Bound | Upper Bound
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue | Endpoint | 1800 | 3.0000 | 1.9900 | 2.0100[*]
No. of No. of Step Objective Current Constraint
Iterations Functions Length Function Accuracy Violations
0 1 0.7262 0.9900
<snip>

48. © 2010 Process Systems Enterprise Limited
Infeasibility recovery schemes
Constraint identification and relaxation: example
<snip>
EVENT
log_time := 0;
event_time := 0;
event_type := Horizon_Point_Relaxation_Change;
process_variable_name := T101.LT001A.MV;
relaxation_factor := 2.0;
<snip>
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue
<snip>
Objective function: 0.7262
Current Values of Constrained Variables
([*] denotes violation of constraint)
Constrained Variable Name | Type | Time | Value | Lower Bound | Upper Bound
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue | Endpoint | 1800 | 3.0000 | 1.9900 | 2.0100[*]
No. of No. of Step Objective Current Constraint
Iterations Functions Length Function Accuracy Violations
0 1 0.7262 0.9900
<snip>

49. © 2010 Process Systems Enterprise Limited
Infeasibility recovery schemes
Constraint identification and relaxation: example
<snip>
EVENT
log_time := 0;
event_time := 0;
event_type := Horizon_Point_Relaxation_Change;
process_variable_name := T101.LT001A.MV;
relaxation_factor := 2.0;
<snip>
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue
<snip>
Objective function: 0.7262
Current Values of Constrained Variables
([*] denotes violation of constraint)
Constrained Variable Name | Type | Time | Value | Lower Bound | Upper Bound
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue | Endpoint | 1800 | 3.0000 | 1.9900 | 2.0100[*]
No. of No. of Step Objective Current Constraint
Iterations Functions Length Function Accuracy Violations
0 1 0.7262 0.9900
<snip>

50. © 2010 Process Systems Enterprise Limited
<snip>
EVENT
log_time := 0;
event_time := 0;
event_type := Horizon_Point_Relaxation_Change;
process_variable_name := T101.LT001A.MV;
relaxation_factor := 2.0;
<snip>
Infeasibility recovery schemes
Constraint identification and relaxation: example
<snip>
Objective function: 0.7262
Current Values of Constrained Variables
([*] denotes violation of constraint)
Constrained Variable Name | Type | Time | Value | Lower Bound | Upper Bound
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue | Endpoint | 1800 | 3.0000 | 1.9900 | 2.0100[*]
No. of No. of Step Objective Current Constraint
Iterations Functions Length Function Accuracy Violations
0 1 0.7262 0.9900
<snip>
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 4.02
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue
HORIZON
1800 : 1800 : 1800
INTERVALS
3
600 : 600 : 600
600 : 600 : 600
600 : 600 : 600
PIECEWISE_CONSTANT
FS.T101.FC001B.SP.ProcessVariable
INITIAL_PROFILE
0 : 0 : 40
0 : 0 : 40
0 : 0 : 40
TIME_INVARIANT
FS.DCS.LT001A.MV.Constraint.Point.ScalingValue
INITIAL_VALUE
1 : 1 : 1
ENDPOINT-INEQUALITY # AT HORIZON
FS.DCS.LT001A.MV.Constraint.Point.ScaledValue
1.99 : 2.01
MINIMISE
FS.DCS.LT002A.SV.Objective.Point.ScaledValue
Implemented in the RTDO engine (ReTO)

51. © 2010 Process Systems Enterprise Limited
Solution methods for RTDO

52. © 2010 Process Systems Enterprise Limited
Dynamic optimisation
Solution strategies
 Computational cost
− Jacobian evaluations
− Numerical perturbation
− Symbolic differentiation (equation-oriented modelling
languages)
− Automatic differentiation (programming languages)
No nline a r Dyna m ic
O p tim iza tio n P ro b le m
Simultaneous Sequential
type Iterative – Infeasible path Iterative – Feasible path
discretisation NLA (orthogonal collocation on
finite elements)
IVP (integration)
NLP size Very large >O(10^6) Relatively small <O(10^2)
determining
cost
Augmented sensitivity system
integration (>80%)

53. © 2010 Process Systems Enterprise Limited
RTDO engine: ReTO

54. © 2010 Process Systems Enterprise Limited
54
RTDO Engine: architecture
Process Data Server
(plant connectivity)
Modelling &
Solution
Engine
Model Server
(arbitrary models)
Solution Engine
(state-of-the-art numerics)
gPROMS-enabled MSE

55. © 2010 Process Systems Enterprise Limited
55
RTDO Engine: architecture (ctd)
Problem Definition Manager
(event interpreter)
Event Manager
(validating event parser)
Solution Feasibility Supervisor
(infeasibility handling)
Solution Interpreter
(solution monitoring)
Constraint Manager
(constraint reformulation)

56. © 2010 Process Systems Enterprise Limited
An industrial case study

57. © 2010 Process Systems Enterprise Limited
Case-study: Industrial continuous pulping
Continuous cooking system

58. © 2010 Process Systems Enterprise Limited
Case-study: Industrial continuous pulping
Continuous cooking system
 heart of pulp and paper mills
 goal: keep selectivity constant and maximise yield
− tight coupling between quality (selectivity)
and throughput (yield)
 main unit: continuous cooking digester
− complex heterogeneous reactor: liquid-solid phases
− multicomponent mixture
− co-current and counter-current flow zones between phases
− multiple stream injection and extraction points
− moderately long time constants and non-intuitive
operation
 auxiliary units: feed line and circulation heaters
 regulatory control system (50+ sensors, 25+ PID controllers)

59. © 2010 Process Systems Enterprise Limited
Case studies and results

60. © 2010 Process Systems Enterprise Limited
Case study: overall set up
 Control architecture:
− RTDO MB-C&O layer provides set-points of
PID regulatory control layer
 Simulation set up:
− Virtual plant and controller use same first-principles model
− Perfect observer
 First-principles model:
− Implemented in gPROMS
− Large-scale* numerical solution (* for APC applications)
− 10,000 DAEs, 1000 states, 100+ DOFs (100+ STNs)

61. © 2010 Process Systems Enterprise Limited
Case study: C&O problem formulation
 Objective function: maximise yield (path)
 Constraints (CVs):
− Production rate change; point
− Selectivity deviation (kappa); point and path
 Controls (MVs):
− Circulation heaters (lower, wash); feed (chip-meter)
 Time parameterisation:
− prediction horizon (P): 7 hr
− control horizon (C): 6 hr
− control window (D): 1 hr
P
C
D

62. © 2010 Process Systems Enterprise Limited
MVs: control trajectories are very similar
Jump production 600 ad.tpd > 650 ad.tpd
NL vs LTI model performance
CV: production transition is accomplished

63. © 2010 Process Systems Enterprise Limited
Jump production 600 ad.tpd > 650 ad.tpd
NL vs LTI model performance
OBJ: NL model is optimal
(+50k US$/year)
CV: very similar CL response
for NL and LTI models
How operators see it…
(zoom to fit control bounds)
Zoom in

64. © 2010 Process Systems Enterprise Limited
Jump production 600 ad.tpd > 700 ad.tpd
NL vs LTI model performance
CV: production transition is accomplished
MV: NL relies more on LCH moves
MV: LTI puts more emphasis on WCH
MV: oscillation on LCH moves

65. © 2010 Process Systems Enterprise Limited
Jump production 600 ad.tpd > 700ad.tpd
NL vs LTI model performance
NL controller fails
to converge on the 3rd cycle;
however, it does not produce
plant infeasibilities and
it fully recovers on the 4th cycle
CV: oscillations;
too aggressive control?
CV: CL response is different
for NL and LTI models
How operators see it…
(zoom to fit control bounds)
Zoom in

66. © 2010 Process Systems Enterprise Limited
Jump production 600 ad.tpd > 700ad.tpd
Infeasibility recovery schemes
IaR: identification and relaxation
RaE: ranking and elimination
IaR vs RaE: identical response
(for this particular run)

67. © 2010 Process Systems Enterprise Limited
A challenging transition
Speed-up/slow-down production at 600 ad.tpd
 Speed-up production 600 ad.tpd > 650 ad.tpd...
 … and “sudden” slow-down
in 2hr, speed-up production
to 650 tpd (~10%)
in 2hr, slow down production
back to 600 tpd
downstream disturbance:
paper machine trip!!!

68. © 2010 Process Systems Enterprise Limited
Speed-up/slow-down production at 600 ad.tpd
NL vs LTI model performance: optimisation tolerance
 Loose tolerance  Tight tolerance

69. © 2010 Process Systems Enterprise Limited
Computational statistics
NL vs LTI model performance
LTI model computes ~4 times faster than NL model!
NL model solution statistics
#C Time
[min]
#I #LS Avg %
SEI
1 28.9 6 6 4.8 75
2 14.4 3 3 4.8 79
3 14.2 3 3 4.7 79
4 8.0 2 2 4.0 84
5 7.6 2 2 3.8 84
6 3.0 1 1 3.0 -
7 7.4 2 2 3.7 83
Avg 11.9 2.7 2.7 4.1 81
LTI model solution statistics
#C Time
[min]
#I #LS Avg %
SEI
1 2.1 2 2 1.1 82
2 3.3 3 3 1.1 81
3 1.9 2 2 1.0 85
4 0.7 2 2 0.4 85
5 3.6 3 3 1.2 79
6 4.0 3 3 1.3 80
7 3.6 3 3 1.2 80
Avg 2.7 2.6 2.6 1.0 82

70. © 2010 Process Systems Enterprise Limited
Speed-up/slow-down production at 600 ad.tpd
NL vs LTI model performance: control window
CV: CL response of LTI model gets
closer to that of NL model

71. © 2010 Process Systems Enterprise Limited
Conclusions
 Controller design and performance:
− LTI model performed rather well, however...
− rigorous, derived by exact linearisation and not by identification
− perfect observer
− LTI was near optimal but exhibited some infeasibilities
− NL controller was optimal and feasible at all times
− Confirmed time parameterisation
 Solution performance:
− Fast real-time computations!!!
− Sufficient slack to perform additional/auxiliary computations!

72. © 2010 Process Systems Enterprise Limited
Summary and outlook

73. © 2010 Process Systems Enterprise Limited
Summary
 Process operations and regulatory control
− Enough degrees-of-freedom for advanced control and
optimisation
− Avoiding complexity at the expense of economic and
environmental performance
 Real-time decision-making support
− Model-based Control & Optimisation (MB-C&O)
Timescale
Frequency
Model-based
Control & Optimisation

74. © 2010 Process Systems Enterprise Limited
Summary
 First-principles models
− Available for use in MB-C&O
 Novel RTDO engine
− Decoupling of model, solution process and problem formulation
− gPROMS-enabled Modelling-and-solution engine (MSE)
− Flexible and transparent “configuration”
 Control-specific event-based mechanism
− Problem formulation
− Interpretation of events into (dynamic) optimisation problem
− Problem solution
− Recovery from infeasibilities

75. © 2010 Process Systems Enterprise Limited
Model-based Process Optimisation and Control
Outlook
Solution algorithms
Models
Control problem
formulation
Model-based Control &
Optimisation
* ) Online adaptation of
control & optimisation
problem structure
>> Controller/optimiser-design
alternatives and performance
1) Parallelisation
(sensitivities, linear algebra)
2) Sensitivity-based updates
(neighbouring extremal control)
3) Modelling-and-solution engines
(general advances)
*) Plant-model mismatch:
Uncertainty and robustness
>> State estimation
Multi-scenario computations

76. © 2010 Process Systems Enterprise Limited
Real-time decision-making support
A model-centric vision*
PROCESS
SIMULATION
PROCESS
SIMULATION
PROCESS
SIMULATION
PROCESS
SIMULATION
PROCESS SYSTEM (INDUSTRIAL PLANT)
CONTROL SYSTEM (DCS / PLC)
PARAMETER
ESTIMATION
CONTROL &
OPTIMISATION
PROCESS
OPTIMISATION
SURROUNDINGS (WORLD / MARKET)
DECISION-MAKERS (OPERATORS / PROCESS ENGINEERS)
FIRST-
PRINCIPLES
MODEL
Past Scenarios
OPTIMAL CONTROL &
PROCESS PERFORMANCE
OPTIMAL NOMINAL
OPERATING POINTRECONCILIED DATA
DATA
ACTIONS/DECISIONS
BIAS ESTIMATES
PARAMETER ESTIMATES
PROCESS DATA
Future Scenarios
FORECAST DATA
DATA
RECONCILIATION
DATA
RECONCILIATION
*Rolandi, PA and Romagnoli, JA; Integrated model-centric framework for support of manufacturing operations. Part I: The framework; Comp & Chem Engng; 34, p17-35.

77. © 2010 Process Systems Enterprise Limited
Acknowledgements
 Prof Jose A Romagnoli (LSU)
 Dr Joseph Zeaiter (Invensys)
 A special thanks to:
− Prof Costas C Pantelides (IC, PSE Ltd)
− Prof Larry T Biegler (CMU)
− Prof Wolfgang Marquardt (RWTH)
− Lynn Wuerth and Fady Assassa

78. © 2010 Process Systems Enterprise Limited
Thank you!