Integrated Process Networks: Nonlinear Control System Design for Optimality and Dynamic Performance Michael Baldea a,b and Prodromos Daoutidis a a University of Minnesota, Minneapolis, MN b Praxair, Inc., Tonawanda, NY Antonio C. Brandao Araujo and Sigurd Skogestad Norwegian University of Science and Technology NO-7491 Trondheim, Norway

Chemical Plant Material recycle Heat integration Feedback interactions within the plant

Control of Tightly Integrated Plants: Challenging and Important! Decentralized control: inherent limitations Fully centralized control: generally impractical –Size / complexity of dynamic models –Ill-conditioning Efficient transient operation : critical –Moves across product slate due to frequent changes in market conditions and economics –Going beyond regulatory control… –Accounting for ‘network’ dynamics

Research on Integrated Process Networks Dynamic Analysis: –Slow response, high sensitivity to disturbances, instability (Gilliland et al. ’64, Denn & Lavie ’82, Skogestad & Morari ’87, Luyben ’93, Mizsey & Kalmar ’96) –Nonlinear dynamics (Morud & Skogestad ’94, ’96, Bildea et al. ’00, Kiss et al. ’06)

Research on Integrated Process Networks Control –Interaction of design and control for reaction-separation networks (Luyben ’93, Luyben M. & Floudas ’94, Yin & Luyben ‘97) –Plant-wide control (Price & Georgakis ’93, Luyben et al. ’97, Ng & Stephanopoulos ’98, Zheng et al. ’99) –Applications to benchmark problems (McAvoy & Ye, ’94, Ricker, ’96, Ricker and Lee, ’95, Larsson et al. ’01, Jockenhovel et al. ’03) –Self – optimizing control (Morari et al. ’80, Skogestad ’00) –Partial control (Shinnar et al. ’96, Tyreus ’99, Kothare et al. ’00) –Passivity based stabilization (Ydstie et al. ’98, ’99) –Dynamic optimization (Tosukhowong et al. ’04) –Time-scale analysis / nonlinear model reduction and control (Kumar and Daoutidis ’02, Baldea et al. ’06, Baldea and Daoutidis ’05 ’06)

Present Work Combining time-scale analysis (dynamics) and self-optimizing control (steady state economics): –Control structure design –Nonlinear supervisory control Prototype reactor-separator-recycle network

Plant-wide Control Hierarchy of Decisions ( Larsson and Skogestad, 2000 ) I. TOP-DOWN Step 1. DEGREES OF FREEDOM Step 2. OPERATIONAL OBJECTIVES Step 3. CONTROLLED VARIABLES Step 4. PRODUCTION RATE II. BOTTOM-UP Step 5. REGULATORY CONTROL LAYER (PID) Step 6. SUPERVISORY CONTROL LAYER (MPC) Step 7. OPTIMIZATION LAYER (RTO) Can we do without? Planning (months - years)

What should we control? Optimization level: Solve Optimal solution: usually at constraints – most degrees of freedom are used to satisfy “active constraints” Control active constraints! –Implementation usually simple What else should we control? –Variables for remaining unconstrained degrees of freedom: acceptable losses in the presence of disturbances and implementation errors

Self-optimizing Control Principle: (Economically) acceptable operation (loss) should be achieved using constant set points for the controlled variables, without the need to re-optimize when disturbances occur. c=c s Planning (months - years)

Controlled Variables Selection of Controlled Variables

Integrated Process Network: Multiple Time Scale Dynamics Low single pass conversion - high recycle rate Impurities present in the feed – small amount Impurities do not separate readily - small purge stream Baldea and Daoutidis, Comp. Chem. Eng., 2006.

Dynamic Model : scaled inputs : large recycle loop flowrates : scaled inputs : medium flowrates : scaled input : small purge flowrate : small parameter – ratio of throughput to recycle : small parameter – ratio of purge to throughput states terms: stiffness, multiple time scales

Model Reduction Time Scale Decomposition Fast time scale (process units) Intermediate time scale (network) Slow time scale (impurity levels) dimensional Equilibrium manifold Manipulated inputs dimensional Equilibrium manifold Manipulated inputs 1-dimensional Manipulated input

Hierarchical Controller Design Manipulated inputsControl objectives (broad)

Optimality and Dynamic Performance Self Optimizing Control –economic insight –selection of controlled variables Time Scale Analysis –dynamic perspective –selection of manipulated inputs Combining: control designs with inherent optimality and good dynamic performance

Case Study Generic Reactor – Condenser Network Slow reaction, large recycle Product nonvolatile Volatile impurity present in the feed Degrees of freedom: R (W), F, P, L

Insights from Time-scale Analysis Control objectives: vapor holdups (pressures) stabilization (fast), liquid holdup stabilization, X B (intermediate) impurity levels (slow) Available degrees of freedom: R,F (fast) L, M RSP, M CSP (intermediate) P (slow)

Hierarchical Controller Design (I) (Baldea and Daoutidis C&ChE, 2006) Time scaleControlled output Manipulated Input Controller FastReactor holdupReactor effluentProportional FastCondenser vapor holdup Recycle rateProportional IntermediateLiquid holdupLiquid flowrateProportional IntermediateProduct purityReactor holdup Set point Nonlinear, model-based, cascade SlowInert levels in reactor Purge flowrateNonlinear, model-based

Control Structure I Reactor pressure allowed to vary Compressor/pressure constraints?

Insights from Self-optimizing Control Disturbances: F O, y A,O, y I,O, x B,T R,k 1 Cost function: J = pW*W - pL*L + pP*L Active constraints: Reactor pressure, product purity Self-optimizing variable: W

Self-optimizing Control Structure (II) No control of impurity Poor dynamics: small purge controls product purity

Hierarchical / Self-optimizing Controller Design (III) Time scaleControlled output Manipulated Input Controller FastReactor holdupReactor effluentProportional Condenser vapor holdup Recycle rate (compressor power) Proportional Intermediate Liquid holdupLiquid flowrateProportional Product purityCondenser vapor holdup set point Nonlinear, model- based, cascade SlowCompressor power Purge flowrateProportional Integral

5% increase in purity setpoint

20% increase in production rate

Concluding Remarks Self-optimizing control / time-scale analysis: complementary perspectives steady-state economics vs dynamics controlled variables vs manipulated inputs Control configurations that are self-optimizing and have good closed - loop response characteristics Well-conditioned nonlinear supervisory controllers based on reduced order models

Acknowledgements National Science Foundation MB partially funded by a University of Minnesota Doctoral Dissertation Fellowship

Integrated Process Networks: Nonlinear Control System Design for Optimality and Dynamic Performance Michael Baldea a,b and Prodromos Daoutidis a a University of Minnesota, Minneapolis, MN b Praxair, Inc., Tonawanda, NY Antonio C. Brandao Araujo and Sigurd Skogestad Norwegian University of Science and Technology NO-7491 Trondheim, Norway