Nonlinear Model Predictive Control for a multi-rotor with heavy slung load

In this paper a novel controller for stable and precise operation of multi-rotors with heavy slung loads is introduced. First, simplified equations of motions for the multi-rotor and slung load are derived. The model is then used to design a Nonlinear Model Predictive Controller (NMPC) that can manage the highly nonlinear dynamics whilst accounting for system constraints. The controller is shown to simultaneously track specified waypoints whilst actively damping large slung load oscillations. A Linear-quadratic regulator (LQR) controller is also derived, and control performance is compared in simulation. Results show the improved performance of the Nonlinear Model Predictive Control (NMPC) controller over a larger flight envelope, including aggressive maneuvers and large slung load displacements. Computational cost remains relatively small, amenable to practical implementation. Such systems for small Unmanned Aerial Vehicles (UAVs) may provide significant benefit to several applications in agriculture, law enforcement and construction.

A computational model for BMP movement in sea urchin embryos

Bone morphogen proteins (BMPs) are distributed along a dorsal-ventral (DV) gradient in many developing embryos. The spatial distribution of this signaling ligand is critical for correct DV axis specification. In various species, BMP expression is spatially localized, and BMP gradient formation relies on BMP transport, which in turn requires interactions with the extracellular proteins Short gastrulation/Chordin (Chd) and Twisted gastrulation (Tsg). These binding interactions promote BMP movement and concomitantly inhibit BMP signaling. The protease Tolloid (Tld) cleaves Chd, which releases BMP from the complex and permits it to bind the BMP receptor and signal. In sea urchin embryos, BMP is produced in the ventral ectoderm, but signals in the dorsal ectoderm. The transport of BMP from the ventral ectoderm to the dorsal ectoderm in sea urchin embryos is not understood. Therefore, using information from a series of experiments, we adapt the mathematical model of Mizutani et al. (2005) and embed it as the reaction part of a one-dimensional reaction–diffusion model. We use it to study aspects of this transport process in sea urchin embryos. We demonstrate that the receptor-bound BMP concentration exhibits dorsally centered peaks of the same type as those observed experimentally when the ternary transport complex (Chd-Tsg-BMP) forms relatively quickly and BMP receptor binding is relatively slow. Similarly, dorsally centered peaks are created when the diffusivities of BMP, Chd, and Chd-Tsg are relatively low and that of Chd-Tsg-BMP is relatively high, and the model dynamics also suggest that Tld is a principal regulator of the system. At the end of this paper, we briefly compare the observed dynamics in the sea urchin model to a version that applies to the fly embryo, and we find that the same conditions can account for BMP transport in the two types of embryos only if Tld levels are reduced in sea urchin compared to fly.

Model-based analysis and optimization of bioreactor for hematopoietic stem cell cultivation

One of the problems to be solved in attaining the full potentials of hematopoietic stem cell (HSC) applications is the limited availability of the cells. Growing HSCs in a bioreactor offers an alternative solution to this problem. Besides, it also offers the advantages of eliminating labour intensive process as well as the possible contamination involved in the periodic nutrient replenishments in the traditional T-flask stem cell cultivation. In spite of this, the optimization of HSC cultivation in a bioreactor has been barely explored. This manuscript discusses the development of a mathematical model to describe the dynamics in nutrient distribution and cell concentration of an ex vivo HSC cultivation in a microchannel perfusion bioreactor. The model was further used to optimize the cultivation by proposing three alternative feeding strategies in order to prevent the occurrence of nutrient limitation in the bioreactor. The evaluation of these strategies, the periodic step change increase in the inlet oxygen concentration, the periodic step change increase in the media inflow, and the feedback control of media inflow, shows that these strategies can successfully improve the cell yield of the bioreactor. In general, the developed model is useful for the design and optimization of bioreactor operation.

The mathematical modelling of cheese ripening

A mathematical model is developed for the ripening of cheese. Such models may assist predicting final cheese quality using measured initial composition. The main constituent chemical reactions are described with ordinary differential equations. Numerical solutions to the model equations are found using Matlab. Unknown parameter values have been fitted using experimental data available in the literature. The results from the numerical fitting are in good agreement with the data. Statistical analysis is performed on near infrared data provided to the MISG. However, due to the inhomogeneity and limited nature of the data, not many conclusions can be drawn from the analysis. A simple model of the potential changes in acidity of cheese is also considered. The results from this model are consistent with cheese manufacturing knowledge, in that the pH of cheddar cheese does not significantly change during ripening.

A novel population balance model for the dilute acid hydrolysis of hemicellulose

Acid hydrolysis is a popular pretreatment for removing hemicellulose from lignocelluloses in order to produce a digestible substrate for enzymatic saccharification. In this work, a novel model for the dilute acid hydrolysis of hemicellulose within sugarcane bagasse is presented and calibrated against experimental oligomer profiles. The efficacy of mathematical models as hydrolysis yield predictors and as vehicles for investigating the mechanisms of acid hydrolysis is also examined. Experimental xylose, oligomer (degree of polymerisation 2 to 6) and furfural yield profiles were obtained for bagasse under dilute acid hydrolysis conditions at temperatures ranging from 110C to 170C. Population balance kinetics, diffusion and porosity evolution were incorporated into a mathematical model of the acid hydrolysis of sugarcane bagasse. This model was able to produce a good fit to experimental xylose yield data with only three unknown kinetic parameters ka, kb and kd. However, fitting this same model to an expanded data set of oligomeric and furfural yield profiles did not successfully reproduce the experimental results. It was found that a ``hard-to-hydrolyse'' parameter, $\alpha$, was required in the model to ensure reproducibility of the experimental oligomer profiles at 110C, 125C and 140C. The parameters obtained through the fitting exercises at lower temperatures were able to be used to predict the oligomer profiles at 155C and 170C with promising results. The interpretation of kinetic parameters obtained by fitting a model to only a single set of data may be ambiguous. Although these parameters may correctly reproduce the data, they may not be indicative of the actual rate parameters, unless some care has been taken to ensure that the model describes the true mechanisms of acid hydrolysis. It is possible to challenge the robustness of the model by expanding the experimental data set and hence limiting the parameter space for the fitting parameters. The novel combination of ``hard-to-hydrolyse'' and population balance dynamics in the model presented here appears to stand up to such rigorous fitting constraints.

Limitations of a laboratory scale model in predicting optimal pilot scale conditions for dilute acid pretreatment of sugarcane bagasse

Pilot and industrial scale dilute acid pretreatment data can be difficult to obtain due to the significant infrastructure investment required. Consequently, models of dilute acid pretreatment by necessity use laboratory scale data to determine kinetic parameters and make predictions about optimal pretreatment conditions at larger scales. In order for these recommendations to be meaningful, the ability of laboratory scale models to predict pilot and industrial scale yields must be investigated. A mathematical model of the dilute acid pretreatment of sugarcane bagasse has previously been developed by the authors. This model was able to successfully reproduce the experimental yields of xylose and short chain xylooligomers obtained at the laboratory scale. In this paper, the ability of the model to reproduce pilot scale yield and composition data is examined. It was found that in general the model over predicted the pilot scale reactor yields by a significant margin. Models that appear very promising at the laboratory scale may have limitations when predicting yields on a pilot or industrial scale. It is difficult to comment whether there are any consistent trends in optimal operating conditions between reactor scale and laboratory scale hydrolysis due to the limited reactor datasets available. Further investigation is needed to determine whether the model has some efficacy when the kinetic parameters are re-evaluated by parameter fitting to reactor scale data, however, this requires the compilation of larger datasets. Alternatively, laboratory scale mathematical models may have enhanced utility for predicting larger scale reactor performance if bulk mass transport and fluid flow considerations are incorporated into the fibre scale equations. This work reinforces the need for appropriate attention to be paid to pilot scale experimental development when moving from laboratory to pilot and industrial scales for new technologies.

A cellular automata model to investigate immune cell–tumor cell interactions in growing tumors in two spatial dimensions

We develop a hybrid cellular automata model to describe the effect of the immune system and chemokines on a growing tumor. The hybrid cellular automata model consists of partial differential equations to model chemokine concentrations, and discrete cellular automata to model cell–cell interactions and changes. The computational implementation overlays these two components on the same spatial region. We present representative simulations of the model and show that increasing the number of immature dendritic cells (DCs) in the domain causes a decrease in the number of tumor cells. This result strongly supports the hypothesis that DCs can be used as a cancer treatment. Furthermore, we also use the hybrid cellular automata model to investigate the growth of a tumor in a number of computational “cancer patients.” Using these virtual patients, the model can explain that increasing the number of DCs in the domain causes longer “survival.” Not surprisingly, the model also reflects the fact that the parameter related to tumor division rate plays an important role in tumor metastasis.

Mathematical models for collective cell spreading

Collective cell spreading is frequently observed in development, tissue repair and disease progression. Mathematical modelling used in conjunction with experimental investigation can provide key insights into the mechanisms driving the spread of cell populations. In this study, we investigated how experimental and modelling frameworks can be used to identify several key features underlying collective cell spreading. In particular, we were able to independently quantify the roles of cell motility and cell proliferation in a spreading cell population, and investigate how these roles are influenced by factors such as the initial cell density, type of cell population and the assay geometry.

Mathematical modelling and numerical simulation of phosphine flow during grain fumigation in leaky cylindrical silos

The phosphine distribution in a cylindrical silo containing grain is predicted. A three-dimensional mathematical model, which accounts for multicomponent gas phase transport and the sorption of phosphine into the grain kernel is developed. In addition, a simple model is presented to describe the death of insects within the grain as a function of their exposure to phosphine gas. The proposed model is solved using the commercially available computational fluid dynamics (CFD) software, FLUENT, together with our own C code to customize the solver in order to incorporate the models for sorption and insect extinction. Two types of fumigation delivery are studied, namely, fan- forced from the base of the silo and tablet from the top of the silo. An analysis of the predicted phosphine distribution shows that during fan forced fumigation, the position of the leaky area is very important to the development of the gas flow field and the phosphine distribution in the silo. If the leak is in the lower section of the silo, insects that exist near the top of the silo may not be eradicated. However, the position of a leak does not affect phosphine distribution during tablet fumigation. For such fumigation in a typical silo configuration, phosphine concentrations remain low near the base of the silo. Furthermore, we find that half-life pressure test readings are not an indicator of phosphine distribution during tablet fumigation.

Low carbon fuels and commodity chemicals from waste gases – systematic approach to understand energy metabolism in a model acetogen

Gas fermentation using acetogenic bacteria offers a promising route for the sustainable production of low carbon fuels and commodity chemicals from abundant, inexpensive C1 feedstocks including industrial waste gases, syngas, reformed methane or methanol. Clostridium autoethanogenum is a model gas fermenting acetogen that produces fuel ethanol and 2,3-butanediol, a precursor for nylon and rubber. Acetogens have already been used in large scale industrial fermentations, they are ubiquitous and known to play a prominent role in the global carbon cycle. Still, they are considered to live on the thermodynamic edge of life and potential energy constraints when growing on C1 gases pose a major challange for the commercial production of fuels and chemicals. We have developed a systematic platform to investigate acetogenic energy metabolism, exemplified here by experiments contrasting heterotrophic and autotrophic metabolism. The platform is built from complete omics technologies, augmented with genetic tools and complemented by a manually curated genome-scale mathematical model. Together the tools enable the design and development of new, energy efficient pathways and strains for the production of chemicals and advanced fuels via C1 gas fermentation. As a proof-of-platform, we investigated heterotrophic growth on fructose versus autotrophic growth on gas that demonstrate the role of the Rnf complex and Nfn complex in maintaining growth using the Wood–Ljungdahl pathway. Pyruvate carboxykinase was found to control the rate-limiting step of gluconeogenesis and a new specialized glyceraldehyde-3-phosphate dehydrogenase was identified that potentially enhances anabolic capacity by reducing the amount of ATP consumed by gluconeogenesis. The results have been confirmed by the construction of mutant strains.

Multiphase porous media model for Intermittent Microwave Convective Drying (IMCD) of food

Intermittent microwave convective (IMCD) drying is an advanced drying technology that improves both energy efficiency and food quality during the drying of food materials. Despite numerous experimental studies available for IMCD, there is no complete multiphase porous media model available to describe the process. A multiphase porous media model considering liquid water, gases and the solid matrix inside the food during drying can provide in depth understanding of IMCD. In this article, firstly a multiphase porous media model was developed for IMCD. Then the model is validated against experimental data by comparing moisture content and temperature distributions after each heating and tempering periods. The profile of vapour pressures and evaporation during IMCD are presented and discussed. The relative contribution of water and vapour fluxes due to gas pressure and diffusion demonstrated that the fluxes due are relatively higher in IMCD compared to convection drying and this makes the IMCD faster.

Modeling study on transport organization methods choice of highway rapid passenger transport in China

Some new types of mathematical model among four key techno - economic indexes of highway rapid passenger through transportation were established based on the principles of transportation economics. According to the research on the feasible solutions to the associated parameters which were then compared to the actual value, found some limitation in the existing transport organization method. In order to conquer that, two new types of transport organization method, namely CD (Collecting and Distributing) Method and Relay Method were brought forward. What’s more, a further research was down to estimate their characteristics, such as feasibilities, operation flows, applicability fields, etc. This analysis proves the two methods can offset the shortage of rapid passenger through transportation. To ensure highway rapid passenger transport develop harmoniously, a three-stage development targets was suggested to fuse different organization methods.

Predicting driver's hypovigilance on monotonous roads: literature review.

Drivers' ability to react to unpredictable events deteriorates when exposed to highly predictable and uneventful driving tasks. Particularly, highway design reduces the driving task mainly to a lane-keeping one. It contributes to hypovigilance and road crashes as drivers are often not aware that their driving behaviour is impaired. Monotony increases fatigue, however, the fatigue community has mainly focused on endogenous factors leading to fatigue such as sleep deprivation. This paper focuses on the exogenous factor monotony which contributes to hypovigilance. Objective measurements of the effects of monotonous driving conditions on the driver and the vehicle's dynamics is systematically reviewed with the aim of justifying the relevance of the need for a mathematical framework that could predict hypovigilance in real-time. Although electroencephalography (EEG) is one of the most reliable measures of vigilance, it is obtrusive. This suggests to predict from observable variables the time when the driver is hypovigilant. Outlined is a vision for future research in the modelling of driver vigilance decrement due to monotonous driving conditions. A mathematical model for predicting drivers’ hypovigilance using information like lane positioning, steering wheel movements and eye blinks is provided. Such a modelling of driver vigilance should enable the future development of an in-vehicle device that detects driver hypovigilance in advance, thus offering the potential to enhance road safety and prevent road crashes.

Constraints on the complete optimization of human motion

In sport and exercise biomechanics, forward dynamics analyses or simulations have frequently been used in attempts to establish optimal techniques for performance of a wide range of motor activities. However, the accuracy and validity of these simulations is largely dependent on the complexity of the mathematical model used to represent the neuromusculoskeletal system. It could be argued that complex mathematical models are superior to simple mathematical models as they enable basic mechanical insights to be made and individual-specific optimal movement solutions to be identified. Contrary to some claims in the literature, however, we suggest that it is currently not possible to identify the complete optimal solution for a given motor activity. For a complete optimization of human motion, dynamical systems theory implies that mathematical models must incorporate a much wider range of organismic, environmental and task constraints. These ideas encapsulate why sports medicine specialists need to adopt more individualized clinical assessment procedures in interpreting why performers' movement patterns may differ.