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Université de Lyon- CNRS-LAGEP, France Paper C-090 Model Predictive Control of the Primary Drying Stage of the Drying of Solutions.

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Presentation on theme: "Université de Lyon- CNRS-LAGEP, France Paper C-090 Model Predictive Control of the Primary Drying Stage of the Drying of Solutions."— Presentation transcript:

1 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr1 Model Predictive Control of the Primary Drying Stage of the Drying of Solutions in Vials: an Application of the MPC@CB Software (Part 1) by: Nawal Daraoui, Pascal Dufour, Hassan Hammouri ADC’07, Hong Kong, August, 13-15 2007

2 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr2 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Conclusions & perspectives Outline

3 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr3 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Conclusions & perspectives Outline

4 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr4 Freeze drying is generally considered to produce higher quality dried products. Here, freeze drying of solutions in vial must be controlled under constraints during the primary stage Control problem statement LiquidFreezed Primary Drying Secondary Drying Vapor Sublimation front Dry Freezed

5 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr5 Control problem statement [Dufour, IDS06] 1979: use of control tools in drying started. Since 1998: joined development of optimal control and first principle model in drying. Use of advanced control tools allows: improving benefits, decreasing energy use and off-spec production. moreover, return on investment is relatively low. More first principle models are now needed ! 60 000 products dried + 100 dryer types: a real potential of new collaborations between control and drying communities exist to improve dryer efficiency !

6 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr6 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Conclusions & perspectives Outline

7 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr7 First principle PDE model A dynamic model of the primary drying stage of the freeze drying process is needed: fundamental mass and energy balance equations are used. One dimensional heat and mass transfer. Sublimation front is planar and parallel to the horizontal section of the vial. Gas phase inside the pores of the dry layer is only composed of pure water vapor. Partial pressure of water vapor at the top of the dry layer = total pressure in the sublimation chamber.

8 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr8 First principle PDE model State variables

9 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr9 First principle PDE model [Liapis et al., 1994] Dynamic equations:

10 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr10 First principle PDE model [Liapis et al., 1994] Boundary conditions: Initial conditions: Control variables

11 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr11 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Conclusions & perspectives Outline

12 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr12 Model predictive control strategy

13 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr13 Model predictive control strategy The function f means: trajectory tracking, processing time minimization, productivity function …

14 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr14 Advantages: - constraints (such as manipulated variables physical limitations, constraints due to operating procedures or safety reasons…) may be specified - a model aims to predict the future behavior of the process and the best one is chosen by a correct optimal control of the manipulated variables. Drawbacks: - computational time needed may limit online use - suboptimal solutions - how to handle unfeasibilities Model predictive control strategy

15 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr15 Originaly developed for nonlinear PDE model control Main idea: decrease the online time needed to compute the PDE model based control Approach: Input constraints: hyperbolic transformation Output constraints: exterior penalty method Linearization + sensitivites computed off line On line use of a time varying linear model On line resolution of a penalized (and so unconstrained) optimization control problem : a modified Levenberg Marquardt Algorithm Model predictive control strategy [Dufour et al, IEEE TCST 11(5) 2003]

16 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr16 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Conclusions & perspectives Outline

17 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr17 1. 1. Developed under Matlab, MPC@CB© solves any user defined :   trajectory tracking problem   operating time minimization problem   any cost function   input/output constraint handled 2. 2. Any user defined continuous model (SISO, MISO, SIMO, MIMO model), including large scale PDE model 3. 3. Easy to introduce a user defined observer 4. 4. Easy to apply the software for simulation or real time application MPC@CB ©: flexibility/ease for a quick use in control ! MPC@CB© software main features

18 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr18 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Conclusions & perspectives Outline

19 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr19 Temperature trajectory tracking with magnitude+velocity input constraints+ output constraint Simulation results

20 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr20 Temperature trajectory tracking with magnitude+velocity input constraints+ output constraint Simulation results

21 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr21 Temperature trajectory tracking with magnitude+velocity input constraints+ output constraint Simulation results

22 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr22 Temperature trajectory tracking with magnitude+velocity input constraints+ output constraint (sampling time=60s) Simulation results

23 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr23 Maximization of the sublimation front velocity with magnitude+velocity input constraints + output constraint (sample size=1 cm) Simulation results

24 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr24 Maximization of the sublimation front velocity with magnitude+velocity input constraints + output constraint (sampling time=60s) Simulation results

25 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr25 Maximization of the sublimation front velocity with magnitude+velocity input constraints + output constraint (sampling time=60s) Simulation results

26 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr26 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Conclusions & perspectives Outline

27 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr27 The real time control of drying of vials is possible Control of such system by a general MPC@CB© software has been shown Conclusions Perspectives Experimental validation Experimental minimization of the drying time under constraints: an observer (model based soft sensor) is under development MPC@CB© may be used for any process: since its development, it is also currently used for control of polymer production, painting curing, pasta drying. To use MPC@CB©: dufour@lagep.univ-lyon1.fr

28 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr28 Thank you Any questions ?

29 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr29 First principle PDE model [Liapis et al., 1994] Need for a change of space coordinates: Then, space and time derivative operators becomes:

30 Université de Lyon- CNRS-LAGEP, France Paper C-090 dufour@lagep.univ-lyon1.fr30 First principle PDE model [Liapis et al., 1994] The PDE model with boundary control is:

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