A NEW APPROACH TO DECENTRALISED PROCESS CONTROL USING PASSIVITY AND SECTOR STABILITY CONDITIONS

A new robust decentralised process control strategy based on the sector stability theorem is proposed in this paper. The interaction between sub-systems is measured by a revised passivity index, which is used in the development of a new stability condition for decentralised control. The controller synthesis method is developed to satisfy the stability condition and H_∞ performance specification. The decentralised control of a boiler furnace is studied as an application example.     

Delay‐range‐dependent guaranteed cost control for batch processes with state delay

A guaranteed cost control scheme is proposed for batch processes described by a two‐dimensional (2‐D) system with uncertainties and interval time‐varying delay. First, a 2‐D controller, which includes a robust feedback control to ensure performances over time and an iterative learning control to improve the tracking performance from cycle to cycle, is formulated. The guaranteed cost law concept of the proposed 2‐D controller is then introduced. Subsequently, by introducing the Lyapunov–Krasovskii function and adding a differential inequality to the Lyapunov function for the 2‐D system, sufficient conditions for the existence of the robust guaranteed cost controller are derived in terms of matrix inequalities. A design procedure for the controller is also presented. Furthermore, a convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the optimal guaranteed cost controller that minimizes the upper bound of the closed‐loop system cost. The proposed control law can stabilize the closed‐loop system as well as guarantee H_∞ performance level and a cost function with upper bounds for all admissible uncertainties. The results can be easily extended to the constant delay case. Finally, an illustrative example is given to demonstrate the effectiveness and advantages of the proposed 2‐D design approach. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2033–2045, 2013     

An LMI Method to Robust Iterative Learning Fault-tolerant Guaranteed Cost Control for Batch Processes

Based on an equivalent two-dimensional Fornasini-Marchsini model for a batch process in industry, a closed-loop robust iterative learning fault-tolerant guaranteed cost control scheme is proposed for batch processes with actuator failures. This paper introduces relevant concepts of the fault-tolerant guaranteed cost control and formulates the robust iterative learning reliable guaranteed cost controller （ILRGCC）. A significant advantage is that the proposed ILRGCC design method can be used for on-line optimization against batch-to-batch process uncertainties to realize robust tracking of set-point trajectory in time and batch-to-batch sequences. For the convenience of implementation, only measured output errors of current and previous cycles are used to design a synthetic controller for iterative learning control, consisting of dynamic output feedback plus feed-forward control. The proposed controller can not only guarantee the closed-loop convergency along time and cycle sequences but also satisfy the H∞ performance level and a cost function with upper bounds for all admissible uncertainties and any actuator failures. Sufficient conditions for the controller solution are derived in terms of linear matrix inequalities （LMIs）, and design procedures, which formulate a convex optimization problem with LMI constraints, are presented. An example of injection molding is given to illustrate the effectiveness and advantages of the ILRGCC design approach.     

Physical aging of bisphenol A polycarbonate

The physical aging of bisphenol A polycarbonate was studied using the differential scanning calorimetry technique. Cowie and Ferguson's model and Williams‐Watts function were used to analyze the data. It is confirmed that the relation ΔH_∞(T_a) = ΔC_p(T_g − T_a), where ΔH_∞(T_a) is the value of the aging enthalpy for t = ∞, T_a the aging temperature, and ΔC_p the difference in the specific heat above and below the glass transition temperature (T_g), can be used to study quantitatively the physical aging of bisphenol A polycarbonate. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 1646–1648, 1999     

Predicting chain conformation and entanglement of polymers from chemical structure

The characteristic ratio C_∞ and the entanglement molecular weight M_e are two key molecular parameters that control melt viscoelasticity, solid mechanical (brittle/ductile) behavior, and adhesion of polymers. We show that the characteristic ratio C_∞ and the entanglement molecular weight M_e can be predicted from chemical structure by group additivity with uncertainties usually less than ～ 7% for C_∞ and ～ 15% for M_e, comparable with the accuracies of experimental values.     

Thixotropic behavior of gel-like systems

The changes of shear stress with time under constant shear rate and temperature of several pigmented acrylic polymer gels were examined. This behavior, known as thixotropy, was interpreted based on a model which separates the stress into two regions. Region I covers the growth of the stress up to the yield point, represented by a peak stress, F₀. Region II covers the decay of the stress from the peak to the point it attains an asymptotic value, F_∞. The material in region I is assumed to be elastic and in region II is represented by a dynamic equilibrium between structure A, which is non-Newtonian and structure B, which is Newtonian. The transitions between A and B represent structure degradation and structure recovery. The concentrations of A and B are solved explicitly. The total shear stress is then evaluated following a theory proposed by Ree and Eyring and is shown to give relationship between shear stress–shear rate–shearing time in good qualitative agreement with experimental observations. The ratio (F₀ ? F_∞)/F_∞, defined as the coefficient of thixotropy, is sensitive to the fundamental physical chemical parameters of the system and is easy to measure. It is shown to be useful in the characterization of thixotropic materials such as gels. Methods for evaluating the elastic modulus and yield stress of the material in the gel state are also illustrated.     

The absorption behavior and crystallization of poly(aryl ether ketone) films

The absorption and subsequent desorption behaviors of amorphous polymer films of PEEK poly(ether ether ketone), PEEKK poly(ether ether ketone ketone), and PEKK poly(ether ketone ketone) in solvent of 1,2-dichloroethane (C₂H₄Cl₂) are investigated and compared. The equilibrium absorption weight (M_∞) of these polymers is related to their molecular ketone content or molecular chain rigidity and also to the experimental conditions. Especially, at a certain temperature, the molecular chains in the solvent can be polarized, which leads to producing greater M_∞ for polymer films; for example, at 60°C, M_∞ = 46% for PEEK and M_∞ = 65% for PEKK. The pseudodiffusion coefficients for PEEK, PEEKK, and PEKK all surpass the 6.0 × 10⁻¹² m² s⁻¹. The polymer's molecular polarization has been proved in concentrated sulfur acid. Results also show that amorphous resin's films become white and creeped in dichloroethane, which is more serious when metaphenyl links are introduced into PEEKK or PEKK molecular main chains. The residual solvent of 1% or so often exists in the films, even though a long desorption time (over 100 h) has been proceeded. Absorption has induced crystallization of amorphous polymer films, but this crystallization process is slightly different from that of the films crystallized from both the glassy state and the melting state in the solvent, which makes the amorphous interlayers grow progressively and more condensely; thus, the crystallized films will have higher T_g's than these crystallized under annealing condition. The morphology results have shown that the solvent-crystallized films are less toughened than the amorphous ones because of the intermediate layer between the induced crystallized area and the amorphous area in the core. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:2065–2075, 1998     

Thermodynamic interactions of solvents with styrene–butadiene–styrene triblock copolymers

Fundamental thermodynamic interaction data for various solvents with two styrene–butadiene–styrene triblock copolymers (Kraton D-1101 and Kraton D-1300X) have been collected by the use of inverse gas chromatography at infinite dilution. Experimental results are presented for nine D-1101/solvent systems and nine D-1300X/solvent systems at 308, 328. and 348 K. Weight-fraction activity coefficients and Flory–Huggins χ interaction parameters have been calculated from the retention volumes. The χ parameter is used as a measure of the strength of interaction and therefore as a guide in the prediction of polymer–solvent compatibility. In addition, partial molar heats of mixing, ΔH_m^∞, and heats of solution, ΔH_s, were determined. The Hildebrand–Scatchard solubility theory was combined with the Flory theory in order to estimate the solubility parameter of the thermoplastic rubbers at the three different temperatures.     

Low temperature cure of epoxy thermosets attaining high Tg using a uniform microwave field

It is demonstrated for the first time that an epoxy thermoset resin can be cured at temperatures well below its T_g∞. This study compared the use of a uniform variable frequency microwave (VFM) field to standard oven curing at temperatures above and below T_g∞. Using T_g, tan δ, modulus, and FTIR measurements, it is shown that the reaction of BFDGE with MDA to attain a product with T_g∞ of 133 °C is achieved by VFM at temperatures from 100 to 140 °C; in contrast, the thermal cure normally requires 170 °C to attain the same T_g∞ and the same extent of cure. By following the pregel cure reaction with ¹³C‐NMR spectroscopy, it was determined that the lower cure temperatures of VFM cure predominately lead to chain extension and smaller amounts of crosslinking compared to the thermal cure. To explain these results, it is suggested that, after gelation, with VFM cure there is higher mobility from dipole rotations that continues the cure to completion without vitrification. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 44222.     

The validity of the compensation rule

Values of ΔH and τ_∞ for the mechanical relaxation times centred at ～ 700 s were obtained for isotactic polypropylene at three temperatures in the α-region by double T-jump. The values of ΔH and τ_∞ varied systematically in accordance with the compensation rule. The compensation temperature was observed to be T_c～240°C. It is shown that the compensation rule is in good agreement with the predictions of theories of Wert and Zener and of Eby.     

Insulin-status-dependent modulation of FoF1-ATPase activity in rat liver mitochondria

Early and late effects of alloxan diabetes and insulin treatment on mitochondrial membrane structure and function were evaluated by studying the kinetic properties of mitochondrial membrane marker enzyme FoF₁-ATPase and its modulation by membrane lipid/phospholipid composition and membrane fluidity. Under all experimental conditions the enzyme displayed three kinetically distinguishable components. In 1wk-old diabetic animals the enzyme activity was unchanged; however, K _m and V _max of component I increased and K _m of component II decreased. Insulin treatment resulted in lowering of K _m and V _max of components II and III. One-mon diabetic state resulted in decreased enzyme activity, whereas insulin treatment caused hyperstimulation. K _m of components I and II decreased together with decreased V _max of all the components. Insulin treatment restored the K _m and V _max values. In late-stage diabetes the catalytic efficiency of components I and II increased; insulin treatment had drastic adverse effect. Binding pattern of ATP was unchanged under all experimental conditions. Diabetic state resulted in progressive decrease in energy of activation in the low temperature range (E _L). Insulin treatment lowered the energy of activation in the high temperature range (E _H) without correcting the E _L values. The phase transition temperatures increased in diabetic state and were not corrected by insulin treatment. Long-term diabetes lowered the total phospholipid content and elevated the cholesterol content; insulin treatment had partial restorative effect. The membrane fluidity decreased in general in diabetic condition and was not corrected by insulin treatment at late stage. Regression analysis studies suggest that specific phospholipid classes and/or their ratios may play a role in modulation of the enzyme activity.     

Experimental Research on Parallel Conversion Control of Drying Temperature in a Closed-Loop Heat Pump Dryer

The paper proposes a method to handle the challenge of temperature control in a closed-loop heat pump dryer that can operate both in heating cycle and refrigeration cycle. It is hard to avoid the violent fluctuations of drying temperature as the operation mode changes. Hence, the parallel conversion control is introduced to realize the accurate control of drying temperature. The main idea of the controller design lies in the use of different membership functions and fuzzy control rules for the two operation modes. Experimental results show that the temperature fluctuations are reduced when using parallel conversion control with fast and stable response as compared to the fixed-frequency and PID control system. One of the parameters, R _f , representing the value of undershoot ratio is 0.4, 0.48, and 0.64 when drying temperature is fixed at 30, 35, and 38°C, respectively, with a parallel conversion controller. In order to study the application prospects of the parallel conversion control system, a comparison experiment with different compressor frequency ranges was also conducted.     

Diffusion and solubility of commercial poly(methyl methacrylate) denture base material modified with dimethyl itaconate and di‐n‐butyl itaconate during water absorption/desorption cycles

This study evaluated the water absorption, solubility, kinetics of water diffusion and residual monomer content of commercial poly(methyl methacrylate) (PMMA) denture base material modified with dimethyl itaconate (DMI) and di‐n‐butyl itaconate (DBI). Water absorption and solubility were measured gravimetrically while the residual monomer content was analysed using high‐performance liquid chromatography with ultraviolet detection. It was found that the addition of di‐n‐alkyl itaconates significantly decreases the residual methyl methacrylate (MMA) content in the polymerized material. Maximum uptake (M_∞) and loss (M′_∞), and diffusion coefficients for absorption (D_a) and desorption (D_d) of water through all materials were established. M_∞ shows a linear decrease with increasing amount of itaconate in the system while D_a shows a linear increase with increasing amount of itaconate, both of these effects being more pronounced when DBI is present compared to DMI. M_∞ is a linear function of the value of Hoy's solubility parameter. The reduction in residual MMA promoted by addition of a small amount of di‐n‐alkyl itaconates can improve the applicative properties and biocompatibility of the PMMA denture base material. Also, it is shown that modification of the denture base material with di‐n‐alkyl itaconates can enable precise control of water absorption in the system. Copyright © 2012 Society of Chemical Industry     

Mathematical models for kinetics of batchwise hydrogenation of shale oil

Hydrogenation of shale oil in a batch autoclave is described by a second order kinetic equation depending on the hydrogen current concentration (H) and on the current value of a total characteristic of the oil (x_i), both approaching to their equilibrium levels (H_∞, x_i∞). Algorithms are proposed to estimate the values of hydrogenation rate coefficient (k) and H_∞ from the plot of decrease in hydrogen concentration in time versus H at isothermal conditions. A new concept “specific change of the characteristic” (β_i = dx_i / dH) is introduced to handle various x_i (oil yield, viscosity, density, iodine number, and yield of the fraction 200–275 °C).The equilibrium constants (K_i) and β_i for the characteristics are estimated on the basis of experimental results. The temperature-dependencies for k, K_i and β_i are determined. A scheme is proposed to predict current values of H and x_i for different H₀, T_max and oil mass under isothermal and non-isothermal conditions.The model deduced and the coefficients and constants found can be applied for quantitative evaluation of catalysts and initial oils for hydrogenation.     

Feedback control of crystal size distribution in a continuous cooling crystallizer

Control of crystal size distribution (CSD) in a 21.8 L continuous cooling KCl crystallizer was attempted. Feed saturated at 54°C with potash, nearly saturated with NaCl and containing 0.75 g MgSO₄/100 g of H₂ O was cooled to the crystallizer temperature at 40°C. The control scheme consisted of a proportional-integral controller with the rate of fines dissolution/removal as the input variable and the fines suspension density (crystals smaller than 150 μm) as the output variable. The measured/controlled variable was a temperature difference, ΔT, corresponding to the temperature of a slurry sample containing representative fines, before and after the fines were dissolved by heating. An increase in the product weight-mean crystal size and a decrease in the coefficient of variation of product were observed in the controlled runs.     

Isothermal transitions of a thermosetting system

A study of the curing reactions of a cycloaliphatic epoxy resin/anhydride system by torsional braid analysis showed the existence of two critical isothermal temperatures. These are T_g∞ (the maximum glass transition temperature of the thermoset system) and T_gg (the glass transition temperature of the material at its gel point). Two rheologically active kinetic transitions occur during isothermal cure which correspond to gelation and vitrification. Three types of isothermal behavior occur: if T_cure > T_g∞, only gelation is observed; if T_g∞ > T_cure > T_gg, both gelation and vitrification are observed; if T_cure < T_gg, only vitrification is observed. T_gg corresponds to the isothermal cure temperature at which gelation and vitrification occur simultaneously. Methods for determining the time to gel and the time to vitrify, and also T_g∞ and T_gg, have been developed. The time to gel obeyed the Arrhenius relationship, whereas the time to vitrify passed through a minimum. Application of these results to thermosetting systems in general is discussed in terms of the influence of molecular structure on the values of T_g∞ and T_gg.     

Polymer rheology: Influence of molecular weight and polydispersity

Literature data on the non-Newtonian flow of bulk polymer and of polymer solutions are correlated on the basis of a four-parameter equation, η = η_∞ + (η₀ ? η_∞)/[1 + (τD)^m], η being the viscosity at shear rate D, and η₀ and η_∞ limiting values at D = 0 and D = ∞, respectively. The parameters η₀, η_∞, and τ all show dependence on molecular weight, and in general there is good correlation between τ and η₀. There is evidence that τ is related to a molecular weight higher than the weight-average. The exponent m shows dependence on molecular weight distribution and approaches an upper limit of unity for a monodisperse linear polymer. For linear unblended polymers it may be expressed empirically by m = (M?_n/M?_w)^1/5.     

On Criteria for Occurrence of Azeotropes in Isothermal and Isobaric Binary Systems

Criteria are developed for the occurrence of azeotropes in binary nonelectrolyte systems for both isothermal and isobaric situations in terms of liquid‐phase activity coefficients at infinite dilution (γ^∞). In the case of isothermal systems at temperature T, for a positive azeotrope, γ^∞_lvc≥ p*_mvc/p*_lvc where lvc refers to the less volatile component, mvc to the more volatile component, and p* to saturation vapour pressure at T; for a negative azeotrope, γ^∞_mvc≤ p*_lvc/p*_mvc. In the case of isobaric systems at pressure P, for a minimum‐boiling azeotrope, γ^∞_lvc(T_Bmvc) ≥ P/p*_lvc(T_Bmvc), where T_B refers to the boiling point at P; for a maximum‐boiling azeotrope, γ^∞_mvc (T_Blvc) ≤ P/p*_mvc(T_Blvc). The criteria are also given in terms of the parameters of selected correlations for the excess molar Gibbs function (g^E). Examples of the use of the criteria are provided. Various methods that generate values of γ^∞ can be used in conjunction with the criteria, for example, in screening procedures.     

Settling of cylinders in power law liquids

New measurements on drag coefficient and wall effects on the free settling motion of cylinders in two shearthinning polymer solutions are reported. The ranges of conditions covered in this study are: 1 < Re_∞∞ < 40; 0.25 < (LID) < 2; 0.079 < dID < 0.4, and n = 0.65 and 0.74. Both wall correction factor and drag coefficient results are in line with the Newtonian behavior provided a modified Reynolds number is used to represent the results.     

ANN-Based Models for Moisture Diffusivity Coefficient and Moisture Loss at Equilibrium in Osmotic Dehydration Process

Equations were developed using artificial neural networks to predict water diffusivity coefficient (D _e ) and moisture loss at equilibrium point (ML _∞) in order to get the moisture loss (ML) at any time in osmotic dehydration of fruits. These models mathematically correlate nine processing variables (temperature and concentration of osmotic solution, water and solid composition of the fruit, porosity, surface area, characteristic length, solution-to-fruit mass ratio, and agitation level) with D _e and ML _∞. Models were developed using a wide variety of data from the literature and they were able to predict D _e (r = 0.98) and ML _∞(r = 0.94) in a wide range of variable conditions. With these two parameters known, ML can be calculated using Crank's solutions of Fick's second law. The wide range of processing variables considered for the formulation of these models, and their easy implementation in a spreadsheet, using a set of equations, makes them very useful and practical for process design and control.