Control Strategy and Comparison of Tuning Methods for Continuous Lactide Ring‐Opening Polymerization

Costa, Liborio I.; Trommsdorff, Ulla

doi:10.1002/ceat.201600235

Cited by 4 publications

(32 citation statements)

References 16 publications

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“…The reaction is taking place in bulk. Using the kinetic scheme of the ROP of lactide [5,12,13], the material balances of the reacting species, the catalyst C , the acid A , and the monomer M , can be described by Equations ()–() respectively:

\frac{\partial C}{\partial t} = - ν \frac{\partial C}{\partial x} - k_{a 1} μ_{0} C + k_{a 2} λ_{0} A,

\frac{\partial A}{\partial t} = - ν \frac{\partial A}{\partial x} + k_{a 1} μ_{0} C - k_{a 2} λ_{0} A,

\frac{\partial M}{\partial t} ≅ - ν \frac{\partial M}{\partial x} - k_{P} λ_{0} M + k_{d} λ_{0} .

…”

Section: Process Modelmentioning

confidence: 99%

“…The boundary conditions consist of the inlet flow rates of monomer, catalyst, cocatalyst, and as contaminates the acid and hydroxyl functions, fed to the first reactor. The catalyst concentration at the inlet is [5]:

C false(x = 0, t false) = \frac{2 p p m_{c a t} ρ_{c a t}}{1 0^{6} M_{c a t}},

where ppm cat is the parts per million of stannous octoate catalyst in the feed, M cat the catalyst molecular weight and x is the axial coordinate.…”

Section: Process Modelmentioning

confidence: 99%

“…Therefore, it is important to account for this coupling in the controller design. Based on the kinetic scheme, these outputs can be controlled by using the catalyst ( ppm cat ) and cocatalyst ( meq ROH ) as manipulated variables [5].…”

Section: Controller Designmentioning

confidence: 99%

“…Section 3 summarizes the control objectives and presents the MPC strategy. For the purpose of comparison, the method based on the PI control proposed by Costa and Trommsdorff to weaken the system coupling [5] and the optimization strategy proposed in our previous work [6] are briefly presented. Section 4 presents the simulation results, with a comparison between the PI controller, the optimization strategy and the MPC.…”

Section: Introductionmentioning

confidence: 99%

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Model predictive control for continuous lactide ring‐opening polymerization processes

Afsi

Othman

Bakir

et al. 2020

Asian Journal of Control

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Polylactic acid (PLA) is an attractive environment‐friendly thermoplastic that is bio‐sourced and biodegradable. PLA is industrially produced by the ring‐opening polymerization of lactide. This reaction is sensitive to drifts in the operating conditions and impurities in the raw materials that may affect the reaction rate as well as the polymer properties, which can be very costly in continuous processes. It is therefore crucial to employ a control strategy that allows recovering the nominal conditions and maintaining the desired properties and conversion level in case of drift. Three control strategies are discussed in this paper: proportional‐integral (PI) controller, dynamic optimization, and model predictive control (MPC). The proposed approaches are validated by simulation of a continuous PLA process constituted of three cascade reactors including one loop reactor in the middle. Besides the coupling of inputs and outputs, the process model is highly nonlinear, and the control is done only on the boundaries. The results show that the open‐loop optimization strategy provides better performance compared to the PI controller if the disturbance is assumed to be measured. The MPC also shows superior performances provided that the disturbance is first estimated. A polynomial model is developed to predict the nonmeasured disturbance based on the measured outputs.

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\frac{\partial C}{\partial t} = - ν \frac{\partial C}{\partial x} - k_{a 1} μ_{0} C + k_{a 2} λ_{0} A,

\frac{\partial A}{\partial t} = - ν \frac{\partial A}{\partial x} + k_{a 1} μ_{0} C - k_{a 2} λ_{0} A,

\frac{\partial M}{\partial t} ≅ - ν \frac{\partial M}{\partial x} - k_{P} λ_{0} M + k_{d} λ_{0} .

…”

Section: Process Modelmentioning

confidence: 99%

C false(x = 0, t false) = \frac{2 p p m_{c a t} ρ_{c a t}}{1 0^{6} M_{c a t}},

where ppm cat is the parts per million of stannous octoate catalyst in the feed, M cat the catalyst molecular weight and x is the axial coordinate.…”

Section: Process Modelmentioning

confidence: 99%

Section: Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Model predictive control for continuous lactide ring‐opening polymerization processes

Afsi

Othman

Bakir

et al. 2020

Asian Journal of Control

Self Cite

View full text Add to dashboard Cite

show abstract

“…[28,35] By solving a few more differential equations (usually 6-12), these approaches still suffer of the necessity of assuming a distribution shape when reconstructing f (x, t), but overcome the remaining issues of the method of moments. Providing average properties accurately and with little computational power, enabled the method of moments and the QMOM to solve PBE in spatially distributed systems [36] and in computational fluid dynamic frameworks. [28,35] When interested in obtaining the full distribution f (x, t) without making assumptions regarding its shape, other approaches such as i) the method of generating functions, ii) finite differences schemes, iii) the method of discretized PBEs, and iv) the method of basis functions can be used.…”

Section: Introductionmentioning

confidence: 99%

Solution of population balance equations by logarithmic shape preserving interpolation on finite elements

Costa¹,

Storti

Lazzari

2018

Computers & Chemical Engineering

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A new numerical approach for solving population balance equations (PBE) is proposed and validated. The method employs a combination of basis functions, defined on finite elements, to approximate the sought distribution function. Similarly to other methods of the same family, the PBE are solved only in a finite number of values of the internal coordinate (grid points). The peculiarity of the method is the use of a logarithmic, shape-preserving interpolation (LSPI) procedure to estimate the values of the distribution in between grid points. The main advantages of the LSPI method compared to other approaches of the same category are: i) the stability of the numerical approach (i.e. the absence of oscillations in the distribution function occurring when using "standard" cubic splines and a low number of elements), and ii) the conceptual and implementation simplicity, as no mathematical manipulation of the PBE is required.

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Model Predictive Control with Integrated Model Reduction for a Continuous Lactide Ring-Opening Polymerization Process

et al. 2022

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Poly(lactic acid) production has received increasing attention, mainly due to its inherent biodegradable thermoplastic properties and to its renewable-resource-based composition. This process is affected by changes in the operating conditions and by raw material impurities which influence the reaction rate and degrade the polymer properties. As the system model is multivariable with coupled dynamics and constraints, linear model predictive control (LMPC) is employed here. A model reduction technique is proposed to obtain an approximate linear representation of the nonlinear system around the operating point to minimize the calculation cost of the controller. The proposed LMPC approach is validated by simulation and is compared to a proportional-integral controller and a nonlinear model predictive control. It is found that LMPC has a superior performance in terms of off-spec time when a disturbance occurs in the feed, and it can restore the target conditions better and faster.

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Control Strategy and Comparison of Tuning Methods for Continuous Lactide Ring‐Opening Polymerization

Cited by 4 publications

References 16 publications

Model predictive control for continuous lactide ring‐opening polymerization processes

Model predictive control for continuous lactide ring‐opening polymerization processes

Solution of population balance equations by logarithmic shape preserving interpolation on finite elements

Model Predictive Control with Integrated Model Reduction for a Continuous Lactide Ring-Opening Polymerization Process

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