1. 1 Approaches to increase the range of use of Model predictive control Miguel Rodriguez Advisor: Cesar De Prada Systems Engineering and Automatic Control Department University of Valladolid, Spain Pisa, October 2008.

2. 2 Outline Motive Control explicit using Multiparametric Programming Approaches for using NMPC in Hybrid Systems –Mixed continuous-batch processes –Hybrid system Reduced Order Model Conclusions Approaches to increase the range of use of Model predictive control

3. 3 Motive MPC is used to controlling a wide range of process industrials. MPC is capable of operating without expert intervention for long periods time. Centralized control, Multi-level, complex plants. Constraint handling, Input saturation, states constraints, etc. But –MPC to require a time of calculation to find the optimal control signal. –The time of calculation is increased when the systems are Hybrid or Nonlinear. –If optimization time is higher that the response time, MPC is impossible to apply. Approaches to increase the range of use of Model predictive control

4. 4 Motive The main objective is find techniques that decreased the optimization time and retain all benefits of MPC approach. Three approach are presented in this work –Control explicit using Multiparametric Programming –Approaches for NMPC to Hybrid Systems Mixed continuous-batch processes Hybrid system –Reduced Order Model Approaches to increase the range of use of Model predictive control

5. 5 Control explicit using Multiparametric Programming Linear MPC without constraints Using the steady states model and making predictions to the horizon prediction Approaches to increase the range of use of Model predictive control

6. 6 Control explicit using Multiparametric Programming Linear MPC without constraints Then Explicit Solution: where Approaches to increase the range of use of Model predictive control

7. 7 Control explicit using Multiparametric Programming Linear MPC with constraints Using multiparametric programming, z is dependent variable of the current states x and the system constraints. with the KKT conditions, we can found, of way iterative, the explicit solution into the region where it solution is valid. Approaches to increase the range of use of Model predictive control

8. 8 Control explicit using Multiparametric Programming Linear MPC without constraints finally, we have an explicit solution for each region CR i Approaches to increase the range of use of Model predictive control

9. 9 Control explicit using Multiparametric Programming DC-DC Converter (Buck-Boost type) Average Model (continuous conduction mode) Search method: binary search tree (Tondel, Johansen and Bemporad, 2002) Approaches to increase the range of use of Model predictive control Control mp-QP EcoSimPro Set point V 0, I L d, R MatLab States estimator States d Disturbance model

10. 10 Control explicit using Multiparametric Programming DC-DC Converter (Buck-Boost type) Controller partition with 51 regions Approaches to increase the range of use of Model predictive control

11. 11 Control explicit using Multiparametric Programming DC-DC Converter Comparison between Slide Model Control and mp-MPC. Approaches to increase the range of use of Model predictive control Load (Ohms) Ref (Volts) V 0 (Volts)

12. 12 Control explicit using Multiparametric Programming Feasibility of implementing the controller. –Ts=0.1 ms –State Estimator ( 16 multiplications + 32 assignations ) ≈ 50 cycles –Signal capture ( 2 input, Voltage and Current)≈ 4 cycles –Search of region (51 regions X 5 operations ) ≈ 205 cycles –Calculation control signal (3 multiplications + 3 assignations) ≈ 6 cycles –Output PWM (3 assignations) ≈ 6 cycles –Total of cycles ≈ 270 cycles  Controller frequency Standard floating point DSP controller (Texas, Microchip, etc) Approaches to increase the range of use of Model predictive control

13. 13 Approaches for NMPC to Hybrid Systems. Mixed continuous-batch processes – Parallel Production Line Hybrid system –Solar Air conditioning plant Approaches to increase the range of use of Model predictive control

14. 14 Parallel Production Line The benchmark is a chemical process proposed by UCL, Belgium Approaches to increase the range of use of Model predictive control

15. 15 Parallel Production Line Aims of control –Maximize the productivity in the presence of uncertainties and disturbances. –Maximize the output flow of storage tank and hold transfer continuously to downstream processing stage. –To avoid the total discharge in the storage tank. Decision variables –Standby times for filling, heating and discharging of both autoclaves. –Outflow of B product from storage tank (F out ST) Non-measured disturbances –Change in the temperature of hot steam (Th) Approaches to increase the range of use of Model predictive control

16. 16 T contraints =T overlap fill +T overlap Heat Parallel Production Line T constraints Approaches to increase the range of use of Model predictive control

17. 17 Parallel Production Line (Simulation Results. Overview) Approaches to increase the range of use of Model predictive control  Values of the parameters of Objective Function:  Values of the weights  Almost, for each batch unit, 3 batches are predicted, 2 of them are controlled. So, Np=3 and Ncb1=Ncb2=2.  4 changes for classical continuous variables F out ST V ST refV ST maxV ST minF out STT constraints Weight (a i )0.1111100 V ST refV ST maxV ST min 254010

18. 18 Parallel Production Line (Simulation Results. Overview) Approaches to increase the range of use of Model predictive control Manipulated variableControlled variable Batch sequences

19. 19 Solar Air conditioning plant (Description) The absorption machine Energy supply systems –solar collector –gas heater –Accumulation tank Aims of control –Maintaining the chilled water temperature (75º-95º) –Minimize the gas used Decision variables –Continuous v B1, vm 3 –Discrete mode of operation (set of on/off valves) Approaches to increase the range of use of Model predictive control Problem MINLP very complex

20. 20 Solar Air conditioning plant (Embedded Logic Control) Fictitious variable u to represent the energy supply to the plant Definition of a set of rules Integration of the rules and the fictitious variable Solution of the associated optimization problem every sampling period Objective function Approaches to increase the range of use of Model predictive control Embedded logic control rules of Operation

21. 21 Solar Air conditioning plant (Sensibility problems) Approaches to increase the range of use of Model predictive control For u(t) we are solving For u(t+Ts) we are solving Sub-optimal solution, but no problem with the sensibility

22. 22 Sequential approach to dynamic optimization Solar Air conditioning plant (Controller implementation) Approaches to increase the range of use of Model predictive control

23. 23 Solar Air conditioning plant (Results) Simulation results Approaches to increase the range of use of Model predictive control Manipulated variables Controlled variable

24. 24 Solar Air conditioning plant (Results) Test real plant Approaches to increase the range of use of Model predictive control Manipulated variables Controlled variable

25. 25 Reduced Order Model (The open plate reactor) It combines heat exchanger and micro-reactor: more efficient but more difficult to control Controlled variables: γ conversion T i temperature along the reactor Manipulated variables: u B1, u B2, feed flows rates of B T feedA, temperature of reactant A, T cool the cooling temperature. A + B → C

26. 26 The open plate reactor (Dynamics and Aims) Aim: Finding a reduced dynamic model that facilitates the use of NMPC Start-up of the plate reactor avoiding ‘hot spots’ Highly non-linear distributed process

27. 27 The open plate reactor ( Proper Orthogonal Decomposition POD) A field x can be represented as a complete series of orthonormal globally defined functions  i A projection is made on a subspace retaining % of the energy of the signals, allowing to obtain a model with a smaller number of ODE’s DFM POD

28. 28 The open plate reactor ( NMPC) NMPC based on continuous time formulation with the POD model and a sequential approach for the NLP problem Results of the reactor start-up Inputs Outputs

29. 29 Conclusions Approaches to apply NMPC in Fast-System and hybrid system have been presented. Transformation of problem discrete variables to Continuous variables. To use NLP approach to solver Mixed integer no linear problem. A study of feasibility to implementing mp-MPC in  controllers has been presented. Approaches to increase the range of use of Model predictive control

30. 30 Reference M. Rodríguez, D. Sarabia, and C. de Prada: Hybrid Predictive Control of a Simulated Chemical Plant. Taming Heterogeneity and Complexity of Embedded Control Systems, International Scientific & Technical Encyclopedia (ISTE), London, Editors: F. Lamnabhi- Lagarrigue, S. Laghrouche, A. Loria and E. Panteley, pp. 617-634, 2007 M. Rodríguez, C. De Prada, F. Capraro, S. Cristea, and R. M. C. De Keyser: Hybrid Predictive Control of a Solar Air Conditioning Plant. 17th IFAC World Congress, Seoul, Korea, 2008. D. Sarabia, C. de Prada, and S. Cristea: A Mixed Continuous-Batch Process: Implementation of Hybrid Predictive Controllers. Proc. 7th IFAC Symp. on Advances in Control Education, 2006, Paper-ID: 148. M. Rodríguez, C. de Prada, A. A. Alonso, C. Vilas and M. García: A nonlinear model predictive controller for the start-up of a open plate reactor, International Workshop on Assessment and Future Directions Of Nonlinear Model Predictive Control, Pavia, Italy, 2008. Approaches to increase the range of use of Model predictive control

31. 31 Questions? Thank you. Approaches to increase the range of use of Model predictive control