Control of a two-stage mixed suspension mixed product removal crystallizer⁎

Proceedings, 10th IFAC International Symposium on Proceedings, 10th IFAC International Symposium on Proceedings, 10th IFAC International Symposium on Advanced Control Chemical Processes Proceedings, 10th of IFAC International Symposium on at www.sciencedirect.com Available online Advanced Control of Chemical Processes Proceedings, 10th IFAC International Symposium on Advanced Control of Chemical Processes Shenyang, Liaoning, China, July 25-27, 2018 Advanced Control of China, Chemical Processes Shenyang, Liaoning, July 25-27, 2018 Advanced Control of Chemical Processes Shenyang, Liaoning, Liaoning, China, China, July July 25-27, 25-27, 2018 2018 Shenyang, Shenyang, Liaoning, China, July 25-27, 2018

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IFAC PapersOnLine 51-18 (2018) 898–903

Control Control Control mixed Control mixed mixed mixed

of a two-stage mixed suspension of of a a two-stage two-stage mixed mixed suspension suspension  product removal crystallizer of a two-stage mixed suspension product removal crystallizer product removal crystallizer  product removal crystallizer ∗ ∗ ¨

Marcella Porru ∗∗ Leyla Ozkan ∗ ¨ ∗ ∗ Marcella Porru ∗∗ Leyla Ozkan ¨ ∗ Marcella ¨ Marcella Porru Porru ∗ Leyla Leyla Ozkan Ozkan ∗ ¨ Eindhoven University of Technology, De Zaale, 5612AJ Eindhoven, Marcella Porru Leyla Ozkan Eindhoven University of Technology, De Zaale, 5612AJ Eindhoven, Eindhoven University of (e-mail: Technology, De Zaale, 5612AJ Eindhoven, TheUniversity Netherlands m.porru;[email protected]). Eindhoven of Technology, De Zaale, 5612AJ Eindhoven, The Netherlands (e-mail: m.porru;[email protected]). Eindhoven University of (e-mail: Technology, De Zaale, 5612AJ Eindhoven, The The Netherlands Netherlands (e-mail: m.porru;[email protected]). m.porru;[email protected]). The Netherlands (e-mail: m.porru;[email protected]). Abstract: In this work, we consider the problem of controlling a two-stage cooling mixed Abstract: In this work, we consider the problem of controlling aa two-stage cooling mixed Abstract: In work, consider the of cooling suspension removal (MSMPR) crystallizer. For this process, the temperature in Abstract: mixed In this thisproduct work, we we consider the problem problem of controlling controlling a two-stage two-stage cooling mixed mixed suspension mixed product removal (MSMPR) crystallizer. For this process, the temperature in Abstract: In this work, we consider the problem of controlling a two-stage cooling mixed suspension mixed removal crystallizer. For this the in the first crystallizer is manipulated for controlling the average dimension (d while it suspension mixed product product removal (MSMPR) (MSMPR) crystallizer. For crystal this process, process, the temperature temperature in 43 ), the first crystallizer is manipulated for controlling the average crystal dimension (d ), while it 43 suspension mixed product removal (MSMPR) crystallizer. For this process, the temperature in 43 thedesired first crystallizer crystallizer is the manipulated for of controlling thecrystallizer average crystal crystal dimension (d ), while it 43 is to maintain temperature the second at the minimum allowed value the first is manipulated for controlling the average dimension (d ), while it 43 is desired to maintain the temperature of the second crystallizer at the minimum allowed value thedesired first crystallizer is the manipulated controlling thecrystallizer average dimension it 43 ), while is to maintain temperature of the second at the minimum allowed value to guarantee maximum yield. Due tofor system nonlinearities and crystal process delays, the(d performance is desired to maintain the temperature of the second crystallizer at the minimum allowed value to guarantee maximum yield. Due to system nonlinearities and process delays, the performance is desired to maintain the temperature of the second crystallizer at the minimum allowed value to guarantee maximum yield. Due to system nonlinearities and process delays, the performance of guarantee traditionalmaximum PID controllers are to poor. A control schemeand is proposed to improve the closed to yield. Due system nonlinearities process delays, the performance of traditionalmaximum PID controllers are poor. A control scheme is proposed to improve the closed to guarantee yield. Due to system nonlinearities and process delays, the performance of PID controllers are poor. A scheme is to the closed loop performance achieve desired objectives. control scheme is based the of traditional traditional PIDand controllers are poor.control A control control schemeThe is proposed proposed to improve improve the on closed loop performance and achieve desired control objectives. The control scheme is based on the of traditional PID controllers are poor. A control scheme is proposed to improve the closed loop performance and achieve control objectives. The control scheme based the coupling of a PI controller anddesired a model-based nonlinear prediction block that is serves ason delay loop performance and achieve desired control objectives. The control scheme is based on the coupling of a PI controller and a model-based nonlinear prediction block that serves as delay loop performance and achieve desired control scheme objectives. The scheme basedasin ondelay the coupling of a PI controller and a model-based nonlinear block serves and disturbance compensator. The proposed hasprediction beencontrol tested on that the issystem case coupling of a PI controller and a model-based nonlinear prediction block that serves as delay and disturbance compensator. The proposed scheme has been tested on the system in case coupling of a PI controller and a model-based nonlinear prediction block that serves as delay and disturbance compensator. The proposed scheme has been tested on the system in case of disturbances the feed concentration, with scheme and without measurement It is observed and disturbancein compensator. The proposed has been tested onerrors. the system in case of disturbances in the feed concentration, with and without measurement It is observed and disturbance compensator. The proposed scheme has been tested onerrors. theresponse system in case of disturbances in the concentration, with and measurement errors. It that the proposed the PI controller by reducing the output settling of disturbances in scheme the feed feedoutperforms concentration, with and without without measurement errors. It is is observed observed that the proposed scheme outperforms the PI controller by reducing the output response settling of disturbances in the feed concentration, with and without measurement errors. It is observed that the scheme outperforms outperforms the the PI PI controller controller by by reducing reducing the the output output response response settling settling time the andproposed overshoot. that scheme time andproposed overshoot. that the proposed scheme outperforms the PI controller by reducing the output response settling time time and and overshoot. overshoot. time andIFAC overshoot. © 2018, (Internationalcontrol, Federation of Automatic Hosting by Elsevier Ltd. All rights reserved. Keywords: Model-based Nonlinear delayControl) compensation, Series of MSMPR crystallisers Keywords: Model-based control, Nonlinear delay compensation, Series of MSMPR crystallisers Keywords: Model-based control, Nonlinear delay compensation, Series of MSMPR crystallisers Keywords: Model-based control, Nonlinear delay compensation, Series of MSMPR crystallisers Keywords: Model-based control, Nonlinear delay compensation, Series of MSMPR crystallisers 1. INTRODUCTION and dynamic operation has been widely (Randolph and dynamic operation has been widely studied studied (Randolph 1. INTRODUCTION 1. and dynamic operation has been studied (Randolph Larson (1962); Shiau and widely Berglund (1987); Tavare 1. INTRODUCTION INTRODUCTION and dynamic operation has been widely studied (Randolph Larson (1962); Shiau and Berglund (1987); Tavare 1. INTRODUCTION Crystallization is an important separation process for the and dynamic operation has been widely studied (Randolph and Larson (1962); Shiau and Berglund (1987); Tavare Chivate (1978); Tavare et al. (1986); Alvarez et al. Crystallization is an important separation process for the and Larson (1962); Shiau and Berglund (1987); Tavare and Crystallization is an important separation process for the Chivate (1978); Tavare et al. (1986); Alvarez et al. production of high-value added chemicals in crystalline and Larson (1962); Shiau and Berglund (1987); Tavare Crystallization is an important separation process for the and Chivate (1978); Tavare et al. (1986); Alvarez et production of high-value added chemicals in crystalline (2011); Power et al. (2015)). However, only a few papers and Chivate (1978); Tavare et al. (1986); Alvarez et al. al. Crystallization is an important separation process for the (2011); Power et al. (2015)). However, only a few papers production high-value in crystalline form. It hasof been widely added used inchemicals pharmaceutical indus- and Chivate (1978); Tavare et al. (1986); Alvarez et al. production of high-value added chemicals in crystalline (2011); Power et al. However, only aa few papers deal with the of these units. Su et al. (2015) form. It has been widely used in pharmaceutical indus(2011); Power etcontrol al. (2015)). (2015)). However, only few papers production of high-value added chemicals in crystalline deal with the control of these units. Su et al. (2015) form. It has been widely used in pharmaceutical industry and carried out traditionally in batch mode. indusHow- (2011); Power et al. (2015)). However, only a few papers form. It has been widely used in pharmaceutical deal with the control of these units. Su et al. (2015) recommend thecontrol use of the concentration for try and traditionally in batch mode. indusHowdeal with the of these units. Su(C-)control et al. (2015) form. It carried hasoperations beenout widely used in pharmaceutical try carried out in batch Howthe use of the concentration (C-)control for ever,and batch suffer from disadvantages such as recommend deal with and the control of these units. Su et (2015a) al. (2015) try and carried out traditionally traditionally in batch mode. mode.such Howrecommend the use of the concentration (C-)control for ever, batch operations suffer from disadvantages as operation start-up control. Yang and Nagy use recommend the use of the concentration (C-)control for try and carried out traditionally in batch mode. However, batch operations suffer from disadvantages such as operation and start-up control. Yang and Nagy (2015a) use lack of batch to batch reproducibility, long processing recommend the use of the concentration (C-)control for ever, batch operations suffer from disadvantages such as operation and start-up control. Yang and Nagy (2015a) use lack of batch to batch reproducibility, long processing a nonlinear model predictive control (NMPC). Conversely, operation and start-up control. Yang (NMPC). and Nagy Conversely, (2015a) use ever, batch operations suffer from disadvantages such as a nonlinear model predictive control lack of batch to batch reproducibility, long processing times,ofscale-up issues, poor controllability,long and observabiloperation and start-up control. Yang and Nagy (2015a) use lack batch to batch reproducibility, processing model predictive control (NMPC). Conversely, studies have been devoted to solve the control probtimes, issues, poor controllability, and a nonlinear nonlinear model predictive control (NMPC). Conversely, lack ofscale-up batch to reproducibility, long processing amore studies have been devoted to solve the control probtimes, scale-up poor controllability, and observabil¨ batch ¨ observabilalem nonlinear model predictive control (NMPC). Conversely, times, scale-up issues, poor controllability, and observability (Porru and issues, Ozkan (2016); Porru and Ozkan (2017)). more ¨ ¨ more studies have been devoted to solve the control probin single stage MSMPR crystallizers. Multiple papers more studies have been devoted to solve the control probtimes, scale-up issues, poor controllability, and observability (Porru and Ozkan (2016); Porru and Ozkan (2017)). ¨ ¨ ity (Porru and Ozkan (2016); Porru and Ozkan (2017)). lem in single stage MSMPR crystallizers. Multiple papers ¨ ¨ more studies have been devoted to solve the control probOn (Porru the other hand, continuous production offers many ity and Ozkan (2016); Porru and Ozkan (2017)). lem in single stage MSMPR crystallizers. Multiple papers report the failure ofMSMPR traditional PID controllers duepapers to the ¨ ¨ lem in single stage crystallizers. Multiple On the other hand, continuous production offers many ity (Porru and Ozkan (2016); Porru and Ozkan (2017)). On the hand, continuous production many report failure traditional PID controllers due to the in the single stageof MSMPR crystallizers. Multiple papers advantages such as higher higher quality, productoffers uniformity On the other other hand, continuous production offers many lem report the failure of traditional PID controllers due to the system nonlinearities (Damour et al. (2010); Grosch et al. advantages such as quality, product uniformity report the failure of traditional PID controllers due to the On the other hand, continuous production offers many system nonlinearities (Damour et al. (2010); Grosch et al. advantages such as higher quality, product uniformity report the failure of traditional PID controllers due to the and process controllability (Su et al. (2015); Yang and advantages such as higher quality, product uniformity system nonlinearities (Damour et al. (2010); Grosch et al. (2008); Yang and Nagy (2015a)). Yang and Nagy (2015a) and process controllability (Su et al. (2015); Yang and system nonlinearities (Damour et al. (2010); Grosch et al. advantages such as higher quality, product uniformity and process controllability (Su et al. (2015); Yang and (2008); Yang and Nagy (2015a)). Yang and Nagy (2015a) nonlinearities (Damour et al. (2010); Grosch etlow al. Nagyprocess (2015a)). Therefore, recent research efforts Yang have been and controllability (Su research et al. (2015); and system (2008); Yang and Nagy (2015a)). Yang and Nagy (2015a) discourage the use of PID-type controllers due to the (2008); Yang and Nagy (2015a)). Yang and Nagy (2015a) Nagy (2015a)). Therefore, recent efforts have been and process controllability (Su et al. (2015); Yang and Nagy (2015a)). Therefore, recent research efforts have been discourage the use of PID-type controllers due to the low Yang and Nagy (2015a)). Yang and Nagy (2015a) directed towards developing continuous crystallisers (Su (2008); Nagy (2015a)). Therefore, recent research efforts have been discourage the use of PID-type controllers due to the low capability of changing operating discourage thedealing use of with PID-type controllers due conditions. to the low directed towards developing continuous crystallisers (Su Nagy Therefore, recent researchcrystallizer efforts havetypes been directed towards developing continuous crystallisers (Su capability of with changing operating conditions. thedealing use of PID-type controllers duecan to the low et al. al. (2015a)). (2015)). A number of continuous continuous directed towards developing continuous crystallizer crystalliserstypes (Su discourage capability of dealing with changing operating conditions. Overall it emerges that the control problem be sucet (2015)). A number of capability of dealing with changing operating conditions. directed towards developing continuous crystallisers (Su Overall it emerges that the control problem can be sucet al. (2015)). A number of continuous crystallizer types capability of dealing with changing operating conditions. and configurations have been applied, such as single stage et al. (2015)). A number of continuous crystallizer types emerges control problem can successfully onlythat by the means of advanced andal.configurations configurations have been been applied, such such as single single types stage Overall Overall it itsolved emerges that the control problem process can be be consucet (2015)).ofAmixed number of continuous crystallizer and have as stage only by means of advanced process Overall itsolved emerges that the control problem can be consucor multistage suspension mixed product removal and configurations havesuspension been applied, applied, such as single stage cessfully cessfully solved only by means of advanced process controllers (APC), able to incorporate kinetic crystallization cessfully solved only by means of advanced process conor multistage of mixed mixed product removal and configurations havesuspension been applied, as Wong single stage or multistage of mixed product removal trollers (APC), able to incorporate kinetic crystallization solved only by means of advanced process con(MSMPR) crystallisers (Alvarez etmixed al. such (2011); et al. cessfully or multistage of mixed suspension mixed product removal trollers (APC), able to incorporate kinetic crystallization information from measurements (i.e. Process Analytical trollers (APC), able to incorporate kinetic crystallization (MSMPR) crystallisers (Alvarez etmixed al. (2011); Wong et al. or multistage suspension product removal (MSMPR) (Alvarez Wong et al. information from measurements (i.e. Process Analytical (APC), able to incorporate kinetic crystallization (2012); Su crystallisers et of al.mixed (2015); Vetter et et al. al.(2011); (2014)), plug flow (MSMPR) crystallisers (Alvarez et al. (2011); Wong etflow al. trollers information from measurements (i.e. Process Analytical Technologies (PAT)) (Ward et al. (2010); Randolph et al. (2012); Su et al. (2015); Vetter et al. (2014)), plug information from measurements (i.e. Process Analytical (MSMPR) crystallisers (Alvarez et al. (2011); Wong et al. Technologies (PAT)) (Ward et al. (2010); Randolph et al. (2012); Su et al. (2015); et al. (2014)), flow information from measurements (i.e. Process Analytical crystallizers (PFC), with Vetter (Alvarez and Myersonplug (2010)), (2012); Su et al. (2015); Vetter et al. (2014)), plug flow Technologies (PAT)) (Ward et al. (2010); Randolph et al. (1987); Grosch et al. (2008)) and/or a (first principle) Technologies (PAT)) (Ward et al. (2010); Randolph et al. crystallizers (PFC), with (Alvarez and Myerson (2010)), (2012); Su et al. (2015); Vetter et al. (2014)), plug flow crystallizers (PFC), with (Alvarez and Myerson (2010)), (1987); Grosch et al. (2008)) and/or a (first principle) Technologies (Ward Randolph et al. al. or without (Ferguson et al.(Alvarez (2013)) static mixers, and more (1987); crystallizers (PFC), with and Myerson (2010)), Grosch et al. (2008)) and/or aa (first principle) process model(PAT)) (Moldov´ anyi et et al. al. (2010); (2005); Damour et (1987); Grosch et al. (2008)) and/or (first principle) or without (Ferguson et al. (2013)) static mixers, and more crystallizers (PFC), with (Alvarez and Myerson (2010)), or without (Ferguson et al. (2013)) static and more process model (Moldov´ aanyi et al. (2005); Damour et al. Grosch et Chianese al. (2008)) and/or a (first principle) recently, PFC with recycle (Cogoni et mixers, al. (2015)), slug (1987); or without (Ferguson et al. (2013)) static mixers, and more process model (Moldov´ nyi et al. (2005); Damour et al. (2010); Bravi and (2003); Abonyi et al. (2002)). process modeland (Moldov´ anyi (2003); et al. (2005); Damour et al. recently, PFC with recycle (Cogoni et al. (2015)), slug or without (Ferguson et al.et(2013)) static mixers, and more recently, PFC recycle (Cogoni et al. slug (2010); Chianese Abonyi et modeland (Moldov´ anyi (2003); et al. (2005); et al. flow crystallizers (Rasche al. (2016)), and periodic flow recently, PFC with with recycle (Cogoni et and al. (2015)), (2015)), slug process (2010); Bravi Bravi Chianese Abonyi Damour et al. al. (2002)). (2002)). flow crystallizers (Rasche et al. (2016)), periodic flow (2010); Bravi and Chianese (2003); Abonyi et al. (2002)). recently, PFC with recycle (Cogoni et al. (2015)), slug flow crystallizers (Rasche et al. (2016)), and periodic flow In this Bravi paper,and an Chianese alternative scheme for average crystal (2010); (2003); Abonyi et al. (2002)). crystallizers (Su et al. (2017)). flow crystallizers (Rasche et al. (2016)), and periodic flow this paper, an alternative scheme for average crystal crystallizers (Su et al. (2017)). flow crystallizers (Rasche et al. (2016)), and periodic flow In In this an alternative scheme average crystal crystallizers (Su (2017)). dimension control an industrial-scale two-stage In this paper, paper, an in alternative scheme for for averageMSMPR crystal crystallizers (Su et et al. al.crystallization (2017)). dimension control in an industrial-scale two-stage MSMPR In this paper, an alternative scheme for average crystal Multistage MSMPR is the most convenient crystallizers (Su et al. (2017)). dimension control in an an industrial-scale industrial-scale two-stage MSMPR crystallizers is proposed and tested in simulations. We Multistage MSMPR crystallization is the most convenient dimension control in two-stage MSMPR crystallizers is proposed and tested in simulations. We Multistage MSMPR crystallization the most convenient control in an industrial-scale two-stage MSMPR route of transition from batch to is continuous operation, dimension Multistage MSMPR crystallization is the most convenient crystallizers is proposed and tested in simulations. We have chosen a control scheme that combines feedback and crystallizers is proposed and tested in simulations. We route of transition from batch to continuous operation, Multistage MSMPR crystallization is the most convenient route of transition from batch to continuous operation, have chosen a control scheme that combines feedback and is proposed and tested in simulations. We since current crystallizers in industry are of the stirred crystallizers route of transition from batch to continuous operation, have chosen a control scheme that combines feedback and prediction elements. This is an effective andfeedback simple way have chosen a control scheme that combines and since current crystallizers in industry are of the stirred route of transition from batch to continuous operation, since current crystallizers in industry the stirred prediction This is an effective and simple way chosenelements. a control scheme that combines feedback and tank type (Power et al. (2015); Chen etare al.of (2011)). The have since current crystallizers in industry are of the stirred prediction elements. This is an effective and simple way to upgrade low level PI controllers to APCs that should prediction elements. This is an effective and that simple way tank type (Power et al. (2015); Chen etare al. The since current crystallizers in the industry of(2011)). theconfigustirred upgrade low level PI controllers to APCs should tank type (Power al. Chen al. The prediction elements. This is an effective and that simple way two-stage cascade system is mostet common tank type cascade (Power et et al. (2015); (2015); Chen etcommon al. (2011)). (2011)). The to to upgrade low level PI controllers to APCs should not require highly skilled personnel for controller commistwo-stage system is the most configuto upgrade low level PI controllers to APCs that should tank type (Power et al. (2015); Chen et al. (2011)). The not require highly skilled personnel for controller commistwo-stage cascade system is the most common configuto upgrade low level PI controllers to APCs that should ration because it guarantees a good trade off between two-stage cascade system is the most common configunot require highly skilled personnel for controller commissioning andhighly maintenance (Shinskeyfor (1990); Porru et al. not require skilled personnel controller commisration because it guarantees a off between two-stage cascade system the most trade common configuration because it aa good good between and maintenance (Shinskey (1990); Porru et al. not require skilled personnel for controller commisoperation complexity and is performance (Yangoff and Nagy sioning ration because it guarantees guarantees good trade trade offand between sioning and maintenance (Shinskey (1990); Porru et (2014)). Thehighly core of the control scheme is a PI controller sioning and maintenance (Shinskey (1990); Porru et al. al. operation complexity and performance (Yang Nagy ration because it guarantees a good trade off between operation complexity and performance (Yang and Nagy (2014)). The core of the control scheme is a PI controller sioning and maintenance (Shinskey (1990); Porru et al. (2015b)). Multistage MSMPR crystallization steady state operation complexityMSMPR and performance (Yangsteady and Nagy (2014)). The core of the control scheme is aa PI controller which manipulates the temperature setpoint in the first (2015b)). Multistage crystallization state (2014)). The core of the control scheme is PI controller operation complexity and performance (Yang and Nagy which manipulates the temperature setpoint in the first (2015b)). Multistage MSMPR crystallization steady state (2014)). The core of the control scheme is a PI controller (2015b)). Multistage MSMPR crystallization steady state which manipulates manipulates the that temperature setpoint indimension the first first crystallizer jacket such the average crystal which the temperature setpoint in the  This workMultistage (2015b)). MSMPR crystallization state crystallizer jacket such that the average crystal has been done within the IMPROVISE steady project in the which manipulates the temperature setpoint indimension theof first  This work has been done within the IMPROVISE project in the crystallizer jacket such that the average crystal dimension is maintained at the desired specification. Because the  crystallizer jacket such that the average crystal dimension This work work has been been done done within the IMPROVISE IMPROVISE project in in the the  This Institute for Sustainable Process Technology (ISPT). project is maintained at the desired specification. Because of the has within the crystallizer jacket such that the average crystal dimension  is maintained at the desired specification. Because of the Institute for Sustainable Process Technology (ISPT). This work has been done within the IMPROVISE project in the is maintained at the desired specification. Because of the Institute for Sustainable Process Technology (ISPT). Institute for Sustainable Process Technology (ISPT). is maintained at the desired specification. Because of the Institute for Sustainable Process Technology (ISPT). ∗ ∗ ∗ ∗ ∗ ∗

2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright © 2018 IFAC 898 Peer review© under responsibility of International Federation of Automatic Control. Copyright 2018 IFAC 898 Copyright © 898 Copyright © 2018 2018 IFAC IFAC 898 10.1016/j.ifacol.2018.09.231 Copyright © 2018 IFAC 898

2018 IFAC ADCHEM Marcella Porru et al. / IFAC PapersOnLine 51-18 (2018) 898–903 Shenyang, Liaoning, China, July 25-27, 2018

Table 2. Physical properties, and kinetic parameters

Table 1. Feed and operating conditions, and cooling specifications Cf Tf Ff T1 T2 τ1 τ2 TJ0 TJF U Cpj

Feed concentration Feed temperature Feed flow rate Temperature in the 1st stage Temperature in the 2nd stage Residence time in the 1st stage Residence time in the 2nd stage Coolant inlet temperature Coolant outlet temperature Overall heat transfer coefficient Specific heat of the coolant

97.2 40 100 14 5 67.2 50.13 -30 -15 450 3263.52

899

Cp ρ kv ρc kg0 Ea kb g b1 b2

g/kg ◦C kg/min ◦C ◦C min min ◦C ◦C W/m2 K J/kg K

large volumes involved, a large time delay between manipulated and controlled variables exists resulting in limitations in the performance of this standard PI controller. Hence, a delay compensator is also used. In this work, the delay compensation block for average crystal dimension prediction consists of the nonlinear dynamic crystallization model with simulation horizon equal to the time delay. Measured disturbances, if available, can be provided to this model-based block. This allows further performance improvements due to the prediction capability of the model. The paper is organized as follows. Section 2 describes the case study, and presents the dynamic model of the process. In section 3 the control problem is formulated. Section 4 describes the proposed control scheme. Closed loop performance of the proposed scheme is reported in section 5. Conclusions are given in section 6. 2. MODEL OF THE TWO-STAGE MSMPR COOLING CRYSTALLIZATION OF PARACETAMOL We consider the cooling crystallization of paracetamol from an aqueous isopropanol mixture as case study (Power et al. (2015)). The dominant crystallization kinetics are nucleation and growth. The crystallization is carried out in a series of two MSMPR crystallizers (Fig. 1), with feed condition, operating condition, and specification of the cooling system as in Table 1. The 50% ethylene glycol is a suitable coolant for this system. Physical properties and kinetic parameters are listed in Table 2. The model of the system consists of material and energy balances for the liquid and solid phase. Under the assumptions of constant volume, no agglomeration and breakage, small variations between the inlet and outlet flow rates, the solid phase dynamics are modelled by means of the moment model (Randolph and Larson (1971)) according to dmj,i 1 = 0j Bi + jGi mj−1,i + (mj,i−1 − mj,i ); (1) dt τi j = 0, .., mm ; i = 1, ..., Nc In eq.(1) the subscript j identifies the j-th moment. In this work it is sufficient to model up to the fourth moment (i.e., mm = 4). The subscript i identifies the i-th crystallizer. Nc is the number of crystallizers in the series. mj,i−1 = 0 for i = 1, because crystal-free feed is considered. Gi , and Bi are the crystal growth and birth rate in the crystallizer i respectively, according to the kinetics laws (eqs. 2) g  −E  C − C a i sat,i (Ti ) (2a) Gi = kg0 exp R Ti Csat,i (Ti ) 899

Specific heat of the liquid Liquid density Shape factor Crystal density Growth rate constant Activation energy Nucleation rate constant Growth order Nucleation order Secondary nucleation order

B i = kb

4564 970 0.866 1332e+3 3.34e−4 1.44e+4 295 1.08 2.14 1.6

J/kg K kg/m3 g/m3 m/s J/mol #/kg s -

b 1 C − C i sat,i (Ti ) (kv ρc m3,i )b2 Csat,i (Ti )

(2b)

The solubility Csat,i [g-solute/kg-solution] in the stage i as function of the temperature Ti [◦ C] is (3) Csat,i = 0.0379 Ti2 + 0.377 Ti + 20.7 The material balance in the liquid phase describes the dynamics of the solute concentration Ci according to  1 dCi = Ci−1 − Ci − 3ρc kv Gi m2,i , i = 1, ..., Nc (4) dt τi Ci−1 = Cf for i = 1 In case of negligible heat of crystallization, constant density ρ and specific heat Cp, the temperature dynamics are 1 Qi dTi = (Ti−1 − Ti ) − , Qi = mc,i Cpj (TJF − TJ0 ) dt τi ρVi Cp where Qi is the power absorbed by the jackets for the cooling. We assume that we are able to supply instantaneously the exact amount of energy required to put the crystallizer temperature at the desired temperature TiSP . Then, the following energy balance holds dTi =0 (5) dt The average crystal dimension of the solid product is given in terms of d43 m4,2 d43 = (6) m3,2 whose dynamics can be obtained with the product rule 1 d(m4,2 ) d  m4,2  d d43 d(m3,2 )−1 = = + m4,2 dt dt m3,2 m3,2 dt dt (7) 1 dm4,2 m4,2 dm3,2 d d43 == − dt m3,2 dt (m3,2 )2 dt The system has initial conditions: SS SS SS mj,i (0) = mSS j,i ; d43 (0) = d43 ; Ti (0) = Ti ; Ci (0) = Ci . The system (eqs. 1-7) is nonlinear and coupled. If the input-output (T1 − d43 ) response is approximated with a first order model plus delay (Ogunnaike and Ray (1994)) one can obtain the following: characteristic time τP = 235 min, process gain KP = 8µ m/◦ C, and time delay td = 50 min. This response is slow with a large time delay. This poses severe limitation on the performance of traditional PI for the control of the crystallization. The model (eqs. 1-7) will be used for control synthesis, and performance testing. 3. CONTROL PROBLEM The crystal size distribution (CSD) is an important property of a crystallization process. It can determine the

2018 IFAC ADCHEM 900 Marcella Porru et al. / IFAC PapersOnLine 51-18 (2018) 898–903 Shenyang, Liaoning, China, July 25-27, 2018

TSP TT

Fin Tin FT FC

TT

TJ1,F

T1 τ1

d43C

d43T

TC

LC

T2 τ2

TJ2,F

TJ1,0

d43 LC

TJ2,0

TC MSMPR 1

MSMPR 2

TT

TC

Fig. 1. The two stages MSMPR crystallizer and its control scheme. efficiency of the downstream operations, as well as the end-use properties (such as bioavailability). The control of the full CSD is not possible in practice. However some of its attributes (average size, coefficient of variation, fines fraction, etc.) can be controlled. The scope of this work is to achieve the control of the average dimension (mean diameter) of the crystals d43 (eq.6) which is also known the De Brucker mean. Figure 1 shows a suitable control scheme for the two stage MSMPR crystallization. Assuming that the d43 can be measured (Mesbah et al. (2011); Nagy and Braatz (2003); Jager et al. (1992)) or estimated (Afsi et al. (2016); Ghadipasha et al. (2015); Zhang et al. (2014)), we propose to control it by varying the temperature of the first crystallizer (T1 ) with a cascade controller. The master controller establishes the temperature set-point T1SP based on the deviation of the d43 from the desired value and a prediction of the future values of the d43 obtained with the model (eqs. 1-7). This predictor functions as a nonlinear delay compensator. The slave controller manipulates the coolant flow rate to maintain the temperature at the desired value. The temperature of the second crystallizer T2 is maintained at the minimum allowed value (5◦ C, see Table 1) to guarantee the maximum yield. For simplification, we assume perfect slave temperatures control (TC) by manipulating the coolant flow rates, and perfect levels control (LC) by manipulating the product flows. We finally assume perfect control of the feed temperature and flow rate (FC). These loops are depicted in grey in Fig. 1. We also assume no model-plant mismatch. Similar assumptions are adopted also in the paper of Yang and Nagy (2015a). In the following, we focus on the design of the master d43 controller (black loop in Fig. 1, and Fig. 2). 4. CONTROL OF THE d43 For the control of the average crystal dimension d43 we propose the use of a PI controller (d43 C) together with a nonlinear delay compensator (NDC). The block diagram of this scheme is summarized in Fig. 2. The control law is    M2 t T1SP = T1N OM + M1 KC S + S (τ )dτ (8) τC 0 τP In eq.(8) KC = , and τC = 3.33td are the controller K P td tuning parameters according to Ziegler and Nichols (1942) and Smith and Corripio (1985). M1 and M2 are multipliers 900

δ=d̂ 43(t+td)-d̂ 43(t) NDC

SP

d43

+-

d

δ -

εs

d43C

u = T1

SP

Process

d43

Fig. 2. Block diagram of the advanced master d43 controller. The block d43 C is the linear PI controller with modified error signal S ; the block NDC is the nonlinear delay compensator, which can incorporate, if available, exogenous disturbance measurements d. for tuning refinement that are adjusted by means of an procedure that minimizes the ITAE =  ∞ optimization SP t |d − d (t)| dt. 43 43 0

The feedback controller (eq.8) sees the error signal S (see Fig. 2) S (t) = dSP (9) 43 − (d43 (t) + δ(t)) where d43 is the measurement signal, and the signal δ(t) is calculated by the NDC block by means of average crystal dimension predictions: δ(t) = dˆ43 (t + td ) − dˆ43 (t) (10)

Practically speaking the NDC block consists of the process dynamic model (eqs. 1-7), and uses the actual control action (eq.8). Based on this information, the process model is run to estimate the actual value of the average crystal size dˆ43 (t), and the value of average dimension of the crystals dˆ43 (t + td ) after the time delay td . In other words, the model runs with a time horizon (t + td ), and the prediction dˆ43 (t + td ) is compared with the estimation at the current time dˆ43 (t) to generate the differential signal δ(t). It must be pointed out that the moment model is not computationally expensive due to the relative low system dimension (13 dynamic states), and the short time horizon. Hence, the proposed dynamic model can be used online. If available, the compensator can incorporate exogenous disturbance measurements, such as variations in the feed concentration. In this way, the delay compensator acts as a feedforward controller without the need to calculate the inverse of the process model. The incorporation of the

2018 IFAC ADCHEM Marcella Porru et al. / IFAC PapersOnLine 51-18 (2018) 898–903 Shenyang, Liaoning, China, July 25-27, 2018

model in the control scheme also allows the monitoring of the control input constrains (T1 | Gi > 0 always) to avoid crystal dissolution.

The control performance is tested under disturbances in feed concentration, and systematic d43 measurements error for (i) the PI control strategy (eq.8 and signal δ(t) = 0), (ii) the PI plus the NDC control strategy (eqs. 8-10), (iii) and the PI, NDC control strategy (eqs. 8-10) and disturbance measurements. In each configuration the controller parameters M1 , M2 minimize the ITAE. Closed loop responses for the system subjected to a feed concentration disturbance  at t < 200 min Cf Cf = (11) Cf − 2 at t ≥ 200 min

are depicted in Fig. 3 in the case of d43 measurements free of errors, and in Fig. 4 in case of systematic error in the d43 measurements (+5µm).

In Fig. 3 it can be observed that the PI controller alone (—–) has poor closed loop performance, with slow settling time (≈ 4.2τp , more than 1000 min). This is in agreement with the findings of Ward et al. (2010). Furthermore, the realization of the controller with delay compensation (—–) outperforms the PI alone (—–) by immediately varying the manipulated variable (Fig. 3b). This control scheme allows to reduce the time to the steady state more than 50% (≈ 1.7τp ). This is because the PI plus NDC accepts a much more aggressive tuning without the destabilization of the closed loop response. If feed concentration measurements are incorporated in the delay compensator, the advanced controller guarantees almost no perturbation of the d43 (— –). In this latter case, the predictor is in fact a feedforward element able to fully and very quickly suppress the effect of the disturbance without the need of the inverse of the model. Also in the case of systematic errors (Fig. 4) the delay compensation, with or without concentration measurements, has a beneficial effect of the closed loop settling time. Optimal tuning of the schemes leads to an ITAE=0.193 for the PI alone, ITAE=0.173 for the PI plus NDC, and ITAE=0.142 for the PI, NDC and disturbance measurements. It could be interesting to exploit the prediction model for measurement bias detection, to further improve the control performance. However, this research question is left for future work, in the understanding that Jager et al. (1992) report that d43 measurements are accurate and reproducible, hence systematic errors can be avoided by using the appropriate PAT. Finally, we have tested the performance of the controllers with their optimal tuning, without measurement errors, for feed concentration disturbances up to 10% the nominal value: 901

M 1 =9.6538 M 2 =336

ITAE=0.056941 NDC=yes Concentration Meas.=no

6.265

M1=0.5623 M 2=388

6.26

d 43,2 [m]

5. RESULTS

× 10-4

(a)

ITAE=6.0202e-05 NDC=yes Concentration Meas.=yes

6.255

M1=0.142 M 2=1.429 ITAE=0.24528 NDC=no Concentration Meas.=no

6.25 6.245 6.24

0

200 400 600 800 100012001400160018002000

Time [min] 14 (b)

13.95

M 1 =9.6538 M 2 =336

NDC=yes Concentration Meas.=no

13.9

M1=0.5623 M 2=388 NDC=yes Concentration Meas.=yes

13.85

T 1 [°C]

This NDC can be seen as a nonlinear realization of the Smith Predictor (Smith (1959)). Overall, the APC can be classified as an observer-based controller for delay systems (Richard (2003)).

6.27

901

13.8

M1=0.142 M 2=1.429 NDC=no Concentration Meas.=no

13.75 13.7 13.65 13.6 13.55 0

200 400 600 800 100012001400160018002000

Time [min]

Fig. 3. (a) d43 closed loop response after disturbance in the feed concentration (eq.11). (b) Manipulated variable (T1 ) load. PI controller without NDC (—). PI controller with NDC (eq.10), without (—) and with (—) feed concentration measurements. Free of measurements error.   Cf     Cf Cf = C f    Cf    Cf

−2 −5 − 10 −5

at at at at at

t < 200 min t ≥ 200 min t ≥ 1200 min t ≥ 2200 min t ≥ 3200 min

(12)

The closed loop performance is presented in Fig. 5a, while the manipulated variable load is depicted in Fig. 5b. One can notice that the designed controllers are able to reject the severe feed concentration disturbances. We observe that the PI alone is very slow in achieving the task leadingto long operating time with off-specification crystal production. The use of the NDC allows to reduce the settling time, and guarantees a lower deviation of the d43 from the desired value. Finally, if disturbance measurements are available, they can be incorporated in the prediction model to reject the disturbance before it causes deviations in d43 .

2018 IFAC ADCHEM 902 Marcella Porru et al. / IFAC PapersOnLine 51-18 (2018) 898–903 Shenyang, Liaoning, China, July 25-27, 2018

×10-4

(a)

d 43,2 [m]

6.25 6.24

M 1 =0.16548 M 2 =0.70727

6.23

NDC=yes Concentration Meas.=yes

ITAE=0.1419

M1=0.51625 M 2=0.95518 ITAE=0.17331 NDC=yes Concentration Meas.=no

6.22

M1=0.1347 M 2=0.4067 ITAE=0.19335 NDC=no Concentration Meas.=no

6.21 6.2

0

200 400 600 800 1000 1200 1400 1600 1800 2000

Time [min] 14.5 (b)

T 1 [°C]

14

13.5

M1=0.16548 M 2=0.707279 NDC=yes Concentration Meas.=yes

13

M1=0.51625 M 2=0.95518 NDC=yes

Concentration Meas.=no

12.5

M1=0.1347

M2=0.4067

NDC=no

12

Concentration Meas.=no

0

200 400 600 800 1000 1200 1400 1600 1800 2000

Time [min]

Fig. 4. (a) d43 closed loop response after disturbance in the feed concentration (eq.11). (b) Manipulated variable (T1 ) load. PI controller without NDC (—). PI controller with NDC (eq.10), without (—) and with (—) feed concentration measurements. Systematic error (+5 µm) in the d43 measurements. 6. CONCLUSIONS In this work, we have designed a controller to maintain the d43 at the desired value under feed concentration disturbances in a two stage MSMPR crystallizer. The controller consists of a PI controller with control action based on a modified error signal. This error signal compares the setpoint with both the d43 measurements and d43 model prediction in order to compensate for dead time and disturbances. The controller achieves decreasing the settling time and the overshoot of the output compared to a traditional PI controller. The work has considered an ideal case of no plant-model mismatch. Further anaylysis is needed for closed loop stability and performance. REFERENCES Abonyi, J., Lakatos, B., and Ulbert, Z. (2002). Modelling and control of isothermal crystallizers by self-organising maps. Chem. Eng. Trans, 1(3), 1329–1334. Afsi, N., Bakir, T., Othman, S., Sheibat-Othman, N., and Sakly, A. (2016). Estimation of the mean crystal size and the moments of the crystal size distribution in batch 902

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2018 IFAC ADCHEM Marcella Porru et al. / IFAC PapersOnLine 51-18 (2018) 898–903 Shenyang, Liaoning, China, July 25-27, 2018

6.3

903

× 10-4

d 43,2 [m]

(a) 6.25 M 1 =0.5623 M 2 =388 ITAE=0.004304 Delay Comp.=yes Concentration Meas.=yes M 1 =9.6538 M 2 =336 ITAE=2.4177 Delay Comp.=yes Concentration Meas.=no

6.2

M 1 =0.142 M 2 =1.429 ITAE=9.1954 Delay Comp.=no Concentration Meas.=no

6.15

0

500

1000

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2500

3000

3500

4000

Time [min] 14 (b)

T 1 [°C]

13.5 13 M 1 =0.5623 M 2 =388 Delay Comp.=yes Concentration Meas.=yes

12.5

M 1 =9.6538 M 2 =336 Delay Comp.=yes Concentration Meas.=no

12 11.5

M 1 =0.142 M 2 =1.429 Delay Comp.=no Concentration Meas.=no

0

500

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Time [min]

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