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

Analysis of Model and Parameter Uncertainty in Simple Phytoplankton Models for Lake Balaton

The principal aim of the investigation is to analyze the major modes of phosphorus exchange between water and sediment from uncertain data of phosphorus fractions in the water. Based on a priori knowledge two relatively simple models have been postulated. State variables are winter and summer algae phosphorus, detritus phosphorus and orthophosphate phosphorus. Most parameters of the model were estimated or inferred from data from independent measurements. Several sensitive parameters, most of them related to the sediment-water interaction processes remain unknown. In the first model coprecipitation of phosphorus with biogenic lime, sedimentation of detritus and release of orthophosphate from the sediment is accounted for. This model predicts a rise in orthophosphate after the spring and autumn blooms not observed in the data. In the second model a mechanism of adsorption/desorption of phosphate to the sediment or suspended particles is postulated, to account for the remarkable stability of orthophosphate over the year. A Monte Carlo simulation is run to find areas in the parameter space where the model produces results fully within specified boundaries drawn around the data to account for the data uncertainty. Data and forcings from 1977 are used for this purpose. Several parameter combinations were found, and the results were analyzed in terms of the model processes. It is concluded that an adsorption/desorption mechanism is likely to occur, but that various modifications of the postulated model would be desirable. Further analysis using 1976 data is needed. The results suggest that it is worthwhile to perform additional field experiments with lake water and sediments in order to confirm or reject the sorption hypothesis

Control vector parameterization with sensitivity based refinement applied to baking optimization

In bakery production, product quality attributes as crispness, brownness, crumb and water content are developed by the transformations that occur during baking and which are initiated by heating. A quality driven procedure requires process optimization to improve bakery production and to find operational procedures for new products. Control vector parameterization (CVP) is an effective method for the optimization procedure. However, for accurate optimization with a large number of parameters CVP optimization takes a long computation time. In this work, an improved method for direct dynamic optimization using CVP is presented. The method uses a sensitivity based step size refinement for the selection of control input parameters. The optimization starts with a coarse discretization level for the control input in time. In successive iterations the step size was refined for the parameters for which the performance index has a sensitivity value above a threshold value.With this selection, optimization is continued for a selected group of input parameters while the other nonsensitive parameters (below threshold) are kept constant. Increasing the threshold value lowers the computation time, however the obtained performance index becomes less. A threshold value in the range of 10–20% of the mean sensitivity satisfies well. The method gives a better solution for a lower computation effort than single run optimization with a large number of parameters or refinement procedures without selection

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

Lake Balaton Eutrophication Study: Present Status and Future Program

The deterioration of lakes' water quality due to artificial eutrophication is a typical symptom of our civilization. To stop this process and to improve the water quality in an economical way requires a systematic and coordinated analysis of many disciplines. The recognition of this fact related to Lake Balaton, one of the primary touristic resorts of Hungary and the largest shallow lake in Middle-Europe, initiated IIASA and the Hungarian Academy of Sciences in 1978 to establish a cooperative research on the development of ecological models and their practical application to the lake. In addition, it was felt that not only a contribution can be given to solve the problem of the Lake Balaton region but the methodologies developed can be generalized for other shallow lakes which represent, in general, a less studies field compared to deep lakes. Since it was also aimed to consider the water quality management problem (besides the understanding and description in lake processes), all the activities should be replaced to an optimization framework: one more aspect of general interest. During the first half of the study many results were achieved. First of all, the establishment of a data base, the development of ecological models, and the increasing interaction among modeling, experimental work, and further data collection should be emphasized. Deriving from the nature of the problem, the modeling of the nutrient loading and water quality management is only at present in a progressing state and in the future, mainly, the activities of these fields should be strengthened. The objective of the authors was to outline the present state of the cooperative research and define the activities planned for the future. This publication is closely related to the earlier background report CP-79-13 and jointly, they summarize all the important information related to the project. Also, the present paper can play a basic role in promoting and harmonizing the further research in the frame of the Case Study

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

Scaling-up vaccine production: implementation aspects of a biomass growth observer and controller

Abstract This study considers two aspects of the implementation of a biomass growth observer and specific growth rate controller in scale-up from small- to pilot-scale bioreactors towards a feasible bulk production process for whole-cell vaccine against whooping cough. The first is the calculation of the oxygen uptake rate, the starting point for online monitoring and control of biomass growth, taking into account the dynamics in the gas-phase. Mixing effects and delays are caused by amongst others the headspace and tubing to the analyzer. These gas phase dynamics are modelled using knowledge of the system in order to reconstruct oxygen consumption. The second aspect is to evaluate performance of the monitoring and control system with the required modifications of the oxygen consumption calculation on pilot-scale. In pilot-scale fed-batch cultivation good monitoring and control performance is obtained enabling a doubled concentration of bulk vaccine compared to standard batch productio

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