1. Integration of Design and Control: A Robust Control Approach by Nongluk Chawankul Peter L. Douglas Hector M. Budman University of Waterloo Waterloo, Ontario, Canada

2. Process design Background  Control performance depends on the controller and the design of the process.  Traditional design procedure:  Step 1: Process design (sizing + nominal operating conditions)  Step 2: Control design  Idea of integrating design and control: Process control + = Integrated approach

3. Background Traditional design and control design Integrated design and control design Step 1: Process design Step 2: Control design Only one step design Cost = capital cost(x) + operating cost(x) + cost related to closed loop system(x,y) where x is design variable y is control tuning parameter  Objective Function (Cost) Two steps design  Process constraints  Equality constraints, h(x) = 0  Inequality constraints, g(x,y)  0 Min Cost(x,y) x,y s.t. h(x) = 0 g(x,y)  0 Cost = Capital cost(x) + operating cost(x) where x is design variable Min Cost(x) x s.t. h(x) = 0 g(x)  0 Optimum design Design controller Closed loop system

4. Nonlinear Dynamic Model (difficult optimization problem) Variability cost not into cost function: Multi-objective optimization Decentralized Control : PI /PID Linear Nominal Model + Model Uncertainty (Simple optimization problem) Variability cost into cost function : One objective function extended to Centralized Control : MPC Previous studies Our study Integrated Design and Control Design

5. Case study Case study II: SISO MPC Case study III: MIMO MPC Feed RR Ethane Propane Isobutane N-Butane N-Pentane N-Hexane A XD*XD* + - Q Feed RR Ethane Propane Isobutane N-Butane N-Pentane N-Hexane A1 MPC XD*XD* + - Q IMC or MPC SISO system MIMO system A2 - + XB*XB* XDXD XBXB XDXD XBXB

6. MIMO case study:  RadFrac model in ASPEN PLUS was used.  Different column designs, 19 – 59 stages were studied.  Product specifications  Mole fraction of propane in distillate product = 0.783  Mole fraction of isobutane in bottom product = 0.1  Design variables are functions of nominal RR at specific product compositions. Case Study III: MIMO MPC

7. U is a vector of design variables. C is a vector of control variables. L m is a set of uncertainty. Optimization MinimizeCost(U,C) = CC(U) + OC(U) + max VC(U,C) U,C L m Such thath(U) = 0(equality constraints) g(U,C)  0 (inequality constraints) Objective Function

9. Capital Cost, CC –Cost of sizing, e.g. number of stages N and column diameter D –Capital cost for distillation column from Luyben and Floudas, 1994 ($/day) Operating Cost, OC –Operating cost from Luyben and Floudas, 1994 ($/day) where  tax = tax factor HD = reboiler duty (GJ/hr) OP = operating period (hrs) UC = Utility cost ($/GJ) Capital Cost (CC) and Operating Cost (OC)

10. Feed RR Ethane Propane Isobutane N-Butane N-Pentane N-Hexane A1 MPC XD*XD* + - Q A2 - + XB*XB* V1 V2 t t t t t - Variability cost, VC = inventory cost - sinusoid disturbance induces process variability - consider holding tank to attenuate the product variation  Variability Cost, VC Variability Cost (VC)

11. Assume, W is sinusoidal disturbance with specific  d. (alternatively, superposition of sinusoids) With phase lag Consider worst case variability : Calculation of Variability Cost (VC) - 1 Related to maximum VC

12. Objective Function (-cont-) Apply Laplace transform The product volume in the holding tank  V Q in Q out  C in  C out Calculation of Variability Cost (VC) - 2 VC1 = W1  P1  V1  (A/P,i,N) VC2 = W2  P2  V2  (A/P,i,N) VC = VC1+ VC2

13. Equality Constraints

14. Process Models: ASPEN PLUS simulations at specific product compositions Equality Constraints: Process models -1 Q(RR)N(RR) HD(RR) D(RR)

15. Process Models: ASPEN PLUS simulations DF(RR) BF(RR) Equality Constraints: Process models - 2

16. Process Models: Input/Output Model for 2  2 system  First Order Model yiyi t S1S1 S2S2 S3S3 SnSn 1% 35% yy 0 y1y1 y2y2 time -35% +35% +1% -1%  Process gains  In a similar fashion, time constants and dead time  p (RR) and  p (Q)   (RR) and  K p1 (RR) for paring x D -RR  K p2 (RR) for paring x B -RR  K p3 (Q)for paring x D -Q  K p4 (Q)for paring x B -Q Equality Constraints: Process models - 3

17. Process gains for 2  2 system Equality Constraints: Process models - 4

18. Process time constants:  p (RR) and  p (Q) Process dead time:  (RR) Equality Constraints: Process models - 5

19.  Model uncertainty Time y S n,upper S n,lower S n,nom x D -RR x B -RR x D -Q x B -Q Equality Constraints: Process models - 6

20. Model Uncertainty for 2  2 system Equality Constraints: Process models - 7

21. Inequality Constraints

22. 1.Manipulated variable constraint Inequality Constraints- 1 is a tuning parameter. Large  less aggressive control Two manipulated variables  Calculate  RR and  Q and

23. 2. Robust stability constraint (Zanovello and Budman, 1999) LiLi Mp K mp c T1T1 T2T2 H N1 W1  W2 N2 Z -1 I ++ + + + + + - + N1 - M  (k+1/k)  u(k) U(k) U(k-1) Z(k)w(k) H H Block diagram of the MPC and the connection matrix M  Z -1 I U(k) U(k+1) M w z Inequality Constraints- 2

24. Two different approaches Integrated Method Traditional Method Robust Performance (Morari, 1989) Where U is manipulated variables

25. Results

26. Results - 1 Results from Integrated design and control design approach w1w2RR* * 11 ND (m) 111.9130.23503.65263.392 511.9110.23413.63263.392 1011.9080.23383.62273.391 1511.7530.23313.03383.370 2011.7530.23323.03383.370 151.9120.18863.64263.392 1101.9090.18483.62263.391 1151.9060.18363.61273.391 1201.9040.18303.60273.390 w1 or w2 increases; -RR* decreases  smaller dead time - 11 decreases  interaction decreases as RR decreases - * decreases  RS constraint is easy to satisfy as 11 decreases

27. Compare Results from Traditional and Integrated design and control design approaches. Results - 2

28. Results - 3 RR max RR* * ND (m)CC ($/day)OC ($/day)VC ($/day)TC ($/day) 2.6331.9130.2350263.392195.98586.2123.34805.53 21.9130.2349263.392195.98586.2123.34805.53 1.91.8540.2024383.370259.76570.4872.62902.86 1.81.7610.2021393.370262.60570.2093.04925.84 Effect of RR max on Total Cost (TC)

29. Conclusions 1- For the case  ≠ 0, using the integrated method, the optimization tends to select smaller RR values which correspond to smaller dead time and smaller interaction. 2- The optimal design obtained using the integrated method resulted in a lower total cost as compared to the traditional method. 3- Limit on manipulated variable affects the closed loop performance and leads to more cost.

30. Process MPC W (Sinusoid unmeasured disturbance) y r=0 - + ++ u Substitute  (k),  u(k-1) into the first equation and apply z-transform Calculation of Variability Cost (VC) -1  Process variability

31. Results - 1 Results from Integrated design and control design approach for  = 0 w1w2RR* * 11 ND (m) 111.9210.25033.68263.393 511.9550.25093.83263.399 1011.9800.25183.95253.404 1512.0120.25214.11253.410 2012.1030.25274.63243.431 151.9600.25113.86263.400 1101.9920.25164.01253.406 1152.1020.25224.63243.431 1202.2340.25405.57233.465 w1 or w2 increases; -RR* increases  uncertainty decreases as RR increases - 11 increases  interaction increases as RR increases - * increases  RS constraint is more difficult to satisfy as 11 increases

32. Results - 4 Compare savings when  = 0 and   0   0  = 0   0