Dynamic State Variables Research Articles

New system theory and its impact on control theory

Real systems can include two types of state variables – dynamic and static. While dynamic state variables are a common part of each system, static variables are not and their presence in a system may cause some problems if standard system theories are used. In this paper, it is shown that, due to a new system theory (NST), it is possible to work correctly with systems and subsystems which include not only dynamic state variables, but also static state variables. If standard system theories are used, static variables in the real system cause not only problems in describing systems but also some challenges in control theory. These challenges involve, for example, some questions of controllability, reachability, or observability of a plant that includes static variables or the optimal control design of a plant that includes statical state variables. Some of the challenges mentioned are addressed in this paper after a brief introduction of the NST.

Experimental rainfall–runoff data: Reconsidering the concept of infiltration capacity

► Combination of a variable rainfall intensity field infiltrometer and photography. ► Final infiltration rates and inundated area increase with rainfall intensity. ► Residues, sealing, microtopography interact with rainfall intensity and inundation. ► We argue for a dynamic rather than constant effective hydraulic conductivity ( K e ). Many infiltration models rely on an effective hydraulic conductivity parameter ( K e ) which is often determined in the field from rainfall simulation experiments on small plots. K e can be defined as the spatially averaged infiltration capacity when the soil is ‘field-saturated’ and steady state is reached. Then it equals the infiltration rate ( f ), provided ponding occurs. When a homogeneous surface is assumed, with negligible ponding depth, K e is constant and does not vary with rainfall intensity ( r ). We developed a drop infiltrometer that allows measuring K e on small plots under simulated rainfall intensities that vary between experiments. Infiltration experiments were conducted on a winter wheat field in the Belgian Loess Belt and various surface and soil properties were measured. Furthermore, photos were taken of the soil surface during the infiltration experiments for the determination of the inundated surface fraction. The results of the experiments show that K e is strongly dependent on rainfall intensity. In a statistical approach a dynamic K e could be estimated with a function of rainfall intensity, tillage treatment, percentage residue cover and bulk density. Observations indicate that microtopography, surface fraction covered by a sedimentary seal and macroporosity interact with rainfall intensity, surface ponding and infiltration. We propose that K e in physically based infiltration models should either be made dependent on dynamic state variables in a mechanistic way, such as ponding depth and water content or made dependent on rainfall intensity using an empirical relationship. With such adaptations, both surface runoff and erosion models might have more potential to deal with scale effects in runoff generation.

Generative Model for Maneuvering Target Tracking

We consider the challenging problem of tracking highly maneuverable targets with unknown dynamics and introduce a new generative maneuvering target model (GMTM) that, for a rigid body target, explicitly estimates not only the kinematics, here considered as effect variables, but also the underlying causative dynamic variables including forces and torques acting on the rigid body target in a Newtonian mechanics framework. We formulate relationships between the dynamic and kinematic state variables in a novel graphical model that naturally facilitates the feedback of physical constraints from the target kinematics to the maneuvering dynamics model in a probabilistic form, thereby achieving improved tracking accuracy and efficiency compared to competing techniques. We develop a sequential Monte Carlo (SMC) inference algorithm that is embedded with Markov chain Monte Carlo (MCMC) steps to generate probabilistic samples amenable to the feedback constraints. The proposed algorithm can estimate both maneuvering dynamics and target kinematics simultaneously. The robustness and efficacy of this approach are illustrated by experimental results obtained from noisy video sequences of both simulated and real maneuvering ground vehicles.

Path Planning and State Estimation for Unmanned Aerial Vehicles in Hostile Environments

Path Planning and State Estimation for Unmanned Aerial Vehicles in Hostile Environments

A model of phytoplankton acclimation to iron–light colimitation

We developed and calibrated a dynamic model for cellular carbon, chlorophyll (Chl), and iron under iron‐light colimitation. The model allows growth rate and two other state variables (Fep :C and Chl : C) to be described as functions of light intensity and the free iron concentration (Fe'). The model requires specification of the values of nine parameters. We obtained values for these parameters using published experimental results for Thalassiosira pseudonana using a combination of a random parameter initialization and a golden section search to minimize the cost function. The tuned model explained 95% of the variability in the observations of growth rate, 94% in Chl : C, and 90% in Fep : C. Although the model is applicable to both balanced and unbalanced growth conditions, data were only available for balanced growth; thus, the dynamics of state variables during unbalanced growth conditions could not be investigated. A limitation in calibrating the model was in the scarcity of suitable experimental data sets under well‐defined environmental forcing. This points to the need for new experimental work on iron‐limited cultures, including measurements of photosynthesis‐light curves and the dynamic responses to changed Fe' and light intensity. This phytoplankton growth model provides a physiological treatment of iron‐light colimitation for implementation within ocean biogeochemical models. By including both growth rate and elemental stoichiometry (e.g., Fep : C) as state variables, the model can be applied to assess both rate and yield limitation.

Development of a simulation-based decision support system for controlling stochastic flexible job shop manufacturing systems

This paper describes a simulation-based decision support system (DSS) to production control of a stochastic flexible job shop (SFJS) manufacturing system. The controller design approach is built around the theory of supervisory control based on discrete-event simulation with an event–condition–action (ECA) real-time rule-based system. The proposed controller constitutes the framework of an adaptive controller supporting the co-ordination and co-operation relations by integrating a real-time simulator and a rule-based DSS. For implementing SFJS controller, the proposed DSS receives online results from simulator and identifies opportunities for incremental improvement of performance criteria within real-time simulation data exchange (SDX). A bilateral method for multi-performance criteria optimization combines a gradient based method and the DSS to control dynamic state variables of SFJS concurrently. The model is validated by some benchmark test problems.

Inventory control as a discrete system control for the fixed-order quantity system

This paper shows how to model a problem to find optimal number of replenishments in the fixed-order quantity system as a basic problem of optimal control of the discrete system. The decision environment is deterministic and the time horizon is finite. A discrete system consists of the law of dynamics, control domain and performance criterion. It is primarily a simulation model of the inventory dynamics, but the performance criterion enables various order strategies to be compared. The dynamics of state variables depends on the inflow and outflow rates. This paper explicitly defines flow regulators for the four patterns of the inventory: discrete inflow – continuous/discrete outflow and continuous inflow – continuous/discrete outflow. It has been discussed how to use suggested model for variants of the fixed-order quantity system as the scenarios of the model. To find the optimal process, the simulation-based optimization is used.

Aerobic Composting of Poultry Manure and Wheat Straw-Kinetic and Reactor Model

Laboratory-scale aerobic composting tests with mixture of poultry manure and wheat straw were conducted in closed thermally insulated column reactors with effective volumes of 1 L and 32 L. Two 14-day experiments with two different mixture ratios (manure to straw, 2.77:1 and 5.25:1 on dry weight, respectively) were performed in order to compare the performances of composting process in both reactors as well to obtain the parameter values in the kinetic model and to validate proposed kinetic and reactor model in this work. The maximum temperature of 64.6°C was reached after 2.1 days in the large reactor and 64.5°C after 1.3 days in the small reactor. The temperature in these reactors was maintained above 55°C for 2 days, which should be sufficient to maximize sanitation and to destroy pathogens. The greatest mass of carbon dioxide was generated during the first 3 days. The maximum consumption of oxygen was noticed in the exit gas mixtures from both reactors after the first day of the process (the small reactor 16.0 vol. %, the large reactor 11.7 vol. %). The maximum emission of ammonia was observed from the small reactor after first day and from large reactor after the third day. The organic matter content of the materials decreased in both reactors during the process, but this reduction was greater in the large reactor (47.60%) than in the small reactor (41.36%). The proposed kinetic and reactor model was described by a differential equation set with 12 dynamic state variables: mass of organic matter, mass of oxygen, mass of dissolved carbon dioxide, mass of dissolved ammonia, mass of water in the substrate, molar amount of O2 (gas phase), molar amount of CO2 (gas phase), molar amount of NH3 (gas phase), molar amount of H2O vapour (gas phase), molar amount of N2 (gas phase), temperature of gas phase, temperature of solid-liquid phase. In the proposed kinetic model, four kinetic parameters were calculated. The model was validated by the results of several experimentally measured dynamic state variables (temperature of substrate, conversion of organic matter conversion, concentration of carbon dioxide, concentration of oxygen). Comparisons of experimental and simulation results showed good agreement during the whole duration of the process in a reactor, except for ammonia (good agreement was achieved for the first four days and for the last three days of the process). Different simulation scenarios were performed with the model in order to study the effects of initial moisture content, airflow rates and air temperature on the substrate temperature and organic matter conversion. A sensitivity analysis showed that two of four kinetic parameters had a great influence on all three objective functions (maximum conversion of organic matter, maximum concentration of carbon dioxide and maximum substrate temperature).

Complexity reduction of biochemical rate expressions

The current trend in dynamical modelling of biochemical systems is to construct more and more mechanistically detailed and thus complex models. The complexity is reflected in the number of dynamic state variables and parameters, as well as in the complexity of the kinetic rate expressions. However, a greater level of complexity, or level of detail, does not necessarily imply better models, or a better understanding of the underlying processes. Data often does not contain enough information to discriminate between different model hypotheses, and such overparameterization makes it hard to establish the validity of the various parts of the model. Consequently, there is an increasing demand for model reduction methods. We present a new reduction method that reduces complex rational rate expressions, such as those often used to describe enzymatic reactions. The method is a novel term-based identifiability analysis, which is easy to use and allows for user-specified reductions of individual rate expressions in complete models. The method is one of the first methods to meet the classical engineering objective of improved parameter identifiability without losing the systems biology demand of preserved biochemical interpretation. The method has been implemented in the Systems Biology Toolbox 2 for MATLAB, which is freely available from http://www.sbtoolbox2.org. The Supplementary Material contains scripts that show how to use it by applying the method to the example models, discussed in this article.

Evaluation of automotive disk brake noise behavior using piezoceramic actuators and sensors

AbstractOne problem of disk brakes is the occurence of noise. This work in particular addresses the occurrence of disk brake squeal with frequencies from 1 up to 12 kHz which does generally not affect the basic functionality of the brake. Nevertheless it is a serious comfort problem and it causes a high amount of costs to design noiseless brake systems. This work examines methods to evaluate the noise behaviour of disk brakes using piezoceramic actuators and sensors. In comparison to conventional methods they provide the advantage to quantify the effect of new design features without the necessity to make the brake squeal. In this paper the investigation of phase shifts between characteristic dynamic state variables is examined more in detail. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Technique for Reducing Discretization Bias from Monte Carlo Simulations: Option Pricing under Stochastic Interest Rates

Control variates are often used to reduce variability in Monte Carlo estimates and their effectiveness is traditionally measured by the so-called speed-up factor. The main objective of this paper is to demonstrate that a control variate can also be applied to reduce the bias stemming from the discretization of the state variable dynamics. This is particularly valuable when stochastic interest rate models are discretized, since bias reduction through more grid points is computationally expensive.

Development and validation of mathematical model for aerobic composting process

Abstract By integrating the reaction kinetics with the mass and heat transfer between the three phases of the system, a new dynamic structured model for aerobic composting process was developed in this work. In order to evaluate kinetic parameters in mathematical model and to validate the model, experiments were performed with the reactor of volume 32 L, in controlled laboratory conditions. Different ratios of poultry manure to wheat straw were mixed and used as a substrate. Rosenbrock optimization method was used for parameter estimation. In order to solve the system of 12 non-linear differential (and corresponding algebraic) equations, Runge–Kutta–Fehlberg method was used, with approximation of fourth and fifth order and adjustment of step size. Both algorithms were implemented in FORTRAN programming language. In order to achieve as accurate description of the process dynamics as possible, the developed mathematical model was validated by the results of several experimentally measured dynamic state variables. Comparisons of experimental and simulation results for temperature of substrate, organic matter conversion, carbon dioxide concentration and oxygen concentration, in general showed good agreement during the whole duration of the process in a reactor. In the case of ammonia, an agreement was achieved for the first 4 days and for the last 3 days of the process. A sensitivity analysis was performed to determine the key parameters of the model. Analysis showed that two parameters had a great influence on the main characteristics of the process. With validated model for aerobic composting of mixture of poultry manure and wheat straw, optimal values were determined: initial moisture content (70%) and airflow ( 0.54 l mi n − 1 k g OM − 1 ) .

Dynamical analysis of corporate bonds based on the yield spread term-quality surface

Our aim of this research is to propose a model which estimates implied relative credit reliability from the yield spread of defaultable bonds and evaluates their spread risk. We introduce “yield spread term-quality surface” (YSTQS) which is defined on the space of duration and credit reliability of the issuers, and express their yield spread. First, we review the general pricing theorem of defaultable bonds with unpredictable recovery in the no-arbitrage context based on the external hazard rates. Second, we show that the dynamics of state variables determine the shape of the YSTQS, and they drive the YSTQS if the loss-adjusted hazard rates are described by a function of them. Finally, we show an empirical analysis of our model with daily yield spread, duration, and the credit ratings of corporate bonds.

Contingent Portfolio Programming for the Management of Risky Projects

Methods for selecting a research and development (R&D) project portfolio have attracted considerable interest among practitioners and academics. This notwithstanding, the industrial uptake of these methods has remained limited, partly because of the difficulties of capturing relevant concerns in R&D portfolio management. Motivated by these difficulties, we develop contingent portfolio programming (CPP), which extends earlier approaches in that it (i) uses states of nature to capture exogenous uncertainties, (ii) models resources through dynamic state variables, and (iii) provides guidance for the selection of an optimal project portfolio that is compatible with the decision maker’s risk attitude. Although CPP is presented here in the context of R&D project portfolios, it is applicable to a variety of investment problems where the dynamics and interactions of investment opportunities must be accounted for.

Beyond Single-Factor Affine Term Structure Models

This article proposes a new approach to testing for the hypothesis of a single priced risk factor driving the term structure of interest rates. The method does not rely on any parametric specification of the state variable dynamics or the market price of risk. It simply exploits the constraint imposed by the no-arbitrage condition on instantaneous expected bond returns. In order to achieve our goal, we develop a Kolmogorov-Smirnov test and apply it to data on Treasury bills and bonds for both the United States and Spain. We find that the single risk factor hypothesis cannot be rejected for either dataset. Copyright 2004, Oxford University Press.

The IWA Anaerobic Digestion Model No 1 (ADM1)

The IWA Anaerobic Digestion Modelling Task Group was established in 1997 at the 8th World Congress on Anaerobic Digestion (Sendai, Japan) with the goal of developing a generalised anaerobic digestion model. The structured model includes multiple steps describing biochemical as well as physicochemical processes. The biochemical steps include disintegration from homogeneous particulates to carbohydrates, proteins and lipids; extracellular hydrolysis of these particulate substrates to sugars, amino acids, and long chain fatty acids (LCFA), respectively; acidogenesis from sugars and amino acids to volatile fatty acids (VFAs) and hydrogen; acetogenesis of LCFA and VFAs to acetate; and separate methanogenesis steps from acetate and hydrogen/CO2. The physico-chemical equations describe ion association and dissociation, and gas-liquid transfer. Implemented as a differential and algebraic equation (DAE) set, there are 26 dynamic state concentration variables, and 8 implicit algebraic variables per reactor vessel or element. Implemented as differential equations (DE) only, there are 32 dynamic concentration state variables.

Estimating salmon stock–recruitment relationships from catch and escapement data

This paper presents an analysis of stock–recruitment data that takes account of natural variation in stock productivity (process error) and inaccurate escapement counts (measurement error). We formulate the model using dynamic state variables and take advantage of related techniques for parameter estimation, such as an extended Kalman filter. Our recruitment function depends explicitly on parameters relevant to management and includes various cases of historical interest. We adopt Bayesian methods for assessing uncertainty and use Markov chain Monte Carlo (MCMC) techniques to obtain posterior samples. A worked example, based on simulated data, illustrates geometric relationships among model choices, estimated recruitment curves, and data interpretations.

Beyond Single-factor Affine Term Structure Models

This paper proposes a new approach for testing the hypothesis of a single priced risk factor driving the term structure of interest rates. The method does not rely on any parametric specification of the state variable dynamics or the market price of risk, and simply exploits the constraint imposed by the no arbitrage condition on instantaneous expected bond returns. Using a Kolmogorov-Smirnov type test, we find that a general single factor term structure model is rejected by a dataset of Spanish Treasury bills and bonds. In particular, historical expected returns on bills and bonds maturing in the short term are lower than those consistent with expected returns on long term bonds under the single-factor hypothesis. We find that a nonparametric two-factor model where the state variables are taken as the level and slope of the yield curve partially accounts for this bias, although the model underestimates medium-term expected returns. Finally, a three-factor model that includes curvature risk greatly improves the fitted term structure of expected returns across all maturities. These results suggest that the significantly lower premium detected by the test in short term treasuries is probably due to their role as a hedge against two additional sources of risk: The risk of long term bond yields rising relative to short yields (slope risk), and the risk of medium-term yields rising relative to both short term and long term yields (curvature risk).

Off-road Vehicle Rollover and Field Testing of Stability Index

Off-road vehicles are often operated in unstable situations and on rough terrain where operators may be subjected to high-risk conditions. Tractor stability and the reduction of injuries related to tractor rollovers are areas that need to be addressed. This article presents typical tractor rollover tests and analyzes tractor stability in terms of the stability index developed by authors. Three radio-controlled tractors were used to complete the tests. Tractors? dynamic state variables, such as roll and pitch angles, roll and pitch velocities, and ground speed, were recorded by the measuring system of tractor stability developed by authors, concurrently the image from videotape was used to identify the stability status of the tractors. The effect of velocity, ramp height, slope, and turning radius on tractor stability was studied. Rotation velocities can also significantly contribute to tractor rollover. The results indicate the validity of the stability index model. Language: en

The sparse formulation of ISPS and its application to voltage stability margin sensitivity and estimation

The sparse formulation of the invariant sub-space parametric sensitivity (ISPS) of the structure preserving power system model is derived. The ISPS is the projection of parametric sensitivity onto a particular critical eigensubspace of interest. In this paper, major modifications are proposed to extend the applicability of the ISPS. ISPS is computed while tracing simultaneously the trajectory of both dynamic and algebraic state variables. By doing so, the sparsity of total Jacobian (the Jacobian that corresponds to both dynamic and algebraic variables) is fully exploited. The authors also derived a new voltage stability margin estimation from the measure of ISPS. It is shown here that the derived margin sensitivity vector can be calculated with essentially no further cost once the measure of ISPS is available. The voltage stability margin for any other parameter variations can be easily estimated without re-computing the P-V curves. With this methodology, effective controls can be easily coordinated by quantifying the relative importance of a wide range of control parameters. Numerical studies with the IEEE New England 39-bus system shows the potential applications of the method.