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Real time dynamic optimisation

P
pablo-rolandi

The document discusses real-time dynamic optimization in the context of process industries, particularly focusing on model-based control and optimization techniques. It highlights the importance of advanced process control, online optimization, and economic drivers for improved efficiency and reduced operational costs. A case study in the pulp and paper industry illustrates the application of these methods to optimize production rates and manage variability in quality and yield.

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© 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
© 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
© 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
© 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
© 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
© 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
© 2010 Process Systems Enterprise Limited Industrial continuous pulping Production rate change: “open-loop” response +0.6rpm
© 2010 Process Systems Enterprise Limited Industrial continuous pulping Production rate change: “open-loop” response +1°C
© 2010 Process Systems Enterprise Limited Industrial continuous pulping Production rate change: “open-loop” response +1°C
© 2010 Process Systems Enterprise Limited Industrial continuous pulping Production rate change: “open-loop” response Minimise variability of selectivity (quality) and maximise yield (throughput)
© 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)
© 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
© 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
© 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
© 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
© 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
© 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
© 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
© 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?
© 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
© 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)
© 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
© 2010 Process Systems Enterprise Limited First-principles models for RTDO
© 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
© 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
© 2010 Process Systems Enterprise Limited RTDO problem formulation
© 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
© 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
© 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
© 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
© 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
© 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
© 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
© 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
© 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
© 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)
© 2010 Process Systems Enterprise Limited RTDO problem solution
© 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
© 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:
© 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
© 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
© 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>
© 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>
© 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>
© 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)
© 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
© 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>
© 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>
© 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>
© 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)
© 2010 Process Systems Enterprise Limited Solution methods for RTDO
© 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%)
© 2010 Process Systems Enterprise Limited RTDO engine: ReTO
© 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
© 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)
© 2010 Process Systems Enterprise Limited An industrial case study
© 2010 Process Systems Enterprise Limited Case-study: Industrial continuous pulping Continuous cooking system
© 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)
© 2010 Process Systems Enterprise Limited Case studies and results
© 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)
© 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
© 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
© 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
© 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
© 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
© 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)
© 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!!!
© 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
© 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
© 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
© 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!
© 2010 Process Systems Enterprise Limited Summary and outlook
© 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
© 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
© 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
© 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.
© 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
© 2010 Process Systems Enterprise Limited Thank you!

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Real time dynamic optimisation

  • 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!