1 Optimal input design for online identification : a coupled observer-MPC approach by: Saida Flila, Pascal Dufour, Hassan Hammouri 10/07/2008 IFAC’08, Korea, July, Université de Lyon, France

2 Outline Preliminaries Case study Case study Outline Control problem statement Simulation results Simulation results software main features software main features Conclusion & perspectives Conclusion & perspectives Control problem statement 1. Control problem statement 2. Preliminaries Parametric sensitivity model Observer for state-affine systems 3. Proposed control approach Model predictive control (MPC) Final control structure 4. Case study Model for powder coating curing process 5. CB software main features Simulation results 6. Simulation results Conclusion & perspectives 7. Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

3 Outline Preliminaries Case study Case study Outline Control problem statement Simulation results Simulation results software main features software main features Conclusion & perspectives Conclusion & perspectives Control problem statement 1. Control problem statement 2. Preliminaries Parametric sensitivity model Observer for state-affine systems 3. Proposed control approach Model predictive control (MPC) Final control structure 4. Case study Model for powder coating curing process 5. CB software main features Simulation results 6. Simulation results Conclusion & perspectives 7. Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

4 Preliminaries Case study Case study Outline Proposed control approach Proposed control approach Control problem statement Simulation results Simulation results software main features software main features Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Problem of parameter estimation needs to be addressed A natural question: how can the input sequence be chosen in such a way that the parameters are optimally estimated? 1974 & 1985: studies on optimal input in linear systems 2002: Kessman and Stigter include analytical solution of optimal input design 2004: Stigter and Kessman have found recursive algorithm solutions But few studies exists for complex model based systems: nonlinear PDE system Control problem tackled here: optimally control online a process based on a nonlinear PDE model to estimate online a set of the model parameters, under input/output constraints Optimal input design

5 Outline Preliminaries Case study Case study Outline Control problem statement Simulation results Simulation results software main features software main features Conclusion & perspectives Conclusion & perspectives Control problem statement 1. Control problem statement 2. Preliminaries Parametric sensitivity model Observer for state-affine systems 3. Proposed control approach Model predictive control (MPC) Final control structure 4. Case study Model for powder coating curing process 5. CB software main features Simulation results 6. Simulation results Conclusion & perspectives 7. Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

6  Parametric sensitivity model Let the model structure: (1) : n-dimensional state vector Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features : r-dimensional input vector : m-dimensional output vector : p-dimensional vector of time-invariant parameters The associated parametric sensitivity model is derived from the model (1) : (2) and Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

7  Observer for state-affine systems [Hammouri and De Leon, 1990] Observer : dynamic system obtained from the nominal model by adding a correction term. Advantage: estimate the states not measured and unknown parameters. Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features The state affine system is in the following form : (3) Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

8  Observer for state-affine systems [Hammouri and De Leon, 1990] Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features is the initial condition and Main idea : find a control law that maximizes, based on the model (1) coupled with the sensitivity function (2) and the observer (4). Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, The observer for system (3) : (4) Proposed control approach Proposed control approach

9 Outline Preliminaries Case study Case study Outline Control problem statement Simulation results Simulation results software main features software main features Conclusion & perspectives Conclusion & perspectives Control problem statement 1. Control problem statement 2. Preliminaries Parametric sensitivity model Observer for state-affine systems 3. Proposed control approach Model predictive control (MPC) Final control structure 4. Case study Model for powder coating curing process 5. CB software main features Simulation results 6. Simulation results Conclusion & perspectives 7. Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

10  Model Predictive Control (MPC) Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

11  Model Predictive Control (MPC) Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features Advantages: constraints (such as manipulated variables physical limitations, constraints due to operating procedures 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 time suboptimal solutions how to handled unfeasibilities Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

12  Model Predictive Control (MPC) Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features The function a means: trajectory tracking, processing time minimization, energy consumption minimization, sensitivity maximization, … Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

13  Model Predictive Control (MPC) Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features [ Dufour et al, IEEE TCST 11(5) 2003] Originally 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 + sensitivities computed off line One line use of a time varying linear model One line resolution of the penalized (and so unconstrained) optimization control problem: as modified Levenberg Marquart Algorithm The turnkey software is used Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

14  Final control structure Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features Cost function to minimize: Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, To maximize the parametric sensitivity of the process output  Proposed control approach Proposed control approach

15  Final control structure Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach Linearized IMC-MPC observer based structure for coupled input design and parameter estimation

16 Outline Preliminaries Case study Case study Outline Proposed control approach Proposed control approach Control problem statement Simulation results Simulation results software main features software main features Conclusion & perspectives Conclusion & perspectives Control problem statement 1. Control problem statement 2. Preliminaries Parametric sensitivity model Observer for state-affine systems 3. Proposed control approach Model predictive control (MPC) Final control structure 4. Case study Model for powder coating curing process 5. CB software main features Simulation results 6. Simulation results Conclusion & perspectives 7. Conclusion & perspectives IFAC’08, Korea, July,

17  Model for powder coating curing process Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features Powder coatings = fine particles of: resin +cross-linker in thermosetting or thermoplastic powder coatings+ pigments + extenders + flow additives and fillers to achieve specific properties (color,…) Schematic drawing of the “substrat + powder” sample Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

18  Model for powder coating curing process Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features Thermal model based on the Fourier law of heat conduction uses: 1.the temperature variable varying in the thickness of the powder coating metal sample 2. the degree of cure conversion variable (ranging from 0+ to 1 and the end) A non linear PDE Boundary control problem has to be tackled Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

19  Model for powder coating curing process Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features [Bombard et al, 2006]  0t,e0,z x)(1xek C ΔHe z t)(z,T Cρ λ t t)(z,T p nm ) t)(z,RT E ( 0 pp 0p 2 p 2 p pc,p p a         Tp(z,t) = temperature across the powder film thickness ep = film thickness (~ 0.1 mm ) x(z,t) = degree of cure  0t,ee,ez z t)(z,T Cρ λ t t)(z,T spp 2 s 2 pss sc, s       Ts(z,t) = temperature across substrate es = film thickness (~ 1 mm ) Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

20  Model for powder coating curing process Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features [Bombard et al, 2006] 3 boundary conditions for the temperature: 0t 0,z at )Tt)(z,(Th)Tt)(z,(Tσε(t)φα z t)(z,T λ extpp 4 4 ppirp p p      Manipulated variable Estimated parameter 0t,ez at z t)(z,T λ z t)(z,T λ p p sc, p p        0t,eez at )Tt)(z,(Th)Tt)(z,(Tσε z t)(z,T λ sp extss 4 4 ss s s      Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

21  Model for powder coating curing process Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features [Bombard et al, 2006] The degree of cure x(z,t) of the powder:  0t,e0,z x)(1xek t t)x(z, p nm ) t)(z,RT E ( 0 p a     Initial conditions: 0t],ee[0,zTt)(z,Tt)(z,T spextsp  0t],e[0,z0t)x(z, p   Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

22 Outline Preliminaries Case study Case study Outline Proposed control approach Proposed control approach Control problem statement Simulation results Simulation results software main features software main features Conclusion & perspectives Conclusion & perspectives Control problem statement 1. Control problem statement 2. Preliminaries Parametric sensitivity model Observer for state-affine systems 3. Proposed control approach Model predictive control (MPC) Final control structure 4. Case study Model for powder coating curing process 5. CB software main features Simulation results 6. Simulation results Conclusion & perspectives 7. Conclusion & perspectives IFAC’08, Korea, July,

23 Preliminaries Case study Case study Outline Proposed control approach Proposed control approach Control problem statement Simulation results Simulation results software main features software main features Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Developed under Matlab, solvers any users defined: trajectory tracking problem maximization of the parameter sensitivity operating time minimization problem any cost function input/output constraint handled Any user defined continuous model (SISO, MISO, SIMO, MIMO model), including large scale PDE model Easy to introduce a user defined observer Easy to apply software for simulation or real time application flexibility/ ease for a quick use in control!

24 Outline Preliminaries Case study Case study Outline Proposed control approach Proposed control approach Control problem statement Simulation results Simulation results software main features software main features Conclusion & perspectives Conclusion & perspectives Control problem statement 1. Control problem statement 2. Preliminaries Parametric sensitivity model Observer for state-affine systems 3. Proposed control approach Model predictive control (MPC) Final control structure 4. Case study Model for powder coating curing process 5. CB software main features Simulation results 6. Simulation results Conclusion & perspectives 7. Conclusion & perspectives IFAC’08, Korea, July,

25 Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features Optimal infrared flow magnitude (input), with output constraint (sample time= 1s) Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

26 Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features Temperature in process output, with magnitude+ velocity input constraints+ output constraint (sample time= 1s) Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

27 Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features Sensitivity of the process output, with magnitude+ velocity input constraints+ output constraint (sample time= 1s) Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

28 Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results software main features software main features Parameter estimation, with magnitude+ velocity input constraints+ output constraint (sample time= 1s) Conclusion & perspectives Conclusion & perspectives IFAC’08, Korea, July, Proposed control approach Proposed control approach

29 Outline Preliminaries Case study Case study Outline Proposed control approach Proposed control approach Control problem statement Simulation results Simulation results software main features software main features Conclusion & perspectives Conclusion & perspectives Control problem statement 1. Control problem statement 2. Preliminaries Parametric sensitivity model Observer for state-affine systems 3. Proposed control approach Model predictive control (MPC) Final control structure 4. Case study Model for powder coating curing process 5. CB software main features Simulation results 6. Simulation results Conclusion & perspectives 7. Conclusion & perspectives IFAC’08, Korea, July,

30 Outline Control problem statement Preliminaries Case study Case study Simulation results Simulation results Conclusion & perspectives Conclusion & perspectives software main features software main features IFAC’08, Korea, July, Conclusions Approach coupling a process model, a parametric sensitivity model, an observer and a predictive controller was used on line for optimal constrained optimization Optimal identification of PDE system by a general software has been shown Perspectives Extended for other process models and for parameter vector case To use : Proposed control approach Proposed control approach

31 Thank you Any questions ? IFAC’08, Korea, July,