What can systems and control theory do for agricultural science?

Abstract: While many professionals with a background in agricultural and bio-resource sciences work with models, only few have been exposed to systems and control theory. The purpose of this paper is to elucidate a selection of methods from systems theory that can be beneficial to quantitative agricultural science. The state space representation of a dynamical system is the corner stone in the mainstream of systems theory. It is not well known in agro-modelling that linearization followed by evaluation of eigenvalues and eigenvectors of the system matrix is useful to obtain dominant time constants and dominant directions in state space, and offers opportunities for science-based model reduction. The continuous state space description is also useful in deriving truly equivalent discrete time models, and clearly shows that parameters obtained with discrete models must be interpreted with care when transferred to another model code environment. Sensitivity analysis of dynamic models reveals that sensitivity is time and input dependent. Identifiability and sensitivity are essential notions in the design of informative experiments, and the idea of persistent excitation, leading to dynamic experiments rather than the usual static experiments can be very beneficial. A special branch of systems theory is control theory. Obviously, control plays an important part in agricultural and bio-systems engineering, but it is argued that also agronomists can profit from notions from the world of control, even if practical control options are restricted to alleviating growth limiting conditions, rather than true crop control. The most important is the idea of reducing uncertainty via feed-back. On the other hand, the systems and control community is challenged to do more to address the problems of real life, such as spatial variability, measurement delays, lacking data, environmental stochasticity, parameter variability, unavoidable model uncertainty, discrete phenomena, variable system structures, the interaction of technical ad living systems, and, indeed, the study of the functioning of life itself

Darcian permeability constant as indicator for shear stresses in regular scaffold systems for tissue engineering

The shear stresses in printed scaffold systems for tissue engineering depend on the flow properties and void volume in the scaffold. In this work, computational fluid dynamics (CFD) is used to simulate flow fields within porous scaffolds used for cell growth. From these models the shear stresses acting on the scaffold fibres are calculated. The results led to the conclusion that the Darcian (k 1) permeability constant is a good predictor for the shear stresses in scaffold systems for tissue engineering. This permeability constant is easy to calculate from the distance between and thickness of the fibres used in a 3D printed scaffold. As a consequence computational effort and specialists for CFD can be circumvented by using this permeability constant to predict the shear stresses. If the permeability constant is below a critical value, cell growth within the specific scaffold design may cause a significant increase in shear stress. Such a design should therefore be avoided when the shear stress experienced by the cells should remain in the same order of magnitud

Modeling and Managing Shallow Lake Eutrophication

The issues discussed in this Executive Report are explored fully in the book "Modeling and Managing Shallow Lake Eutrophication--With Application to Lake Balaton," published by Springer-Verlag. An abstract is included under BK-86-401 in this index

Low Temperature Drying With Air Dehumidified by Zeolite for Food Products: Energy Efficiency Aspect Analysis

Developments in low temperature drying of food products are still an interesting issue; especially with respect to the energy efficiency. This research studies the energy efficiency that can be achieved by a dryer using air which is dehumidified by zeolite. Experimental results are fitted to a dynamic model to find important variables for the drying operation. The results show that ambient air temperature as well as the ratio between air flow for drying and air flow for regeneration, affect the energy efficiency significantly. Relative humidity of used air, and shift time have a minor effect on the dryer performance. From the total work, it can be noted that the dryer efficiency operated at 50-60°C achieves 75 percent, which is attractive for drying of food products

Sensitivity to Uncertainty in a Phytoplankton-Oxygen Model for Lowland Streams

The applicability of water quality models depends upon the quality of the parameter estimates. A phytoplankton-oxygen model developed for canalized lowland streams is tested against data from a limited plug following measurement program. The accuracy of the parameter estimates is limited by the inaccuracy of the BOD measurement in the presence of algae. Other sources of parameter uncertainties are: (i) site dependency of parameters lumping complex subsystems, such as the BOD decay rate coefficient, having a higher value directly after a waste discharge, and (ii) time dependency of lumped parameters, such as the algal death rate coefficient. A sensitivity analysis, based on the solution of the sensitivity equations of the model, is then performed to provide some insight into the effects of parameter uncertainties on model results. It appears that the growth and death rates of algae dominate the phytoplankton, BOD and oxygen behaviour, and that a separate estimate in the absence of accurate BOD measurements is difficult to obtain without additional information

Uncertainty in the Parameters and Predictions of Phytoplankton Models

A methodology is developed to evaluate in quantitative terms the effect of uncertainty in the data and the model on the reliability of parameter estimates in phytoplankton models, and to assess the effect of the resulting parameter uncertainty on model predictions. The method of maximum likelihood is adopted as the basis of the analysis, resulting in a weighted least squares estimation problem. The analysis provides an estimate for both the weights and the model errors, where the weights appear to be determined by the data errors and the model errors simultaneously. A preliminary application of the method is presented for a 16 state variable, 20 parameter phytoplankton model for Lake Ontario. Extensive data for 14 of the 36 state variables is used to calculate the parameter uncertainty covariance matrix and model error variances. The degree of uncertainty of parameters and their mutual cross-correlations are assessed in terms of the subjective options held by workers in the field. Also a preliminary estimate of the effects of the quantity of data available is presented. Finally, the consequences of parameter uncertainty on the prediction error are indicated. It follows that the presence of cross-correlation in the parameter set resulting from the calibration considerably mitigates the error of prediction

Toward optimal control of flat plate photobioreactors: the greenhouse analogy?

Abstract: The cultivation of algae in photo-bioreactors shows similarities to crop cultivation in greenhouses, especially when the reactors are driven by sun light. Advanced methodologies for dynamic optimization and optimal control for greenhouses are known from earlier research. The aim here is to extend these methodologies to microalgae cultivated in a flat plate photo-bioreactor. A one-state space model for the algal biomass in the reactor is presented. The growth rate vs. light curve is parameterized on the basis of experimental evidence. Spatial distribution of light and growth rate between the plates is also considered. The control variable is the dilution rate. Dynamic optimal control trajectories are presented for various choices of goal function and external solar irradiation trajectories over a horizon of 3 days. It was found that the algae present in the reactor at final time represent a value for the future. Numerical and theoretical results suggest that the control is bang-(singular-)bang, with a strong dependence on the weather. The optimal biomass also depends on the available light, and achieving it to reach a new optimal steady cycle after a prolonged change in weather may take several days. A preliminary theoretical analysis suggests a control law that maximizes the effective growth rate. The analysis shows that like in the greenhouse case, the co-state of the algal biomass plays a pivot role in developing on-line controllers

A Watershed Development Approach to the Eutrophication Problem of Lake Balaton (A Multiregional and Multicriteria Model)

The approach to long-term management of the eutrophication of a lake proposed in this paper is based on the hypothesis that a close relation exists between the human activity in the watershed and the degree of eutrophication in the adjacent waterbody. The method builds on the watershed development approach applied earlier to water resources planning. To test the basic hypothesis and to investigate the relationship in quantitative form an application to the eutrophication problem of Lake Balaton has been attempted. For this purpose the Balaton catchment was separated into regional units with differing degrees of development. In view of the main water transport direction in Lake Balaton, the adjacent waterbodies can be considered as a hierarchical system. For this multiregional, hierarchical system a model was formulated in which the effects of the relevant watershed development factors and natural factors on the nutrient loading from the watershed are expressed in one condensed watershed development figure. Comparison of the development figure for various time instants and various regions with historical and spatial data for the degree of eutrophication should then allow the specification of the relation in a numerical form. The actual application presented in this paper is of preliminary nature because data for the existing level of watershed development (1975-76) were available only. A system of 25 nutrient loading effecting watershed development criteria was designed on the basis of 50 development and natural factors selected from available statistical data. The 25 criteria were then composed into a development indicator for the four watershed regions using 7 alternative weighting systems. The results were compared with 3 alternative eutrophication indices derived from phytoplankton biomass data. The model relationship was analyzed by means of correlation analysis, and a tentative assessment was made of the sensitivity to weighting system and eutrophication index. The first numerical results support the idea behind the basic hypothesis of the watershed development approach. The quantitative results agree with subjective opinions on the present situation in the Balaton region. The overall conclusion is that it is worthwhile to pursue the line of research of this report as a perspective tool in the simulation of the effects of long-term watershed development policies on the eutrophication of the lake. The collection of the necessary historical data for this purpose is highly recommended