Batch-to-batch strategies for cooling crystallization

Transcription

1 Batch-to-batch strategies for cooling crystallization Marco Forgione 1, Ali Mesbah 1, Xavier Bombois 1, Paul Van den Hof 2 1 Delft University of echnology Delft Center for Systems and Control 2 Eindhoven University of echnology Delft Center for Systems and Control 51 th IEEE Conference on Decision and Control Grand Wailea, Maui, Hawaii Marco Forgione (U Delft) B2B strategies CDC / 19

2 Motivation Many operations are performed in batch mode. Batch processes bring both challenges and opportunities for control. Challenges Wide dynamical range Limited measurements* Opportunities Slow dynamics Repetitive nature * In this presentation: batch-to-batch learning control for cooling crytallization which exploit the repetitive nature. Iterative Learning Control (ILC) Iterative Identification Control (IIC). Marco Forgione (U Delft) B2B strategies CDC / 19

3 Motivation Many operations are performed in batch mode. Batch processes bring both challenges and opportunities for control. Challenges Wide dynamical range Limited measurements* Opportunities Slow dynamics Repetitive nature * In this presentation: batch-to-batch learning control for cooling crytallization which exploit the repetitive nature. Iterative Learning Control (ILC) Iterative Identification Control (IIC). Marco Forgione (U Delft) B2B strategies CDC / 19

4 Outline 1 Batch crystallization 2 Batch-to-batch Strategies: ILC and IIC 3 Simulation Results Marco Forgione (U Delft) B2B strategies CDC / 19

5 Batch Crystallization Process Description Separation and purification process of industrial interest. A solution is cooled down, solid crystals are produced. 1 Hot solution fed into the vessel. 2 Start cooling. 3 Introduce seeds. 4 Cool to final temperature. Seeds grow, new crystal are generated. 5 Remove final product. Marco Forgione (U Delft) B2B strategies CDC / 19

6 Batch Crystallization Process Description Separation and purification process of industrial interest. A solution is cooled down, solid crystals are produced. 1 Hot solution fed into the vessel. 2 Start cooling. 3 Introduce seeds. 4 Cool to final temperature. Seeds grow, new crystal are generated. 5 Remove final product. Marco Forgione (U Delft) B2B strategies CDC / 19

7 Batch Crystallization Process Description Separation and purification process of industrial interest. A solution is cooled down, solid crystals are produced. 1 Hot solution fed into the vessel. 2 Start cooling. 3 Introduce seeds. 4 Cool to final temperature. Seeds grow, new crystal are generated. 5 Remove final product. Marco Forgione (U Delft) B2B strategies CDC / 19

8 Batch Crystallization Process Description Separation and purification process of industrial interest. A solution is cooled down, solid crystals are produced. 1 Hot solution fed into the vessel. 2 Start cooling. 3 Introduce seeds. 4 Cool to final temperature. Seeds grow, new crystal are generated. 5 Remove final product. Marco Forgione (U Delft) B2B strategies CDC / 19

9 Batch Crystallization Process Description Separation and purification process of industrial interest. A solution is cooled down, solid crystals are produced. 1 Hot solution fed into the vessel. 2 Start cooling. 3 Introduce seeds. 4 Cool to final temperature. Seeds grow, new crystal are generated. 5 Remove final product. Marco Forgione (U Delft) B2B strategies CDC / 19

10 Batch Crystallization Modeling Process described by: hermal Dynamics from the actuator to the vessel temperature. Linear, known or easy to derive/estimate. Crystallization Dynamics from the reactor temperature to the crystallization properties. Nonlinear PDE, parametric + structural uncertainties possible. e Batch crystallizer Y J Y Y emperature Dynamics Crystallization Dynamics Marco Forgione (U Delft) B2B strategies CDC / 19

11 Batch Crystallization Control Strategies: industrial practice Only the crystallizer temperature is measured and controlled on-line. r emperature Controller J hermal Dynamics Batch crystallizer Crystallization Dynamics e Y Y Y e Control strategies such as MPC proposed in the literature. hey rely on reliable on-line measurements, not always available. Alternative approach based on Batch-to-batch Control. Marco Forgione (U Delft) B2B strategies CDC / 19

12 Batch Crystallization Control Strategies: industrial practice Only the crystallizer temperature is measured and controlled on-line. r emperature Controller J hermal Dynamics Batch crystallizer Crystallization Dynamics e Y Y Y e Control strategies such as MPC proposed in the literature. hey rely on reliable on-line measurements, not always available. Alternative approach based on Batch-to-batch Control. Marco Forgione (U Delft) B2B strategies CDC / 19

13 Batch Crystallization Control Strategies: industrial practice Only the crystallizer temperature is measured and controlled on-line. r emperature Controller J hermal Dynamics Batch crystallizer Crystallization Dynamics e Y Y Y e Control strategies such as MPC proposed in the literature. hey rely on reliable on-line measurements, not always available. Alternative approach based on Batch-to-batch Control. Marco Forgione (U Delft) B2B strategies CDC / 19

14 Batch-to-batch Control Architecture A framework for batch-to-batch control. r k Built on top of the standard industrial control. updated from batch to batch. Can use measurements available at the end of the batch. B2B (ILC or IIC) r emperature Controller J hermal Dynamics Batch crystallizer Crystallization Dynamics(θ) e Y Y Y e Objective for batch k: tracking of supersaturation profile S k. Marco Forgione (U Delft) B2B strategies CDC / 19

15 Batch-to-batch Control Architecture A framework for batch-to-batch control. r k Built on top of the standard industrial control. updated from batch to batch. Can use measurements available at the end of the batch. B2B (ILC or IIC) r emperature Controller J hermal Dynamics Batch crystallizer Crystallization Dynamics(θ) e C C C e SC (, ) S Objective for batch k: tracking of supersaturation profile S k. Marco Forgione (U Delft) B2B strategies CDC / 19

16 Batch-to-batch Strategies Iterative Learning Control ILC based on an additive correction of a nominal model from r to S. Ŝ( r ) Ŝ k ( r ) Ŝ( r ) + α k nominal model corrected model Note: r, α k vectors of samples R N (N = batch length). We describe the system in discrete, finite time (static mapping). A nonparametric model correction. α k can compensate for model mismatch (along a particular trajectory) effect of repetitive disturbances Marco Forgione (U Delft) B2B strategies CDC / 19

17 Batch-to-batch Strategies Iterative Learning Control ILC based on an additive correction of a nominal model from r to S. Ŝ( r ) Ŝ k ( r ) Ŝ( r ) + α k nominal model corrected model Note: r, α k vectors of samples R N (N = batch length). We describe the system in discrete, finite time (static mapping). A nonparametric model correction. α k can compensate for model mismatch (along a particular trajectory) effect of repetitive disturbances Marco Forgione (U Delft) B2B strategies CDC / 19

18 Iterative Learning Control Correction vector How to obtain the correction vector α? In principle, match the measurement from the previous batch. α k+1 = S k Ŝ(r k ) = model error k Due to nonrepetitive disturbances on S k, this is not a good solution. ake into account the deviation from α k. α k+1 = arg min α R N S k (Ŝ(r ) + α) 2 Q α + α α k 2 S α Careful tuning of Q α, S α is delicate. Marco Forgione (U Delft) B2B strategies CDC / 19

19 Iterative Learning Control Correction vector How to obtain the correction vector α? In principle, match the measurement from the previous batch. α k+1 = S k Ŝ(r k ) = model error k Due to nonrepetitive disturbances on S k, this is not a good solution. ake into account the deviation from α k. α k+1 = arg min α R N S k (Ŝ(r ) + α) 2 Q α + α α k 2 S α Careful tuning of Q α, S α is delicate. Marco Forgione (U Delft) B2B strategies CDC / 19

20 Iterative Learning Control Correction vector How to obtain the correction vector α? In principle, match the measurement from the previous batch. α k+1 = S k Ŝ(r k ) = model error k Due to nonrepetitive disturbances on S k, this is not a good solution. ake into account the deviation from α k. α k+1 = arg min α R N S k (Ŝ(r ) + α) 2 Q α + α α k 2 S α Careful tuning of Q α, S α is delicate. Marco Forgione (U Delft) B2B strategies CDC / 19

21 Iterative Learning Control Algorithm Steps of the ILC algorithm. At each batch k: 1 r k is set as the input to the controller, the batch is executed. S k is estimated from measurements. 2 An additive correction of the nominal model is performed: Ŝ k ( r ) Ŝ( r ) + α k. 3 he corrected model is used to design r k+1 for the next batch: r k+1 = arg min r R N S k+1 Ŝ k ( r ) 2 B2B (ILC or IIC) r emperature Controller J hermal Dynamics Batch crystallizer Crystallization Dynamics(θ) e C C C e SC (, ) S Marco Forgione (U Delft) B2B strategies CDC / 19

22 Iterative Learning Control Algorithm Steps of the ILC algorithm. At each batch k: 1 r k is set as the input to the controller, the batch is executed. S k is estimated from measurements. 2 An additive correction of the nominal model is performed: Ŝ k ( r ) Ŝ( r ) + α k. 3 he corrected model is used to design r k+1 for the next batch: r k+1 = arg min r R N S k+1 Ŝ k ( r ) 2 B2B (ILC or IIC) r emperature Controller J hermal Dynamics Batch crystallizer Crystallization Dynamics(θ) e C C C e SC (, ) S Marco Forgione (U Delft) B2B strategies CDC / 19

23 Iterative Learning Control Algorithm Steps of the ILC algorithm. At each batch k: 1 r k is set as the input to the controller, the batch is executed. S k is estimated from measurements. 2 An additive correction of the nominal model is performed: Ŝ k ( r ) Ŝ( r ) + α k. 3 he corrected model is used to design r k+1 for the next batch: r k+1 = arg min r R N S k+1 Ŝ k ( r ) 2 B2B (ILC or IIC) r emperature Controller J hermal Dynamics Batch crystallizer Crystallization Dynamics(θ) e C C C e SC (, ) S Marco Forgione (U Delft) B2B strategies CDC / 19

24 Iterative Identification Control Implementation IIC is based on a parametric correction assuming a certain model structure. Ŝ( r, θ) Ŝ k ( r, ˆθ k ) model structure IIC corrected model Iterative estimation of ˆθ k combining information from previous measurement. Given a new measurement Ỹ k = ( k C k ): he a posteriori probability of θ is computed (Bayes rules): ˆθ k+1 is taken as arg max over θ of the distribution (MAP estimate) In our case (under simplifying assumptions) ( ˆθ k+1 = arg min C k Ĉ( k, θ) 2 + θ ˆθ θ Σ 1 k 2 ) e Σ 1 θ k A Nonlinear Least Squares problem with a regularization term. Marco Forgione (U Delft) B2B strategies CDC / 19

25 Iterative Identification Control Implementation IIC is based on a parametric correction assuming a certain model structure. Ŝ( r, θ) Ŝ k ( r, ˆθ k ) model structure IIC corrected model Iterative estimation of ˆθ k combining information from previous measurement. Given a new measurement Ỹ k = ( k C k ): he a posteriori probability of θ is computed (Bayes rules): ˆθ k+1 is taken as arg max over θ of the distribution (MAP estimate) In our case (under simplifying assumptions) ( ˆθ k+1 = arg min C k Ĉ( k, θ) 2 + θ ˆθ θ Σ 1 k 2 ) e Σ 1 θ k A Nonlinear Least Squares problem with a regularization term. Marco Forgione (U Delft) B2B strategies CDC / 19

26 Iterative Identification Control Implementation IIC is based on a parametric correction assuming a certain model structure. Ŝ( r, θ) Ŝ k ( r, ˆθ k ) model structure IIC corrected model Iterative estimation of ˆθ k combining information from previous measurement. Given a new measurement Ỹ k = ( k C k ): he a posteriori probability of θ is computed (Bayes rules): ˆθ k+1 is taken as arg max over θ of the distribution (MAP estimate) In our case (under simplifying assumptions) ( ˆθ k+1 = arg min C k Ĉ( k, θ) 2 + θ ˆθ θ Σ 1 k 2 ) e Σ 1 θ k A Nonlinear Least Squares problem with a regularization term. Marco Forgione (U Delft) B2B strategies CDC / 19

27 Iterative Identification Control Algorithm Steps of the IIC algorithm. At each k: is set as the input to the controller, the batch is executed. ( C k, k ) are measured. 1 r k 2 he updated parameter ˆθ k is computed and the corrected model is defined as Ŝ k ( r ) Ŝ( r, ˆθ k ). 3 he corrected model is used to design r k+1 for the next batch to track a set-point S k+1 r k+1 = arg min r R N S k+1 Ŝk( r ) 2 Marco Forgione (U Delft) B2B strategies CDC / 19

28 Simulation Results Scenario N it = 30 iterations (batches) Objective: tracking of a set-point S k Set-point change in batch 11 r updated from batch to batch using ILC and IIC B2B (ILC or IIC) r emperature Controller J hermal Dynamics Batch crystallizer Crystallization Dynamics(θ) e C C C e SC (, ) S Marco Forgione (U Delft) B2B strategies CDC / 19

29 Simulation Results Cases Simulation study in two different scenarios Case 1: Disturbances + parametric model mismatch B2B (ILC or IIC) r emperature Controller J hermal Dynamics Batch crystallizer Crystallization Dynamics(θ) e C C C e Marco Forgione (U Delft) B2B strategies CDC / 19

30 Simulation Results Cases Simulation study in two different scenarios Case 2: Disturbances + structural model mismatch B2B (ILC or IIC) r emperature Controller J hermal Dynamics Batch crystallizer Crystallization Dynamics(θ) e C C C e Marco Forgione (U Delft) B2B strategies CDC / 19

31 Simulation Results Case 1 Results for Case 1 emperature (C) Supersaturation (g/l) Batch Iterative Learning Control Batch 10 Batch 11 Batch ime (min) ime (min) emperature (C) Supersaturation (g/l) Iterative Identification Control Batch Batch 10 Batch 11 Batch ime (min) ime (min) α (g/l) ime (min) 1 1 IIC: faster convergence Marco Forgione (U Delft) B2B strategies CDC / 19

32 Simulation Results Case 2 Results for Case 2 emperature (C) Supersaturation (g/l) Batch Iterative Learning Control Batch 10 Batch 11 Batch ime (min) ime (min) emperature (C) Supersaturation (g/l) Iterative Identification Control Batch Batch 10 Batch 11 Batch ime (min) ime (min) α (g/l) ime (min) 1 1 ILC: convergence despite mismatch Marco Forgione (U Delft) B2B strategies CDC / 19

33 Simulation Results Summary Iterative Learning racking in presence of structure mismatch Close-form algorithm Slower convergence of the algorithm Learning of a trajectory: degradation if we change the set-point Iterative Identification Faster convergence with right model structure Learning of the full dynamics: easy to follow different setpoint Performance degradation with mismatches Numerical solution NLSQ required Marco Forgione (U Delft) B2B strategies CDC / 19

34 Conclusions A batch-to-batch architecture for cooling crystallization. Uses measurements available at the end of a batch. Built on top of standard control. Can cope with model mismatches and disturbances. Experiments going on. Future work Introduce excitation signals Combine ILC and IIC strategies. Marco Forgione (U Delft) B2B strategies CDC / 19

35 hank you. Questions? Marco Forgione (U Delft) B2B strategies CDC / 19