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Within a recent development of algorithms to establish local structural identifiability, local observability and local strong accessibility of nonlinear systems, it turned out that sensitivities, governed by linear time-varying dynamics, are fundamental. As to local strong accessibility of nonlinear systems, the algorithm essentially checks controllability of linearizations along trajectories of the nonlinear system. In the literature concerning local controllability of nonlinear systems on the other hand, examples are regularly presented illustrating that controllability of linearizations is a stronger property than local strong accessibility. This paper clarifies these apparently contradicting results by using an important theoretical result from the literature and several illustrative examples. These reveal that the Lie algebraic rank condition (LARC), that is currently used to check local strong accessibility, may indeed be replaced by a rank condition based on sensitivities (SERC), that essentially checks controllability of linearizations along trajectories, provided that these trajectories are taken to be non-singular. This replacement is important for two reasons. One is that the computation of LARC requires a finite, but a-priori unknown number of steps, which may be very large. The other is especially important for large-scale nonlinear systems, for which the large number of symbolic differentiations involved in LARC results in excessive computation times or even renders the calculation infeasible. Both phenomena are also illustrated with examples.

Dairy cow houses are a major contributor to ammonia (NH3) emission in many European countries. To understand and predict NH3 emissions from cubicle dairy cow houses a mechanistic model was developed and a sensitivity analysis was performed to assess the contribution to NH3 emission of each input variable related to a single urine puddle. Results showed that NH3 emission was most sensitive for five puddle-related input variables: pH, depth, initial urea concentration, area and temperature. Unfortunately, cow house data of these variables are scarce due to a lack of proper measurement methods. In this study we focused on a method to assess the urine puddle depth, which can vary between 0.10 mm and 2.00 mm. Our objective was to develop a measurement method for the urine puddle depth capable of assessing this variable on the floor in commercial dairy cow houses with a measurement uncertainty of at least 0.1 mm. In this study we compared two measurement methods being the balance method as golden standard and the ultrasonic method to use in practical dairy cow houses. We measured water puddles in an experimental setup under various conditions. We concluded that the ultrasonic sensor, attached to an X-Y table, can measure puddle depth and can determine depth differences between puddles both with a measurement uncertainty of 0.1 mm. The comparison between the balance and the ultrasonic method gave a mean difference of

Brassinosteroid (BR) signaling is essential for plant growth and development. In Arabidopsis (Arabidopsis thaliana), BRs are perceived by the BRASSINOSTEROID INSENSITIVE1 (BRI1) receptor. Root growth and hypocotyl elongation are convenient downstream physiological outputs of BR signaling. A computational approach was employed to predict root growth solely on the basis of BRI1 receptor activity. The developed mathematical model predicts that during normal root growth, few receptors are occupied with ligand. The model faithfully predicts root growth, as observed in bri1 loss-of-function mutants. For roots, it incorporates one stimulatory and two inhibitory modules, while for hypocotyls, a single inhibitory module is sufficient. Root growth as observed when BRI1 is overexpressed can only be predicted assuming that a decrease occurred in the BRI1 half-maximum response values. Root growth appears highly sensitive to variation in BR concentration and much less to reduction in BRI1 receptor level, suggesting that regulation occurs primarily by ligand availability and biochemical activity.

Emission of ammonia (NH3) from animal husbandry, and specially from the dairy sector, contributes significantly to acidification and eutrophication, and affects sensitive natural areas. In the nineties Monteny (1998) introduced a mechanistic model to understand and predict the NH3 emissions from cubicle dairy cow houses. Although a limited sensitivity analysis was carried out, we still lack information that essential for further development of the model. Our aim is that the model can predict and assess the NH3 emission from dairy cow houses under practical circumstance. The objective of this research was 1) to determine the relevance and irrelevance of a limited set of input factors, and 2) assess options for further development of the model for use in practice. A full factorial sensitivity analysis was carried out for eight variables related to NH3 emission from a urine puddle on the floor. Relative importance and R2 of the regression model factors were determined. The NH3 emission varied strongly with both high and low emissions. Strongly contributing process variables were puddle pH, initial urea concentration, urination frequency, puddle depth and puddle area. We conclude that deviations in these influencing variables lead to large fluctuations in the NH3 emission, which means that precise quantification of these variables in practice is essential for accurate predictions. Moreover, the results also show that the model may be over-parameterized, having several inputs that seem hardly relevant for the level of NH3 emission.

¿We present and apply an alternative method for the investigation of the well-known parameter identifiability question for non-linear system models. The method is based on a geometric analysis of the parametric output sensitivities and is, in fact, an application of the tools that are available in non-linear control theory to an augmented system, including the parametric output sensitivities. Accessibility Lie algebras are calculated that yield insight (through a simple rank test) in the controllability of this augmented system. The method is demonstrated in an example that is due to Dochain et al [4]. Results are confirmed by the method that has certain advantages in comparison to, for example, the Taylor series approach that seeks for identifiable combinations of parameters through inspection of the individual terms in a Taylor series expansion of the output signal, i.e. application of the well-known method of Pohjanpalo [15]. Parametric output sensitivities (as already noted by D¨otsch and Van den Hof [5] and Peeters and Hanzon [13]) play a crucial role in identifiability analysis and we further elaborate on this insight in the current paper. Our goals are (i) to present an interesting method for addressing the (local) identifiability question for non-linear systems and (ii) to gain better understanding in the role of parametric state- and output sensitivities in the identifiability question that stems from an alternative perspective, and that has not been presented in the identification literature. Of course, we are aware of other algorithms and software that establishes an answer to the identifiability question, albeit from a different perspective, e.g. [19], but seek in the current paper mainly for another interpretation and computational framework to address the question of local identifiability, shedding some new light on the problem.

A lumped model is developed for shell-and-tube heat exchangers driven by natural convection, which is based on a one-dimensional approximation. The heat flux is driven by the logarithmic mean temperature difference. The volumetric air flow rate is driven by the buoyant force. Based on the Boussinesq aproximation, this force is characterised by an analytic expression of the inflow and outflow temperatures. The lumped model is finished by relating the buoyant force to the friction force via the drag coefficient. The model was calibrated and validated based on Computational Fluid Dynamics calculations and physical measurements.

We have investigated obstructed two-dimensional turbulent channel flow. The objective is to provide a simple building block for design models and to gain physical insight in this type of flow. We have designed a simple model with some unknown parameters to be calibrated against a CFD model. The model divides the domain between an area of main flow and recirculation areas. The model approximates these areas by polygonal shapes. The locations of the vertices of these polygons are the parameters in the model. This way, we can evaluate the simple model using the Schwarz-Christoffel integral. As a consequence, the model can be evaluated much more quickly than CFD models. The main flow is modeled to be irrotational. The recirculation area behind the obstacle is modeled as a stretched monopolar vortex and this requires 4 extra parameters. The other areas of separated flow are simply modeled to be stationary. By calibrating the simple model we have demonstrated that this physical description works reasonably well. Using only 9 parameters, the simple model reaches an error of 22\% of the inflow velocity.

A solar greenhouse has been designed that maximizes solar energy use and minimizes fossil energy consumption. It is based on a conventional Venlo greenhouse extended with a heat pump, a heat exchanger, an aquifer and ventilation with heat recovery. The aim is to minimize fossil energy consumption, while maximizing crop dry weight, keeping temperature and humidity within certain limits and satisfying a temperature integral. These requirements are defined in a goal function, which is minimized by optimal control. A greenhouse with crop model is used to simulate the process behaviour to determine closed loop optimal control trajectories. The boiler use is reduced, thereby reducing fossil energy use. Gas use is decreased by 77% compared to a conventional greenhouse with optimal control.