Montevideo 13 Nov 2013

1. Current Trends in Advanced Process Control and Real-Time Optimization Argimiro R. Secchi Programa de Engenharia Química – COPPE Centro de Tecnologia – UFRJ Rio de Janeiro – RJ Montevideo 13 Nov 2013

2. Outline • Advanced Process Control • Model Predictive Control • Modeling and Identification • Real-Time Optimization • Dynamic Real-Time Optimization • Final Remarks

3. Basic Concepts Advanced Process Control (APC): is a term that can include a range of methodologies, including model predictive control (MPC), fuzzy logic, statistical control, etc. The common objective is to find a way to manage complex interactions within a process better than traditional regulatory control.

4. Complex Processes Plantwide control of transalkylation and disproportionation of toluene process (TADP) * Klafke N., 2011. M.Sc. Thesis, Universidade Federal do Rio de Janeiro.

5. Process Control Overview Planning and Scheduling weeks DSC Plantwide computer Process computer Real-Time Optimization hours Advanced Process Control minutes Regulatory Control seconds Process

6. Classical Process Control Lead / Lag filters Switches Min, Max selectors If / Else logics Sequence logics • Regulation • Constraint handling • Local optimization ad hoc strategies

7. Example: Blending system Setpoint • Control rA and rB • Control q if possible • Flowratesof additives are limited Classical solution * J. H. Lee, 2005. Model Predictive Control. PASI, Iguazú, Argentina.

8. Classical Solution • Model is not explicitly used inside the control algorithm • No clearly stated objective and constraints • Questionable performance • Complex control structure • Not robust to changes and failures • Focus on the performance of a local unit • Model is not explicitly used inside the control algorithm • No clearly stated objective and constraints • Questionable performance • Complex control structure • Not robust to changes and failures • Focus on the performance of a local unit

9. APC Solution Prediction horizon Control horizon

10. Classical vs. APC Solution * T. Badgwell, 2003. Spring AIChE Meeting, New Orleans.

11. APC Objectives • Maximize production • Ensure product specifications • Minimize energy and water consumption • Minimize process variability • Minimize loss of products • Respect process constraints • Safeguard environmental laws Constrained optimization problem

12. Timeline * E. Almeida Nt, 2011. Ph.D. Thesis, UFRGS.

13. Open-Loop Optimal Control Controller Plant set-point input output u(t) r(t) y(t) model constraints path constraints terminal constraints

14. Open-Loop Optimal Control Controller Plant set-point input output u(t) r(t) y(t) measurements • Open-loop optimal solution is not robust • Must be coupled with on-line state / model parameter update • Requires on-line solution for each updated problem • Analytical solution possible only in a few cases (LQ control) • Computational limitation for numerical solution • Open-loop optimal solution is not robust • Must be coupled with on-line state / model parameter update • Requires on-line solution for each updated problem • Analytical solution possible only in a few cases (LQ control) • Computational limitation for numerical solution

15. Model Predictive Control (MPC) (desired output) Open-loop optimal control problem: Find current and future manipulated inputs that best meet a desired future output trajectory. next sample time Feedback nature: Implement first “control move” then correct for model mismatch. (desired output) Major issue:disturbances vs. model uncertainty. * B.W. Bequette, 1998. Process Dynamics. Modeling, Analysis, and Simulation, Prentice Hall.

16. Open questions in MPC • Type of model for predictions? • linear: state space, TF, step response, impulse response, ARX • nonlinear: first principles, NN, Volterra, Wiener, Hammerstein, multiple model, fuzzy, NARX • Information needed at step k for predictions? • outputs, state estimates, measured disturbances, model parameters • Objective function and optimization technique? • quadratic (QP), absolute values (LP), economics, nonlinear (NLP) • Correction for model error? • additive output, disturbance estimation (KF, EKF, MHE)

17. Implementation of APC • Control structuredesign • Check instrumentation and retune regulatory control • Pre-tests and design of inferences (soft sensors) • Plant test and identification of dynamic models • Controller configuration and closed-loop simulation • Commissioning and tuning of the controller • Monitoring the APC performance • Training of operators and documentation

18. Retuning Regulatory Control Regulatory control is essential for the success of APC Gas Processing Plant * M.C.M. Campos, 2011. Advanced Control Systems, PASI, Angra dos Reis, Brazil.

19. Monitoring the APC Performance MPC performance can degrade due to: • Changes in the unit operations objectives; • Equipment efficiency losses (fouling); • Changes in the feed quality; • Problems in instruments and in soft sensors; • Lacks of qualified personnel for the controller's maintenance.

20. Linear MPC applications * S.J. Qin, T.A. Badgwell, 2003. Control Engineering Practice,11, 733–764.

21. Nonlinear MPC applications Linear ARX Static polynomials Linear ARX Neural Networks Nonlinear State Space Neural Networks Nonlinear State Space First Principles Nonlinear State Space First Principles Nonlinear State Space First Principles, NN, … * S.J. Qin, T.A. Badgwell, 2003. Control Engineering Practice,11, 733–764.

22. Evolution of LMPC Technology Linear Quadratic Gaussian Linear state-space model Kalman (1960) * S.J. Qin, T.A. Badgwell, 2003. Control Engineering Practice,11, 733–764.

23. LMPC Generations • Second Generation • QDMC • Cutler, Morshedi& Haydel (1983), • Garcia and Morshedi(1986) • Step response model • Solution using QP • First Generation • Identification and Command (IDCOM) • Richaletet al. (1976, 1978); at Adersa • Impulse response model • Heuristic iterative algorithm • Dynamic Matrix Control (DMC) • Cutler & Ramaker (1979); at Shell in 70’s • Step response model, LS solution • Third Generation • IDCOM-M (Setpoint), HIECON (Adersa) • Grosdidieret al. (1988) • Multi-objective formulation (output | input) • Soft, hard and ranked constraints • SMOC (Shell Multivariable Opt. Control) • Marquis & Broustail (1998) • Bridge between state-space and MPC • Disturbance model; KF • Fourth Generation • DMC-plus, RMPCT • Steady-state target optimization • QP and economic objectives • Model uncertainties • Prioritized control objectives • Graphical user interface

24. Weakness of LMPC Generations • First Generation • Constraints handling on ad hocbasis • Second Generation • No clear way to handle infeasible solution • Weighted sum of objectives does not allow the designer to reflect the true performance requirements • Third Generation • Limited model choices • Poor user interfaces • Fourth Generation • Finite horizon formulation does not inherit strong stabilizing properties • Lack of robust stability

25. MPC Calculations Read MV, DV, CV from process - Constant output disturbance - Integrating output disturbance - Kalman filter Output feedback (state estimation) - Critical CV failure - Non-critical CV failure - MV saturation or failure Determine controlled process subset - Singular value thresholding - Input move suppression Remove ill-conditioning - LP or QP - Multiple objectives and ranked CVs | MVs Local Steady-State Optimization - QP (y*, u*, u) with hard and soft constraints - Output trajectories: setpoint, zone, funnel - Single move (M=1), multiple moves, blocking, BF Dynamic Optimization Output MV's to process

26. Dynamic Optimization error from desired output trajectory (yr) where error from desired steady state input (us)

27. Output Trajectories * J. H. Lee, 2005. Model Predictive Control. PASI, Iguazú, Argentina.

28. Horizons Prediction horizon (P) Control horizon (M) (with blocking) Base Functions

29. Identification Technologies • Most products use PRBS-like or multiple steps test signals. Glide (Adersa) uses non-PRBS signals • Most products use FIR, ARX or step response models • - Glide uses transfer function G(s) • - RMPCT uses Box-Jenkins • - SMOC uses state space models • Most products use least squares type parameter estimation • - RMPCT uses prediction error method • - Glide uses a global method to estimate uncertainty • Connoisseur has adaptive capability using RLS • A few products (DMC-plus, SMOC) have subspace identification methods available for MIMO identification • Most products have uncertainty estimate, but most products do not make use of the uncertainty bound in control design

30. Challenges for MPC • Optimization problem • - infinite prediction horizon • - multiple objectives • Simplifying the model development process • - plant testing & system identification • - nonlinear model development • - intensive use of dynamic simulators • - model reduction techniques • State Estimation • - Lack of sensors and sensor location for key variables • Reducing computational complexity • - approximate solutions, preferably with some guaranteed properties • - modern computation (sparse matrices, better numerical methods) • Better management of “uncertainty” • - creating models with uncertainty information (e.g., stochastic model) • - on-line estimation of parameters / states • - “robust” solution of optimization • - self-tuning and adaptive MPC

31. Real-Time Optimization (RTO) Planning & Scheduling

32. Plant Optimization Hierarchy Planning & Scheduling Plant Information System product quality & production plant economics strategic and inventory constraints operating conditions on-line analyzers Lab data strategic model updates Real-Time Optimization - rigorous steady state model - on-line tuning - targets automatically implemented optimal targets operating conditions and constraints APC Controller APC Controller APC Controller

33. Needs for Plant Optimization To maintain/increase profitability process plant must go beyond standard practices Product specification Variation in feedstock New regulations Interruption of utilities Equipment wear & tear Competition * A. Ahmad, 2008, Plant Operations, Malaysia.

34. Potentials for Optimization • Sales limited by production • - Plant throughput should be increased • Sales limited by market • - Plant efficiency must be improved • Large throughputs • - Small savings in productivity costs are greatly magnified • High raw material or energy consumption • - Mass or heat integration should be analyzed • Losses of valuable or hazardous components through waste streams • - Mass exchange network should be optimized • Product quality over specified • - Plant should operate near constraints

35. RTO Calculations No steady state ? steady state ? wait Yes Plant data Gross error detection Data reconciliation Model updating Steady state optimization No Yes APC targets Solution implementation

36. Successful RTO Requires APC • Optimal operating conditions often located near constraints • - Benefits are achieved by consistently pushing the process to the most • profitable constraints • Traditional PID-type constraint-selector controllers give poor performance • against multiple constraints • - Pairing of constraints and manipulated variables is fixed in controller design • - Retuning needed as constraints change • MPC are designed to run at multiple constraints • - Predictive nature allows constrained variables to be corrected before they reach the constraints

37. APC and RTO Benefits RTO APC ARC DCS Regulatory Control: DCS + ARC (Advanced Regulatory Control)

38. RTO Limitations • Steady state detection is necessary before optimization • Large-scale problems require high computational demand • The same steady state is needed when implementing the targets • Large set-point changes should be avoided for safety reasons

39. Efforts to Circumvent RTO Limitations • Besl et al. (1998) – RTO system that do not wait for steady state. • Cheng & Zafiriou (2000) – simultaneous optimization and model updating. • Becerra et al. (1998); Nath & Alzein (2000); Tvrzská & Odloak (1998) – Economic objectives in the MPC (one-layer RTO+APC). • Sorensen & Cutler (1998); Rao & Rawlings (1999); Qin & Badgwell (1997); Ying et al. (1999) – RTO results are sent to a local steady state optimizer (LP or QP) coupled to the MPC.

40. RTO Set-points Measures LP – QP Steady state target calculation ----------------------------- MPC LP – QP Steady state target and economic calculation ----------------------------- MPC Measures / disturbances Measures / disturbances SS target SS target Process Process Alternative RTO Formulations One-layer RTO+APC RTO with target calculation

41. Dynamic Real-Time Optimization (D-RTO)

42. Production Planing model updating for RTO / D-RTO feed specification, product and market inferences D-RTO / RTO y*(t) u*(t) model updating for LMPC / NMPC MPC y(t) data pre-processing and dynamic data reconciliation u(t) Process + Regulatory Control Y(t) d(t) Model server (rigorous, empiric, hybrid, reduced) RTO vs. D-RTO, LMPC vs. NMPC

43. Production Scheduling Information _ _ x u D-RTO Time- scale separator xref uref MPC State Estimator ~ ~ x u u x u Production Scheduling Information Plant– Regulatory Control ^ ^ ^ ^ x u x u State Estimator D-RTO u x u Plant – Regulatory Control Alternative D-RTO Formulations One layer Two layers

44. _ _ x u ~ ~ Dx Du ~ ~ x u Production Scheduling Information _ _ x u D-RTO Large time-scale estimator xref uref Production Scheduling Information LMPC Production Scheduling Information Large time-scale estimator u _ _ x u x u D-RTO Plant– Regulatory Control D-RTO Time- scale separator Time- scale separator xref uref xref uref MPC Short time-scale estimator State Estimator ~ ~ x u NMPC u x u u x u Plant– Regulatory Control Plant– Regulatory Control ^ ^ ^ ^ x u x u Alternative D-RTO Formulations Time-scale separators * Kadam et al., 2002; Helbig et al., 2000.

45. Production Scheduling Information _ _ x u D-RTO Time-scale separator Result validation xref uref State Estimator ~ ~ x u MPC x u u Plant– Regulatory Control Production Scheduling Information _ _ x u D-RTO D-RTO Trigger xref uref MPC State Estimator ~ ~ x u u x u Plant– Regulatory Control ^ ^ x u ^ ^ x u Alternative D-RTO Formulations Result validation D-RTO Trigger * Kadam & Marquardt, 2004.

46. Alternative D-RTO Formulations D-RTO with infeasibilities treatment * Ameida & Secchi, 2012.

47. Dynamic Optimization Methods

48. Piecewise Constant Function Piecewise Linear Function Control Parameterization

49. Partial Discretization (Sequential Methods) Single shooting (Pollard & Sargent, 1970; Sargent & Sullivan, 1977) Multiple shooting (Bock & Plitt, 1984) Full Discretization (Simultaneous Methods) Orthogonal Collocation on Finite Elements (Cuthrell & Biegler, 1987) Numerical Methods

50. Single Shooting