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Integration of Design and Control: A Robust Control Approach

Integration of Design and Control: A Robust Control Approach. by Nongluk Chawankul Peter L. Douglas Hector M. Budman University of Waterloo Waterloo, Ontario, Canada. Background. Control performance depends on the controller and the design of the process.

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Integration of Design and Control: A Robust Control Approach

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  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. 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: Integrated approach Process design Process control + =

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

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

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

  6. Case Study III: MIMO MPC 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.

  7. Optimization Minimize Cost(U,C) = CC(U) + OC(U) + max VC(U,C) U,CLm Such that h(U) = 0 (equality constraints) g(U,C)  0 (inequality constraints) Objective Function U is a vector of design variables. C is a vector of control variables. Lm is a set of uncertainty.

  8. Objective Function

  9. Capital Cost (CC) and Operating Cost (OC) • 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)

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

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

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

  13. Equality Constraints

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

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

  16. y -35% 35% +35% y1 -1% 1% y2 +1% time 0 Process Models: Input/Output Model for 22 system Equality Constraints: Process models - 3 yi Sn S3 • First Order Model S2 S1 t  Process gains and • Kp1(RR) for paring xD-RR • Kp2(RR) for paring xB-RR • Kp3(Q) for paring xD-Q • Kp4(Q) for paring xB-Q • In a similar fashion, time constants and dead time • p(RR) and p(Q) • (RR)

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

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

  19. y Time Equality Constraints: Process models - 6 • Model uncertainty Sn,upper Sn,nom xD-RR Sn,lower xB-RR xD-Q xB-Q

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

  21. Inequality Constraints

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

  23. Inequality Constraints- 2 Block diagram of the MPC and the connection matrix M M Z(k) w(k) U(k) W1  W2 Z-1I (k+1/k) u(k) U(k-1) + T2 N1 + Li Kmpc T1 + + H + - 2. Robust stability constraint (Zanovello and Budman, 1999) H N1 + + Mp H - + N2 Z-1I U(k+1) U(k) M z w 

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

  25. Results

  26. Results 1 Smaller RR* smaller delay smaller interaction easier to control

  27. Results - 2 Results from Integrated design and control design approach • 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

  28. Results - 3 Compare Results from Traditional and Integrated design and control design approaches. Why? In the traditional method the RR is determined only once by the minimization of CC and OC and does not change with product price as in the integrated approach!

  29. Results - 4 Effect of RRmax on Total Cost (TC)

  30. 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.

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

  32. Results - 1 Results from Integrated design and control design approach for  = 0 • 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

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

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