Economic model predictive control of nonlinear process systems using Lyapunov techniques

In this work, we develop model predictive control (MPC) designs, which are capable of optimizing closed‐loop performance with respect to general economic considerations for a broad class of nonlinear process systems. Specifically, in the proposed designs, the economic MPC optimizes a cost function, which is related directly to desired economic considerations and is not necessarily dependent on a steady‐state—unlike conventional MPC designs. First, we consider nonlinear systems with synchronous measurement sampling and uncertain variables. The proposed economic MPC is designed via Lyapunov‐based techniques and has two different operation modes. The first operation mode corresponds to the period in which the cost function should be optimized (e.g., normal production period); and in this operation mode, the MPC maintains the closed‐loop system state within a predefined stability region and optimizes the cost function to its maximum extent. The second operation mode corresponds to operation in which the system is driven by the economic MPC to an appropriate steady‐state. In this operation mode, suitable Lyapunov‐based constraints are incorporated in the economic MPC design to guarantee that the closed‐loop system state is always bounded in the predefined stability region and is ultimately bounded in a small region containing the origin. Subsequently, we extend the results to nonlinear systems subject to asynchronous and delayed measurements and uncertain variables. Under the assumptions that there exist an upper bound on the interval between two consecutive asynchronous measurements and an upper bound on the maximum measurement delay, an economic MPC design which takes explicitly into account asynchronous and delayed measurements and enforces closed‐loop stability is proposed. All the proposed economic MPC designs are illustrated through a chemical process example and their performance and robustness are evaluated through simulations. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

<Superscript>1</Superscript>H-NMR Spectroscopy as a New Tool in the Assessment of the Oxidative State in Edible Oils

Within the course of lipid peroxidation, hydroperoxides are formed as primary products. They can be used as analytical markers to assess the deterioration status of oils and fats. Here a new ¹H-NMR assay to determine the hydroperoxide amount in edible oils is presented. We were able to show that the analytical performance of the method is similar to that of the commonly used peroxide value (PV) according to Wheeler. A total of 290 edible oil samples were analyzed using both methods. For some oil varieties considerable discrepancies were found between the results obtained. In the case of black seed and olive oil, two substances could be identified that cause positive (black seed oil) and negative (olive oils) deviations from the theoretical PV expected from the NMR values.     

Design,Synthesis, and in vitro Evaluation of P2X7 Antagonists

The P2X7 receptor is a promising target for the treatment of various diseases due to its significant role in inflammation and immune cell signaling. This work describes the design, synthesis, and in vitro evaluation of a series of novel derivatives bearing diverse scaffolds as potent P2X7 antagonists. Our approach was based on structural modifications of reported (adamantan-1-yl)methylbenzamides able to inhibit the receptor activation. The adamantane moieties and the amide bond were replaced, and the replacements were evaluated by a ligand-based pharmacophore model. The antagonistic potency of the synthesized analogues was assessed by two-electrode voltage clamp experiments, using Xenopus laevis oocytes that express the human P2X7 receptor. SAR studies suggested that the replacement of the adamantane ring by an aryl-cyclohexyl moiety afforded the most potent antagonists against the activation of the P2X7 cation channel, with analogue 2-chloro-N-[1-(3-(nitrooxymethyl)phenyl)cyclohexyl)methyl]benzamide ( 56 ) exhibiting the best potency with an IC₅₀ value of 0.39 μM.     

Flame extension and the near field under the ceiling for travelling fires inside large compartments

Structures need to be designed to maintain their stability in the event of a fire. The travelling fire methodology (TFM) defines the thermal boundary condition for structural design of large compartments of fires that do not flashover, considering near field and far field regions. TFM assumes a near field temperature of 1200°C, where the flame is impinging on the ceiling without any extension and gives the temperature of the hot gases in the far field from Alpert correlations. This paper revisits the near field assumptions of the TFM and, for the first time, includes horizontal flame extension under the ceiling, which affects the heating exposure of the structural members thus their load-bearing capacity. It also formulates the thermal boundary condition in terms of heat flux rather than in terms of temperature as it is used in TFM, which allows for a more formal treatment of heat transfer. The Hasemi, Wakamatsu, and Lattimer models of heat flux from flame are investigated for the near field. The methodology is applied to an open-plan generic office compartment with a floor area of 960 m² and 3.60 m high with concrete and with protected and unprotected steel structural members. The near field length with flame extension (fTFM) is found to be between 1.5 and 6.5 times longer than without flame extension. The duration of the exposure to peak heat flux depends on the flame length, which is 53 min for fTFM compared with 17 min for TFM, in the case of a slow 5% floor area fire. The peak heat flux is from 112 to 236 kW/m² for the majority of fire sizes using the Wakamatsu model and from 80 to 120 kW/m² for the Hasemi and Lattimer models, compared with 215 to 228 kW/m² for TFM. The results show that for all cases, TFM results in higher structural temperatures compared with different fTFM models (600°C for concrete rebar and 800°C for protected steel beam), except for the Wakamatsu model that for small fires, leads to approximately 20% higher temperatures than TFM. These findings mitigate the uncertainty around the TFM near field model and confirm that it is conservative for calculation of the thermal load on structures. This study contributes to the creation of design tools for better structural fire engineering.     

Free-radical synthesis of narrow polydispersed 2-hydroxyethyl methacrylate-based tetrapolymers for dilute aqueous base developable negative photoresists

Novel (meth)acrylate tetrapolymers based on 2-hydroxyethyl methacrylate (HEMA) were synthesized via free-radical polymerization in refluxing xylene under monomer-starved conditions for use in negative photoresist formulations. 2,2′-Azobis(2-methylbutyronitrile) was used as initiator and 2-mercaptoethanol as chain transfer agent. Optimized resist formulations were obtained with a relatively narrow polydispersed (D=1.86) low molecular weight copolymer (M_n=1677) of 2-hydroxyethyl methacrylate (HEMA), isobornyl methacrylate (IBMA), cyclohexyl methacrylate (CHMA) and acrylic acid (AA), in a 40/30/23/7 weight ratio. A novel high-resolution single layer negative tone photoresist suitable for 193 nm and e-beam lithography that meets basic performance requirements (aqueous-base development, enhanced etch resistance, sub-0.2 μm resolution) was developed from the aforementioned (meth)acrylate tetrapolymer, the poly(2-hydroxyethyl methacrylate-co-cyclohexyl methacrylate-co-isobornyl methacrylate-co-acrylic acid) (PHECIMA) and a sulfonium salt photo acid generator. The key-components for the negative image formation (photoacid induced crosslinking) are the hydroxyl groups of the HEMA moieties. The swelling-free negative resist material was developed in diluted aqueous base [tetramethyl ammonium hydroxide, (TMAH) 0.26×10⁻²N] and presented enhanced etch resistance without the use of etch resistance promoters. 0.20-0.14 μm lines were obtained upon 193 nm and/or e-beam lithography.     

Synthesis, Characterization and Photocatalytic Activity of Titania Loaded Cd-MCM-41

Catalysts consisting of cadmium incorporated into MCM-41 mesoporous molecular sieves (Cd-MCM-41) with Si/Cd = 80 have been synthesized by the hydrothermal method using cadmium acetate as the source of cadmium. This was then loaded with titania via the sol-gel method to explore the photoactivity in UV light. These two materials were characterized by various physicochemical techniques such as N₂ physisorption, O₂ chemisorption, diffuse reflectance UV-vis, X-ray diffraction (XRD), Raman and X-ray photoelectron spectroscopy (XPS). The pore size of the Cd-MCM-41 was higher and the BET surface area was lower than those commonly found in our siliceous MCM-41. This is due to the partial pore breakage, as recorded by pore size distribution analysis. The oxygen chemisorption results shows that the dispersion of cadmium is quite high, and decreased after loading of titania. The XRD patterns of Cd-MCM-41 and 25%TiO₂/Cd-MCM-41 are similar to those of siliceous MCM-41; however, the intensity of the d ₁₀₀ peak is decreased and the unit-cell parameter increased with titania loading. Raman spectra could not detect any peaks, whereas peaks were detected at 144, 397, 518 and 641 cm_-1 with loading of titania, these peaks being associated with the anatase phase of titania. The surface composition and binding energy of the Cd 3d_5/2 peak for Cd-MCM-41 and 25%TiO₂/Cd-MCM-41 was analyzed by XPS and showed considerable infusion of cadmium ions on to the surface upon loading of titania. The Cd/Si surface atomic ratio measured by XPS increases 10 times with loading of titania on Cd-MCM-41, indicating that the two separate surface electronic levels such as Cd-O-Si and Cd-O-Ti were found for 25%TiO₂/Cd-MCM-41. The 25%TiO₂/Cd-MCM-41 showed higher activity than 25%TiO₂/MCM-41 for photocatalytic degradation of formic acid. The activity results are compared with the pure titania based on the transformation per site of Ti.     

Economic model predictive control of nonlinear time‐delay systems: Closed‐loop stability and delay compensation

Closed‐loop stability of nonlinear time‐delay systems under Lyapunov‐based economic model predictive control (LEMPC) is considered. LEMPC is initially formulated with an ordinary differential equation model and is designed on the basis of an explicit stabilizing control law. To address closed‐loop stability under LEMPC, first, we consider the stability properties of the sampled‐data system resulting from the nonlinear continuous‐time delay system with state and input delay under a sample‐and‐hold implementation of the explicit controller. The steady‐state of this sampled‐data closed‐loop system is shown to be practically stable. Second, conditions such that closed‐loop stability, in the sense of boundedness of the closed‐loop state, under LEMPC are derived. A chemical process example is used to demonstrate that indeed closed‐loop stability is maintained under LEMPC for sufficiently small time‐delays. To cope with performance degradation owing to the effect of input delay, a predictor feedback LEMPC methodology is also proposed. The predictor feedback LEMPC design employs a predictor to compute a prediction of the state after the input delay period and an LEMPC scheme that is formulated with a differential difference equation (DDE) model, which describes the time‐delay system, initialized with the predicted state. The predictor feedback LEMPC is also applied to the chemical process example and yields improved closed‐loop stability and economic performance properties. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4152–4165, 2015     

Effects of Drying and Extraction Methods on the Quality and Antioxidant Activity of Sea Buckthorn (Hippophae rhamnoides) Berries and Leaves

Sea buckthorn is a promising source of bioactive compounds. However, there is limited information on the effect of post harvest drying and extraction of sea buckthorn on its antioxidant capacity. The effect of freeze, air, and solar dryingon the extraction yield of sea buckthorn berries and leaves was evaluated with respect to their bioactive content. Sequential extraction with solvents of different polarity and solvent-free microwave-assisted extraction were applied. Freeze-drying has better performance in the berries’ extracts, while air-drying has better performance in the leaves’ extracts. All data were analyzed by Multi Factor Analysis of Variance (ANOVA) and Duncan's post-hoc tests at a level of α = .05. Although the extraction yield in the sequential extraction of sea buckthorn berries is significantly better, the leaves’ extracts exhibit superior radical scavenging ability. Accelerated solar drying appears to preserve sea buckthorn leaves without degrading their antioxidant content. The components responsible for the high antioxidant activity of leaves’ extracts were found to be several flavonoids and polyphenols. The extract obtained by the microwave extraction of fresh berries exhibits moderate antioxidant activity compared to the polar extracts of freeze-dried berries.     

Modeling and Control of a Titania Aerosol Reactor

We focus on modeling and control of an aerosol flow reactor used to produce titania powder. We initially present a detailed population balance model for the process which accounts for simultaneous nucleation, Brownian and shearinduced coagulation, and convective transport and describe the spatio-temporal evolution of the aerosol volume distribution. Then, under the assumption of lognormal aerosol volume distribution, the method of moments is employed for the derivation of a model that describes the evolution of the three leading moments of the volume distribution. The moment model, together with the fundamental model that describes the temperature in the reactor and concentrations of the gas-phase species, are subsequently used to synthesize a nonlinear output feedback controller which manipulates the temperature of the reactor wall to achieve an aerosol size distribution in the outlet of the reactor with desired geometric average particle diameter. The nonlinear controller is successfully implemented on the process model and is shown to deal effectively with external disturbances.     

Distributed model predictive control of switched nonlinear systems with scheduled mode transitions

A method for the design of distributed model predictive control (DMPC) systems for a class of switched nonlinear systems for which the mode transitions take place according to a prescribed switching schedule is presented. Under appropriate stabilizability assumptions on the existence of a set of feedback controllers that can stabilize the closed‐loop switched, nonlinear system, a cooperative DMPC architecture using Lyapunov‐based model predictive control (MPC) in which the distributed controllers carry out their calculations in parallel and communicate in an iterative fashion to compute their control actions is designed. The proposed DMPC design is applied to a nonlinear chemical process network with scheduled mode transitions and its performance and computational efficiency properties in comparison to a centralized MPC architecture are evaluated through simulations. © 2013 American Institute of Chemical Engineers AIChE J, 59:860‐871, 2013