Machine Learning for Ionic Liquid Toxicity Prediction

In addition to proper physicochemical properties, low toxicity is also desirable when seeking suitable ionic liquids (ILs) for specific applications. In this context, machine learning (ML) models were developed to predict the IL toxicity in leukemia rat cell line (IPC-81) based on an extended experimental dataset. Following a systematic procedure including framework construction, hyper-parameter optimization, model training, and evaluation, the feedforward neural network (FNN) and support vector machine (SVM) algorithms were adopted to predict the toxicity of ILs directly from their molecular structures. Based on the ML structures optimized by the five-fold cross validation, two ML models were established and evaluated using IL structural descriptors as inputs. It was observed that both models exhibited high predictive accuracy, with the SVM model observed to be slightly better than the FNN model. For the SVM model, the determination coefficients were 0.9289 and 0.9202 for the training and test sets, respectively. The satisfactory predictive performance and generalization ability make our models useful for the computer-aided molecular design (CAMD) of environmentally friendly ILs

Representation/prediction of physico-chemical properties of ionic liquids through different computational methods.

Ph. D. University of KwaZulu-Natal, Durban 2014.The “green” industrial chemical processes are of great interest to scientists and engineers due to elimination of environmental pollution, especially air pollution. One of the most important air pollutants is class of materials called volatile organic compounds (VOCs) which are widely used in different industrial chemical processes. The recent research has revealed that ionic liquids (ILs) are generally the best possible alternative to the conventional solvents; because in general, the ILs have interesting properties such as very low vapor pressure, nonflammability, and high physical and chemical stability. Ionic liquids are constituted of ions, typically a cation and an anion, and their thermophysical properties are strongly dependent on the type and chemical structure of the cation and anion. As a result, in theory, they can be designed for specific applications with certain properties by choosing the appropriate combination of anion/cation pair. For this purpose, a predictive model is required to estimate the target property based on the chemical structure of ions. At the initial step of this study, the NIST Standard Reference Database #103b as well as the published papers in the literature was chosen as the source of experimental data of ionic liquids. As a result, a large database was collected covering several thermophysical properties of ILs. Thereafter, the collected data were examined carefully and the duplicated and erroneous data were screened. Speed of sound, heat capacity, refractive index, viscosity, infinite dilution activity coefficient () , and critical temperature of various ionic liquids were modeled by means of two well-known property estimation methods, Group Contribution (GC) and Quantitative Structure-Property Relationship (QSPR) methods. These methods were combined with different computational and regression techniques such as genetic function approximation (GFA) and least square support vector machine (LS-SVM). The combined routines then were applied to select reasonable number of parameters from thousands of variables and to develop the predictive models for representation/prediction of chosen temperature-dependent thermophysical properties of ionic liquids. Speed of sound in ionic liquids was modeled successfully and two models were developed, one GC and one QSPR model. These models were the first GC and QSPR models developed for this property in the literature. Both models had better accuracy in terms of average absolute relative deviation (the AARD% of 0.36 for the GC and 0.92% for the QSPR models over 41 ILs) and covered a wider range of ionic liquids compared with the previous models published (AARD% of 1.96% over 14 ILs) and consequently, they were more applicable. Liquid heat capacity of ionic liquids was studied and one GC and one QSPR model were developed. Both models covered 82 ILs which was a larger number of ionic liquids compared with the best available model in the literature (32 ILs with an AARD% of 0.34%) and had relatively low AARD%. The AARD% of the models was 1.68% and 1.70% for the GC and QSPR models, respectively. In addition, the QSPR model was the first model developed for this property through the QSPR approach. For the refractive index of ionic liquids, little attention had been given to modeling and consequently, one new GC (AARD% = 0.34%) and the first QSPR (AARD% = 0.51%) models were developed to predict this property using the experimental data for 97 ionic liquids. Both models covered a wider range of ionic liquids and showed very good prediction ability compared with the best available model (an AARD% of 0.18% for 24 ILs). Viscosity of Fluorine-containing ionic liquids was studied because the insertion of fluorinated moieties in the molecular structure of ionic liquids could result in reduction of viscosity. As a result, one QSPR (AARD% = 2.91%) and two GC models were developed using two different databases, one with fewer number of ionic liquids but with more reliable data (AARD% = 3.23%), the one with larger number of ionic liquids but with lower reliability (AARD% = 4.85%). All of the models developed had better prediction ability compared with the previous models and covered a wider range of fluorinated ionic liquids. Infinite dilution activity coefficient (γ∞) of organic solutes was modeled by developing six different models for different types of solutes (alkane, alkene, aromatic, etc.). The model developed were the first GC models for the prediction of γ∞ of solutes in ionic liquids. They were much easier to use, more comprehensive, and much more accurate compared with the UNIFAC model. Ultimately, the theoretical critical temperature (Tc) of ionic liquids was tried to model using the GC and QSPR approaches. The experimental data of surface tension of 106 ionic liquids were used to calculate the critical temperature and then, these values were used to develop the models. It was found that the only available model in the literature was not accurate and predictive enough when its output was compared with the abovementioned Tc values. In addition, it was found that both of the models developed were not predictive enough to calculate the Tc of various types of ionic liquids as the models were developed using a few number of ionic liquids; however both models were accurate enough to fit the used values of Tc. The GC model has an AARD% of 5.17% and the QSPR model showed the AARD% of 4.69%. It this thesis, much larger databases were used to develop the models compared with the models published previously in the literature. It was found that thermophysical properties of ionic liquids can be modeled fairly well by combination of the GC or QSPR methods with an appropriate regression technique. In addition, the developed models improved significantly the quality of fit and predictions for a wider range of ionic liquids compared with the previous models. Consequently, the models proposed are more predictive and can be used to design the ionic liquids with desired property for specific applications.Please note that the symbol that appears after "coefficient " that appears in brackets "( )" could not be copied. Please refer to page i of the thesis abstract to look at the symbol

CO₂ capture using ionic liquids: thermodynamic modeling and molecular dynamics simulation

Global climate change is happening now, and the average temperature of Earth is rising. Several evidences show that one of the main reasons for global warming is the increased concentration of greenhouse gases (GHGs) in the atmosphere, particularly carbon dioxide (CO₂). CO₂ is mostly producing from burning fossil fuels. One of the effective strategies to reduce CO₂ emissions is implementing carbon capture in fossil fuel power plants. Current post-combustion carbon capture techniques typically employ amine-based solvents, such as monoethanolamine (MEA), for the absorption of CO₂. Although alkanol amines have an acceptable absorption capacity, their high vapor pressure, solvent loss during desorption, and high corrosion rate make amines absorption plants energy-intensive. In recent years, Ionic Liquids (ILs) have been emerged as promising alternative solvents for physisorption and chemisorption of acid gases due to their unique physiochemical properties, including negligible vapor pressure, high thermal stability, tunability, and being environmentally safe. ILs require to be screened based on technical, economical, and environmental aspects. The main challenges of using ILs are increasing CO₂ capture capacity of ILs, and detailed understanding of the diffusivity of CO₂ in ILs, the effect of additives in solubility, selectivity features of ILs, phase behavior of gas-IL systems, and absorption mechanism. These challenges can be addressed using either experiment, thermodynamic modeling, and/or molecular simulations. In this study, the potential of the screened imidazolium-based ILs is investigated using thermodynamic modeling. The extended Peng–Robinson (PR) and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) EOSs are implemented to evaluate the solubility and selectivity of CO₂ in pure ILs and their mixture with water and toluene. The effects of water and toluene on solubility and viscosity of ILs are investigated. Low concentrations of water (< 1 wt%) do not affect solubility; however, with increasing water concentration, the solubility of CO2 is decreased. On the other hand, with increasing water content, the IL viscosity significantly decreases, which is in the favor of using viscous ILs for CO₂ separation. In this thesis, Molecular Dynamics (MD) simulation is performed to determine the properties of ILs ([Bmim][BF₄] and [Bmim][Ac]), their structures, and molecular dynamics. A great agreement is noticed between the density and viscosity of the studied ILs from MD simulations and experimental data, indicating the accuracy of our simulation runs. This study also includes the effect of temperature and anion type on the structuring of ions and their self-diffusivities. Bulk systems of ILs and CO₂ are studied to evaluate the influence of temperature and types of ions on the diffusivity of CO₂ in the solvent as well as structural characteristics. A comprehensive analysis of the characteristics of the interface of IL/CO₂ is performed to explore species distribution, gas behavior at the interface, and molecule orientation. At the interface, CO₂ creates a dense layer which interrupts the association of cations and anions, leading to a decrease in the surface tension. In addition, a comprehensive study on hydrophilic IL, 1-Butyl-3-methylimidazolium acetate or [Bmim][Ac], is conducted to evaluate the thermophysical properties, excess energy, structure, and dynamic characteristics of IL/Water and IL/Water/CO2 systems, using MD simulation approach. The effect of water on radial distribution functions, coordination numbers, water clusters, hydrogen bonding, and diffusivity coefficients of the ions is assessed. The presence of water in IL mixture, even at high concentrations of water (>0.8 mole fraction), increases the diffusivity of cation, anion, water, and CO2 molecules in the mixture due to hydrophilicity of [Bmim][Ac] IL. MD simulations generate reliable and accurate results while dealing with systems including water, CO₂, and IL for carbon capture. In this thesis, novel and robust computational approaches are also introduced to estimate the solubility of CO₂ in a large number of ILs within a wide range of temperatures and pressures. Four connectionist tools- Least Square Support Vector Machine (LSSVM), Decision Tree (DT), Random Forest (RF), and Multilinear Regression (MLR)- are employed to obtain CO₂ solubility in a variety of ILs based on thermodynamic properties and Quantitative Structure-Activity Relationship (QSPR) model. Among different types of descriptors, the most important input variables (e.g., Chi_G/D 3D and Homo/Lumo fraction (anion); SpMax_RG and Disps (cation)) are selected using Genetic Algorithm (GA)-MLR method. A great agreement between the predicted values and experimental measurements is attained while using RF and DT techniques developed based on descriptors and thermodynamics properties. The structural descriptors-based models are more accurate and robust than those built on critical properties

Kritična svojstva i acentrični čimbenici modeliranja čistih spojeva primjenom modela QSPR-SVM i algoritma Dragonfly

This work aimed to model the critical pressure, temperature, volume properties, and acentric factors of 6700 pure compounds based on five relevant descriptors and two thermodynamic properties. To that end, four methods were used, namely, multi-linear regression (MLR), artificial neural networks (ANNs), support vector machines (SVMs) using sequential minimal optimisation (SMO), and hybrid SVM with Dragonfly optimisation algorithm (SVM-DA) to model each property. The results suggested that hybrid SVM-DA had better prediction performance compared to the other models in terms of average absolute relative deviation (AARD%) of {0.7551, 1.962, 1.929, and 2.173} and R2 of {0.9699, 0.9673, 0.9856, and 0.9766} for critical temperature, critical pressure, critical volume, and acentric factor, respectively. The developed models can be used to estimate the property of newly designed compounds only from their molecular structure.Cilj ovog rada bio je modeliranje kritičnog tlaka, temperature, volumnih svojstava i acentričnih čimbenika 6700 čistih spojeva na temelju pet relevantnih deskriptora i dva termodinamička svojstva. U tu svrhu primijenjene su četiri metode: višestruka linearna regresija (MLR), umjetna neuronska mreža (ANN), metoda potpornih vektora (SVM) i algoritam optimizacije Dragonfly (SVM-DA), koji se za modeliranje svakog svojstva koriste sekvencijalnom minimalnom optimizacijom (SMO) i hibridnim SVM-om. Rezultati su pokazali da hibridni SVM-DA daje bolje predviđanje u odnosu na ostale modele u smislu postotka prosječnog apsolutnog relativnog odstupanja (AARD%) od {0,7551, 1,962, 1,929 i 2,173} i R2 od {0,9699, 0,9673, 0,9856, i 0,9766} za kritičnu temperaturu, kritični tlak, kritični volumen i acentrični faktor. Razvijeni modeli mogu se primjenjivati za procjenu svojstava novodizajniranih spojeva samo iz njihove molekularne strukture

Leveraging atomistic simulations and machine learning for the design of ionic liquids as electrolytes for battery application

Ionic liquids are classes of salts that are often found in a liquid state composed entirely of ions. They have gained widespread interest in the research community because of several unique and desirable features, such as negligible vapor pressure, environmental friendliness, and high thermal stability. They are currently studied for various industrial applications as a replacement for conventional solvents. Among them, it has caught the interest of the energy community as a potential electrolyte for battery applications. The current electrolytes found in lithium-ion batteries are based on carbonate solvents known for their excellent performance and low material cost. However, they are plagued with numerous safety concerns as the solvent is highly volatile and prone to flammability during thermal runaway or short circuit. Growing demand for lithium-ion batteries for technology such as electric vehicles has mandated the need for safer and more sustainable batteries. This has made ionic liquids a potential electrolyte candidate as they have impeccable thermal and chemical stability with negligible vapor pressure, eliminating any concerns related to safety. However, the performance of ILs is still far behind in matching the performance of current carbonate electrolytes. Finding the appropriate ionic liquid candidate with high stability and performance can be challenging because of the vast ionic liquid chemical space, as synthesizing and testing each ionic liquid would be expensive and unfeasible. Running atomistic simulations to complement the experimental techniques would be tedious as the ionic liquid space is estimated to be in billions, which can be computationally expensive. Instead, machine learning methods can be an excellent tool to search for and design ionic liquids suited for battery applications as they can be easily trained on existing data to generate additional new data at a very low cost in a short time. Thus, the work in this dissertation is focused on developing machine learning models to correlate properties of ionic liquids geared towards battery application. The developed models are then used to generate additional data to search for high-performance ionic liquids that are on par with conventional organic electrolytes, thus expanding the list of potential electrolyte candidates. The latter part of the work utilizes an advanced deep learning method to discover an entirely new family of ionic liquid cations in search of candidates that can operate at high voltage conditions

Prediction of the physical properties of pure chemical compounds through different computational methods.

Ph. D. University of KwaZulu-Natal, Durban 2014.Liquid thermal conductivities, viscosities, thermal decomposition temperatures, electrical conductivities, normal boiling point temperatures, sublimation and vaporization enthalpies, saturated liquid speeds of sound, standard molar chemical exergies, refractive indices, and freezing point temperatures of pure organic compounds and ionic liquids are important thermophysical properties needed for the design and optimization of products and chemical processes. Since sufficiently purification of pure compounds as well as experimentally measuring their thermophysical properties are costly and time consuming, predictive models are of great importance in engineering. The liquid thermal conductivity of pure organic compounds was the first investigated property, in this study, for which, a general model, a quantitative structure property relationship, and a group contribution method were developed. The novel gene expression programming mathematical strategy [1, 2], firstly introduced by our group, for development of non-linear models for thermophysical properties, was successfully implemented to develop an explicit model for determination of the thermal conductivity of approximately 1600 liquids at different temperatures but atmospheric pressure. The statistical parameters of the obtained correlation show about 9% absolute average relative deviation of the results from the corresponding DIPPR 801 data [3]. It should be mentioned that the gene expression programing technique is a complicated mathematical algorithm and needs a significant computer power and this is the largest databases of thermophysical property that has been successfully managed by this strategy. The quantitative structure property relationship was developed using the sequential search algorithm and the same database used in previous step. The model shows the average absolute relative deviation (AARD %), standard deviation error, and root mean square error of 7.4%, 0.01, and 0.01 over the training, validation and test sets, respectively. The database used in previous sections was used to develop a group contribution model for liquid thermal conductivity. The statistical analysis of the performance of the obtained model shows approximately a 7.1% absolute average relative deviation of the results from the corresponding DIPPR 801 [4] data. In the next stage, an extensive database of viscosities of 443 ionic liquids was initially compiled from literature (more than 200 articles). Then, it was employed to develop a group contribution model. Using this model, a training set composed of 1336 experimental data was correlated with a low AARD% of about 6.3. A test set consists of 336 data point was used to validate this model. It shows an AARD% of 6.8 for the test set. In the next part of this study, an extensive database of thermal decomposition temperature of 586 ionic liquids was compiled from literature. Then, it was used to develop a quantitative structure property relationship. The proposed quantitative structure property relationship produces an acceptable average absolute relative deviation (AARD) of less than 5.2 % taking into consideration all 586 experimental data values. The updated database of thermal decomposition temperature including 613 ionic liquids was subsequently used to develop a group contribution model. Using this model, a training set comprised of 489 data points was correlated with a low AARD of 4.5 %. A test set consisting of 124 data points was employed to test its capability. The model shows an AARD of 4.3 % for the test set. Electrical conductivity of ionic liquids was the next property investigated in this study. Initially, a database of electrical conductivities of 54 ionic liquids was collected from literature. Then, it was used to develop two models; a quantitative structure property relationship and a group contribution model. Since the electrical conductivities of ionic liquids has a complicated temperature- and chemical structure- dependency, the least square support vector machines strategy was used as a non-linear regression tool to correlate the electrical conductivity of ionic liquids. The deviation of the quantitative structure property relationship from the 783 experimental data used in its development (training set) is 1.8%. The validity of the model was then evaluated using another experimental data set comprising 97 experimental data (deviation: 2.5%). Finally, the reproducibility and reliability of the model was successfully assessed using the last experimental dataset of 97 experimental data (deviation: 2.7%). Using the group contribution model, a training set composed of 863 experimental data was correlated with a low AARD of about 3.1% from the corresponding experimental data. Then, the model was validated using a data set composed of 107 experimental data points with a low AARD of 3.6%. Finally, a test set consists of 107 data points was used for its validation. It shows an AARD of 4.9% for the test set. In the next stage, the most comprehensive database of normal boiling point temperatures of approximately 18000 pure organic compounds was provided and used to develop a quantitative structure property relationship. In order to develop the model, the sequential search algorithm was initially used to select the best subset of molecular descriptors. In the next step, a three-layer feed forward artificial neural network was used as a regression tool to develop the final model. It seems that this is the first time that the quantitative structure property relationship technique has successfully been used to handle a large database as large as the one used for normal boiling point temperatures of pure organic compounds. Generally, handling large databases of compounds has always been a challenge in quantitative structure property relationship world due to the handling large number of chemical structures (particularly, the optimization of the chemical structures), the high demand of computational power and very high percentage of failures of the software packages. As a result, this study is regarded as a long step forward in quantitative structure property relationship world. A comprehensive database of sublimation enthalpies of 1269 pure organic compounds at 298.15 K was successfully compiled from literature and used to develop an accurate group contribution. The model is capable of predicting the sublimation enthalpies of organic compounds at 298.15 K with an acceptable average absolute relative deviation between predicted and experimental values of 6.4%. Vaporization enthalpies of organic compounds at 298.15 K were also studied in this study. An extensive database of 2530 pure organic compounds was used to develop a comprehensive group contribution model. It demonstrates an acceptable %AARD of 3.7% from experimental data. Speeds of sound in saturated liquid phase was the next property investigated in this study. Initially, A collection of 1667 experimental data for 74 pure chemical compounds were extracted from the ThermoData Engine of National Institute of Standards and Technology [5]. Then, a least square support vector machines-group contribution model was developed. The model shows a low AARD% of 0.5% from the corresponding experimental data. In the next part of this study, a simple group contribution model was presented for the prediction of the standard molar chemical exergy of pure organic compounds. It is capable of predicting the standard chemical exergy of pure organic compounds with an acceptable average absolute relative deviation of 1.6% from the literature data of 133 organic compounds. The largest ever reported databank for refractive indices of approximately 12 000 pure organic compounds was initially provided. A novel computational scheme based on coupling the sequential search strategy with the genetic function approximation (GFA) strategy was used to develop a model for refractive indices of pure organic compounds. It was determined that the strategy can have both the capabilities of handling large databases (the advantage of sequential search algorithm over other subset variable selection methods) and choosing most accurate subset of variables (the advantages of genetic algorithm-based subset variable selection methods such as GFA). The model shows a promising average absolute relative deviation of 0.9 % from the corresponding literature values. Subsequently, a group contribution model was developed based on the same database. The model shows an average absolute relative deviation of 0.83% from corresponding literature values. Freezing Point temperature of organic compounds was the last property investigated. Initially, the largest ever reported databank in open literature for freezing points of more than 16 500 pure organic compounds was provided. Then, the sequential search algorithm was successfully applied to derive a model. The model shows an average absolute relative deviations of 12.6% from the corresponding literature values. The same database was used to develop a group contribution model. The model demonstrated an average absolute relative deviation of 10.76%, which is of adequate accuracy for many practical applications

Marco de trabajo termodinámico integrado para la absorción de refrigerantes fluorados en líquidos iónicos

El sector de la refrigeración y aire acondicionado tiene un elevado impacto ambiental ocasionado por las emisiones indirectas asociadas al consumo de energía de los equipos de refrigeración, así como a las emisiones directas de los gases refrigerantes de efecto invernadero. Esta tesis está consagrada al desarrollo de un marco de trabajo que combina estudios experimentales, modelado matemático y herramientas computacionales novedosas destinado a la selección de líquidos iónicos que proporcionen las características termodinámicas más adecuadas para su uso como disolventes de hidrofluorocarbonos e hidrofluoroolefinas en dos tipos de aplicaciones: i) sistemas de refrigeración por absorción con eficiencia energética mejorada, y ii) destilaciones extractivas para separar mezclas de refrigerantes obtenidas a partir de dispositivos al final de su vida útil, y recuperar los gases con bajo potencial de calentamiento atmosférico para su reutilización. La presente tesis doctoral contribuye a la evolución del sector de la refrigeración hacia la economía circular y propone las herramientas necesarias para el desarrollo de procesos que faciliten esta transición y la mitigación de los efectos del cambio climático.The refrigeration and air conditioning sector has an elevated environmental impact resulting from the indirect emissions derived of its energy consumption, and from the direct emissions of GWP hydrofluorocarbons from equipment at its end of life. This thesis develops an integrated framework that combines experimental studies, mathematical modeling, and novel computational tools for the selection of ionic liquids with the adequate thermodynamic properties for their use as solvents of hydrofluorocarbons and hydrofluoroolefins in two applications: i) absorption refrigeration systems that increase the efficiency of the refrigeration devices, and ii) extractive distillations aimed to separate azeotropic and close-boiling-point mixtures of fluorinated gases, with the goal of recovering low-GWP refrigerants from end-of-life equipment. This doctoral thesis contributes to the evolution of the refrigeration sector towards the circular economy and proposes the necessary tools for the development of processes that facilitate this transition, as well as the mitigation of the effects of climate change.Además, la investigación de esta tesis ha sido parcialmente financiada por el Fondo Europeo de Desarrollo Regional en el marco del programa Interreg-Sudoe a través del proyecto KET4F-Gas-SOE2/P1/P0823 “KET4F-GAS: Reducción del impacto ambiental de los gases fluorados en el espacio SUDOE mediante tecnologías facilitadoras esenciales” y por el Ministerio de Ciencia e Innovación a través de la Agencia Estatal de Investigación (MCIN/AEI/10.1039/501100011033) en el marco del proyecto PID2019-105827RB-I00 “Funcionalización de membranas como elemento clave en el desarrollo de procesos avanzados de separación”, correspondiente a la convocatoria de 2019 «Proyectos de I+D+i», en el marco del Programa Estatal de Generación de Conocimiento y Fortalecimiento Científico y Tecnológico del Sistema de I+D+i Orientada a los Retos de la Sociedad, del Pla Estatal de Investigación Científica y Técnica y de Innovación 2017-2020

Modelling and optimisation of post-combustion carbon capture process integrated with coal-fired power plant using computational intelligence techniques

PhD ThesisCoal-fired power plants are the major source of CO2 emission which contributes significantly to global climate change. An effective way to reduce CO2 emission in coal-fired power plants is post-combustion carbon dioxide (CO2) capture (PCC) with chemical absorption. The aim of this project is to carry out some research in model development, process analysis, controller design and process optimization for reliable, optimal design and control of coal-fired supercritical power plant integrated with post-combustion carbon capture plant. In this thesis, three different advanced neural network models are developed: bootstrap aggregated neural networks (BANNs) model, bootstrap aggregated extreme learning machine (BAELM) model and deep belief networks (DBN) model. The bootstrap aggregated model can offer more accurate predictions than a single neural network, as well as provide model prediction confidence bounds. However, both BANNs and BAELM have a shallow architecture, which is limited to represent complex, highly-varying relationship and easy to converge to local optima. To resolve the problem, the DBN model is proposed. The unsupervised training procedure is helpful to get the optimal solution of supervised training. The purpose of developing neural network models is to find a best model which can be used in the optimization of the CO2 capture process precisely. This thesis also presents a comparison of centralized and decentralized control structures for post-combustion CO2 capture plant with chemical absorption. As for centralized configuration, a dynamic multivariate model predictive control (MPC) technique is used to control the post-combustion CO2 capture plant attached to a coal-fired power plant. When consider the decentralized control structures based on multi-loop proportional-integral-derivative (PID) controllers, two different control schemes are designed using relative disturbance gain (RDG) analysis and dynamic relative gain array (DRGA) analysis, respectively. By comparing the two control structures, the MPC structure performs better in terms of closed-loop settling time, integral squared error, and disturbance injection