Plantwide control: Towards a systematic procedure Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Tecnology (NTNU) Trondheim, Norway March 2002 Trondheim, 2002 Internet: www.ntnu.no/

Outline Introduction Plantwide control procedure Top-down Bottom-up What to control I: Primary controlled variables Inventory control - where set production rate What to control II: Secondary controlled variables Decentralized versus multivariable control Trondheim, 2002 Internet: www.ntnu.no/

Related work Page Buckley (1964) - Chapter on “Overall process control” (still industrial practice) Alan Foss (1973) - control system structure George Stephanopoulos and Manfred Morari (1980) Bill Luyben (1975- ) - “snowball effect” Ruel Shinnar (1981- ) - “dominant variables” Jim Douglas and Alex Zheng (Umass) (1985- ) Jim Downs (1991) - Tennessee Eastman process Larsson and Skogestad (2000): Review of plantwide control Trondheim, 2002 Internet: www.ntnu.no/

Alan Foss (``Critique of chemical process control theory'', AIChE Journal,1973): The central issue to be resolved ... is the determination of control system structure. Which variables should be measured, which inputs should be manipulated and which links should be made between the two sets? There is more than a suspicion that the work of a genius is needed here, for without it the control configuration problem will likely remain in a primitive, hazily stated and wholly unmanageable form. The gap is present indeed, but contrary to the views of many, it is the theoretician who must close it. Carl Nett (1989): Minimize control system complexity subject to the achievement of accuracy specifications in the face of uncertainty. Trondheim, 2002 Internet: www.ntnu.no/

Idealized view of control (“Ph.D. control”) Trondheim, 2002 Internet: www.ntnu.no/

Practice I: Tennessee Eastman challenge problem (Downs, 1991) Trondheim, 2002 Internet: www.ntnu.no/

Practice II: Typical P&ID diagram (PID control) Trondheim, 2002 Internet: www.ntnu.no/

Practice III: Hierarchical structure Trondheim, 2002 Internet: www.ntnu.no/

Plantwide control Not the tuning and behavior of each control loop, But rather the control philosophy of the overall plant with emphasis on the structural decisions: Selection of controlled variables (“outputs”) Selection of manipulated variables (“inputs”) Selection of (extra) measurements Selection of control configuration (structure of overall controller that interconnects the controlled, manipulated and measured variables) Selection of controller type (PID, decoupler, MPC etc.). Trondheim, 2002 Internet: www.ntnu.no/

Stepwise procedure plantwide control I. TOP-DOWN Step 1. DEGREE OF FREEDOM ANALYSIS Step 2. WHAT TO CONTROL? (primary variables) Step 3. MANIPULATED VARIABLES Step 4. PRODUCTION RATE Trondheim, 2002 Internet: www.ntnu.no/

II. BOTTOM-UP (structure control system): Step 5. REGULATORY CONTROL LAYER 5.1 Stabilization (including level control) 5.2 Local disturbance rejection (inner cascades) What more to control? (secondary variables) Step 6. SUPERVISORY CONTROL LAYER Decentralized or multivariable control (MPC)? Pairing? Step 7. OPTIMIZATION LAYER (RTO) Trondheim, 2002 Internet: www.ntnu.no/

I. Top-down Define operational objectives Identify degrees of freedom Identify primary controlled variables (look for self-optimizing variables) Determine where to set the production rate Trondheim, 2002 Internet: www.ntnu.no/

Step 1. Degree of freedom (DOF) analysis Nm : no. of dynamic (control) DOFs (valves) Nss = Nm- N0 : steady-state DOFs N0 : liquid levels with no steady-state effect (N0y)+ purely dynamic control DOFs (N0m) Cost J depends normally only on steady-state DOFs Trondheim, 2002 Internet: www.ntnu.no/

Distillation column with given feed Nm = 5, N0y = 2, Nss = 5 - 2 = 3 (2 with given pressure) Trondheim, 2002 Internet: www.ntnu.no/

Heat-integrated distillation process Trondheim, 2002 Internet: www.ntnu.no/

Heat exchanger with bypasses Trondheim, 2002 Internet: www.ntnu.no/

Alternatives structures for optimizing control What should we control? Trondheim, 2002 Internet: www.ntnu.no/

Step 2. What should we control? (primary controlled variables) Intuition: “Dominant variables” (Shinnar) Systematic: Define cost J and minimize w.r.t. DOFs Control active constraints (constant setpoint is optimal) Remaining DOFs: Control variables c for which constant setpoints give small (economic) loss Loss = J - Jopt(d) when disturbances d occurs Trondheim, 2002 Internet: www.ntnu.no/

Self-optimizing control (Skogestad, 2000) Loss L = J - Jopt (d) Self-optimizing control is achieved when a constant setpoint policy results in an acceptable loss L (without the need to reoptimize when disturbances occur) Trondheim, 2002 Internet: www.ntnu.no/

Loss with constant setpoints Trondheim, 2002 Internet: www.ntnu.no/

Effect of implementation error on cost Trondheim, 2002 Internet: www.ntnu.no/

Tennessee Eastman plant J c = Purge rate Nominal optimum setpoint is infeasible with disturbance 2 Oopss.. bends backwards Conclusion: Do not use purge rate as controlled variable Trondheim, 2002 Internet: www.ntnu.no/

c = Temperature top of column Example sharp optimum. High-purity distillation : c = Temperature top of column Temperature Ttop Water (L) - acetic acid (H) Max 100 ppm acetic acid 100% water: 100 C 99.99 % water: 100.01C Trondheim, 2002 Internet: www.ntnu.no/

Procedure for selecting (primary) controlled variables (Skogestad, 2000) Step 2.1 Determine DOFs for optimization Step 2.2 Definition of optimal operation J (cost and constraints) Step 2.3 Identification of important disturbances Step 2.4 Optimization (nominally and with disturbances) Step 2.5 Identification of candidate controlled variables Step 2.6 Evaluation of loss with constant setpoints for alternative controlled variables Step 2.7 Final evaluation and selection (including controllability analysis) Case studies: Tenneessee-Eastman, Propane-propylene splitter, recycle process, heat-integrated distillation Trondheim, 2002 Internet: www.ntnu.no/

Application: Recycle process J = V (minimize energy) 5 4 1 Given feedrate F0 and column pressure: 2 Nm = 5 N0y = 2 Nss = 5 - 2 = 3 3 Trondheim, 2002 Internet: www.ntnu.no/

Recycle process: Selection of controlled variables Step 2.1 DOFs for optimization: Nss = 3 Step 2.2 J=V (minimize energy with given feed) Step 2.3 Most important disturbance: Feedrate F0 Step 2.4 Optimization: Constraints on Mr and xB always active (so Luybens structure is not optimal) Step 2.5 1 DOF left, candidate controlled variables: F, D, L, xD, ... Step 2.6 Loss with constant setpoints. Good: xD, L/F. Poor: F, D, L Trondheim, 2002 Internet: www.ntnu.no/

Recycle process: Loss with constant setpoint, cs Large loss with c = F (Luyben rule) Negligible loss with c = L/F Trondheim, 2002 Internet: www.ntnu.no/

“Snowball effect” Forget Luyben’s rule about fixing a flow in each recycle loop Trondheim, 2002 Internet: www.ntnu.no/

Recycle process: Proposed control structure J = V (minimize energy) Active constraint Mr = Mrmax Active constraint xB = xBmin Trondheim, 2002 Internet: www.ntnu.no/

Good candidate controlled variables c (for self-optimizing control) Requirements: The optimal value of c should be insensitive to disturbances c should be easy to measure and control The value of c should be sensitive to changes in the steady-state degrees of freedom (Equivalently, J as a function of c should be flat) For cases with more than one unconstrained degrees of freedom, the selected controlled variables should be independent. Singular value rule (Skogestad and Postlethwaite, 1996): Look for variables that maximize the minimum singular value of the appropriately scaled steady-state gain matrix G from u to c Trondheim, 2002 Internet: www.ntnu.no/

Step 3. Manipulated variables Check that there are enough manipulated variables (DOFs) - both dynamically and at steady-state Otherwise: Need to add equipment extra heat exchanger bypass surge tank ……. Trondheim, 2002 Internet: www.ntnu.no/

Step 4. Where set production rate? Very important! Determines structure of remaining inventory (level) control system Set production rate at (dynamic) bottleneck Link between Top-down and Bottom-up parts Trondheim, 2002 Internet: www.ntnu.no/

Production rate set at inlet : Inventory control in direction of flow Trondheim, 2002 Internet: www.ntnu.no/

Production rate set at outlet: Inventory control opposite flow Trondheim, 2002 Internet: www.ntnu.no/

Production rate set inside process Trondheim, 2002 Internet: www.ntnu.no/

Definition of bottleneck A unit (or more precisely, an extensive variable E within this unit) is a bottleneck (with respect to the flow F) if - With the flow F as a degree of freedom, the variable E is optimally at its maximum constraint (i.e., E= Emax at the optimum) - The flow F is increased by increasing this constraint (i.e., dF/dEmax > 0 at the optimum). A variable E is a dynamic( control) bottleneck if in addition - The optimal value of E is unconstrained when F is fixed at a sufficiently low value Otherwise E is a steady-state (design) bottleneck. Trondheim, 2002 Internet: www.ntnu.no/

Heat integrated distillation process: Given feedrate with production rate set at inlet Trondheim, 2002 Internet: www.ntnu.no/

Heat integrated distillation process: Reconfiguration required when reach bottleneck (max. cooling in column 2) Trondheim, 2002 Internet: www.ntnu.no/

Heat integrated distillation process: Given feedrate with production rate adjusted at bottleneck (column 2) SET Trondheim, 2002 Internet: www.ntnu.no/

Recycle process: Given feedrate Trondheim, 2002 Internet: www.ntnu.no/

Bottleneck in column MAX Trondheim, 2002 Internet: www.ntnu.no/

II. Bottom-up Determine secondary controlled variables and structure (configuration) of control system (pairing) A good control configuration is insensitive to parameter changes Trondheim, 2002 Internet: www.ntnu.no/

Step 5. Regulatory control layer Purpose: “Stabilize” the plant using local SISO PID controllers to enable manual operation (by operators) Main structural issues: What more should we control? (secondary cv’s, y2) Pairing with manipulated variables (mv’s) y1 = c y2 = ? Trondheim, 2002 Internet: www.ntnu.no/

Selection of secondary controlled variables (y2) The variable is easy to measure and control For stabilization: Unstable mode is “quickly” detected in the measurement (Tool: pole vector analysis) For local disturbance rejection: The variable is located “close” to an important disturbance (Tool: partial control analysis). Trondheim, 2002 Internet: www.ntnu.no/

Partial control Primary controlled variable y1 = c Local control of y2 (supervisory control layer) Local control of y2 using u2 (regulatory control layer) Setpoint y2s : new DOF for supervisory control Trondheim, 2002 Internet: www.ntnu.no/

Step 6. Supervisory control layer Purpose: Keep primary controlled outputs c=y1 at optimal setpoints cs Degrees of freedom: Setpoints y2s in reg.control layer Main structural issue: Decentralized or multivariable? Trondheim, 2002 Internet: www.ntnu.no/

Decentralized control (single-loop controllers) Use for: Noninteracting process and no change in active constraints + Tuning may be done on-line + No or minimal model requirements + Easy to fix and change - Need to determine pairing - Performance loss compared to multivariable control - Complicated logic required for reconfiguration when active constraints move Trondheim, 2002 Internet: www.ntnu.no/

Multivariable control (with explicit constraint handling - MPC) Use for: Interacting process and changes in active constraints + Easy handling of feedforward control + Easy handling of changing constraints no need for logic smooth transition - Requires multivariable dynamic model - Tuning may be difficult - Less transparent - “Everything goes down at the same time” Trondheim, 2002 Internet: www.ntnu.no/

Step 7. Optimization layer (RTO) Purpose: Identify active constraints and compute optimal setpoints (to be implemented by supervisory control layer) Main structural issue: Do we need RTO? (or is process self-optimizing) Trondheim, 2002 Internet: www.ntnu.no/

Conclusion Procedure plantwide control: I. Top-down analysis to identify degrees of freedom and primary controlled variables (look for self-optimizing variables) II. Bottom-up analysis to determine secondary controlled variables and structure of control system (pairing). Trondheim, 2002 Internet: www.ntnu.no/

References http://www.chembio.ntnu.no/users/skoge/ Larsson, T., 2000. Studies on plantwide control, Ph.D. Thesis, Norwegian University of Science and Technology, Trondheim. Larsson, T. and S. Skogestad, 2000, “Plantwide control: A review and a new design procedure”, Modeling, Identification and Control, 21, 209-240. Larsson, T., K. Hestetun, E. Hovland and S. Skogestad, 2001, “Self-optimizing control of a large-scale plant: The Tennessee Eastman process’’, Ind.Eng.Chem.Res., 40, 4889-4901. Larsson, T., M.S. Govatsmark, S. Skogestad and C.C. Yu, 2002, “Control of reactor, separator and recycle process’’, Submitted to Ind.Eng.Chem.Res. Skogestad, S. (2000). “Plantwide control: The search for the self- optimizing control structure”. J. Proc. Control 10, 487-507. See also the home page of S. Skogestad: http://www.chembio.ntnu.no/users/skoge/ Trondheim, 2002 Internet: www.ntnu.no/