Tillage Options for Productivity and Profitability of Food Forage Based Production System in Indo Gangetic Plains of India

Food – Forage based systems are the pre-requisite for sustainable rural development mainly as they provide support to small and marginal farmers by adjusting a substantial part of their land exclusively for forage production in grain crop based rotations (Kumar and Faruqui, 2009). In addition, the high cost of cultivation of intensive cropping systems is a major bottleneck in sustainable and profitable crop production. Presently, new innovations in tillage has revolutionized agriculture worldwide mainly due to reducing cost of cultivation, bulk density of soil and trafficabiltiy and also improving soil organic carbon resulting into high soil fertility. In addition, zero tillage provides extra benefit of time saving so that one short duration crop may be included in the crop rotation and increase cropping intensity. Therefore, the reduced tillage and zero tillage both have special attention among farming communities. Considering the increasing popularity about reduced and zero tillage, the present study was undertaken to assess the impact of tillage options in quality forage production in Indo-Gangetic plains of India Will the objectives. 1. To find out the suitable tillage options for forage production, 2. To study the effect of tillage options on productivity and profitability of forage production, and 3. To assess the impact of tillage options on soil fertility

Invariance feedback entropy of uncertain nonlinear control systems

In der klassischen Kontrolltheorie geht man üblicherweise davon aus, dass Sensoren und Regler durch Punkt-zu-Punkt-Verkabelung miteinander verbunden sind. In vernetzten Kontrollsystemen (VKS) sind Sensoren und Regler oft räumlich verteilt und Daten werden mittels eines digitalen Kommunikationsnetzwerks übertragen. Im Vergleich zu klassischen Kontrollsystemen bieten VKS viele Vorteile wie z.B. reduzierte Verkabelung, geringe Installations- und Instandhaltungskosten, größere Systemflexibilität und einfache Modifizierbarkeit. VKS haben Anwendungen in vielen Bereichen, z.B. in der Fahrzeugtechnik, intelligenten Gebäuden und Transportnetzwerken. Jedoch macht die Verwendung von Kommunikationsnetzwerken in Regelschleifen die Analyse und den Entwurf von VKS wesentlich komplexer. Die Verwendung digitaler Kanäle in VKS beschränkt aufgrund der endlichen Bandbreite die Datenmenge, die pro Zeiteinheit von Sensoren zu Reglern übertragen werden kann. Dies führt zu Quantisierungsfehlern, welche die Regelungsperformance ungünstig beeinflussen können. Das Problem der Regelung und Zustandsschätzung über einen digitalen Kommunikationskanal mit beschränkter Bitrate hat in den letzten zwei Jahrzehnten viel Aufmerksamkeit erhalten. Eine scharfe untere Schranke der Datenrate eines digitalen Kanals zwischen dem Kodierer (in Sensornähe) und dem Regler, die zum Erreichen eines Regelungsziels wie z.B. Stabilisierung oder Invarianz benötigt wird, kann durch einen passenden Entropiebegriff als intrinsische Größe des Systems charakterisiert werden, und hängt nicht von der Wahl des Kodierers und Reglers ab. Im ersten Teil der Arbeit beschreiben wir die Invarianz-Feedback-Entropie (IFE), die den Begriff der Invarianz-Entropie für deterministische nichtlineare Kontrollsysteme auf unsichere Systeme erweitert. Die IFE charakterisiert die Zustandsinformation, die von einem Regler benötigt wird, um eine Teilmenge Q des Zustandsraums invariant zu machen. Wir diskutieren eine Anzahl von elementaren Eigenschaften der IFE, z.B. Bedingungen für ihre Endlichkeit und die im deterministischen Spezialfall vorliegende Äquivalenz zum wohlbekannten Begriff der Invarianz-Entropie (IED). Wir analysieren unsichere lineare Kontrollsysteme und leiten eine universelle Unterschranke der IFE her. Im zweiten Teil der Arbeit betrachten wir vernetzte Kontrollsysteme und streben eine obere Schranke der IFE eines Netzwerks in Termen der IFE der Teilsysteme an. Außerdem präsentieren wir drei technische Resultate. Zuerst zeigen wir, dass die IFE einer nichtleeren Teilmenge Q des Zustandsraums eines zeitdiskreten unsicheren Kontrollsystems nach oben durch die größte IFE der Mengen in einer beliebigen endlichen Partition von Q beschränkt ist. Im zweiten Resultat betrachten wir unsichere Kontrollsysteme S1 und S2 mit identischen Zustands- und Eingangsräumen. Die mengenwertigen Übergangsfunktionen F1 und F2 der beiden Systeme sind nach Annahme so beschaffen, dass das Bild eines beliebigen Zustands-Eingangs-Paars unter F1 in dem entsprechenden Bild unter F2 enthalten ist. Für eine gegebene nichtleere Teilmenge des Zustandsraums zeigen wir, dass die IFE von S2 größer oder gleich derjenigen von S1 ist. Das dritte Resultat zeigt, dass die IFE niemals kleiner wird, wenn man die Menge der Kontrolleingänge verkleinert. Um die Effektivität der Resultate zu illustrieren, berechnen wir eine Ober- und eine Unterschranke der IFE eines Netzwerks von unsicheren, linearen, zeitdiskreten Systemen, welche den zeitlichen Verlauf der Temperaturen in 100 Räumen eines zirkulären Gebäudes beschreiben. Im letzten Teil der Arbeit präsentieren wir Algorithmen für die numerische Abschätzung der IFE. Dazu betrachten wir zunächst eine Partition einer gegebenen Teilmenge Q des Zustandsraums. Dann wird ein Regler in Form einer Suchtabelle berechnet, die jedem Element der Partition eine Menge von Kontrollwerten zuordnet, welche die Invarianz von Q garantieren. Nach der Reduktion der Suchtabelle von einer mengenwertigen zu einer einwertigen Abbildung, wird ein gewichteter Graph konstruiert. Für deterministische Systeme liefert der Logarithmus des Spektralradius einer Übergangsmatrix, die aus dem Graphen ermittelt wird, eine obere Schranke der Entropie. Für unsichere Systeme stellt das maximale durchschnittliche Zyklusgewicht des Graphen eine Oberschranke der IFE dar. Im deterministischen Fall zeigen wir, dass der Wert der ersten Oberschranke nicht größer als derjenige der zweiten Oberschranke ist. Als nächstes präsentieren wir die Ergebnisse der Algorithmen angewandt auf drei deterministische Beispielsysteme, für welche der exakte Wert der IED bekannt ist oder durch andere Methoden abgeschätzt werden kann. Zusätzlich liefert unser Algorithmus ein statisches Kodierungs- und Regelungsprotokoll, das der Schranke an die Datenrate entspricht. Schließlich präsentieren wir die berechneten Oberschranken der IFE eines unsicheren linearen Kontrollsystems.In classical control theory, the sensors and controllers are usually connected through point-to-point wiring. In networked control systems (NCS), sensors and controllers are often spatially distributed and involve digital communication networks for data transfer. Compared to classical control systems, NCS provide many advantages such as reduced wiring, low installation and maintenance costs, greater system flexibility and ease of modification. NCS find applications in many areas such as automobiles, intelligent buildings, and transportation networks. However, the use of communication networks in feedback control loops makes the analysis and design of NCS much more complex. In NCS, the use of digital channels for data transfer from sensors to controllers limits the amount of data that can be transferred per unit of time, due to the finite bandwidth of the channel. This introduces quantization errors that can adversely affect the control performance. The problem of control and state estimation over a digital communication channel with a limited bit rate has attracted a lot of attention in the past two decades. A tight lower bound on the data rate of a digital channel between the coder (near the sensor) and the controller, to achieve some control task such as stabilization or invariance, can be characterized in terms of some appropriate notion of entropy which is described as an intrinsic property of the system and is independent of the choice of the coder-controller. In the first part of this thesis, we describe invariance feedback entropy (IFE) that extends the notion of invariance entropy of deterministic nonlinear control systems to those with uncertainty. The IFE characterizes the necessary state information required by any controller to render a subset Q of the state space invariant. We discuss a number of elementary properties of the IFE, e.g. conditions for its finiteness and its equivalence to the well-known notion of invariance entropy (IED) in the deterministic case. We analyze uncertain linear control systems and derive a universal lower bound of the IFE. In the second part of this thesis, we consider interconnected control systems and seek to upper bound the IFE of the network using the IFE of the subsystems. In addition, we present three technical results related to the IFE. First, we show that the IFE of a nonempty subset Q of the state space of a discrete-time uncertain control system is upper bounded by the largest possible IFE among the members of any finite partition of Q. Second, we consider two uncertain control systems, S1 and S2, that have identical state spaces and identical control input sets. The set valued transition functions, F1 and F2, of the two systems are such that the image of any state-input pair under F1 is a subset of that under F2. For a given nonempty subset of the state space, we show that the IFE of S2 is larger than or equal to the IFE of S1. Third, we show that the IFE will never decrease by reducing the set of control inputs. To illustrate the effectiveness of the results, we compute an upper bound and a lower bound of the IFE of a network of uncertain, linear, discrete-time subsystems describing the evolution of temperatures of 100 rooms in a circular building. In the last part of this thesis, we present algorithms for the numerical estimation of the IFE. In particular, given a subset Q of the state space, we first partition it. Then a controller, in the form of a lookup table that assigns a set of control values to each cell of the partition, is computed to enforce invariance of Q. After reduction of the lookup table to a single-valued map from a set-valued one, a weighted directed graph is constructed. For deterministic systems, the logarithm of the spectral radius of a transition matrix obtained from the graph gives an upper bound of the entropy. For uncertain systems, the maximum mean cycle weight of the graph upper bounds the IFE. For deterministic systems, the value of the first upper bound is shown to be lower than or equal to the value of the second upper bound. Next, we present the results of the algorithms applied to three deterministic examples for which the exact value of the IED is known or can be estimated by other techniques. Additionally, our algorithm provides a static coder-controller scheme corresponding to the obtained data-rate bound. Finally, we present the computed upper bounds of the IFE for an uncertain linear control system

Shrinkage Effect of Close Components in Spectroscopic Instruments

Neglecting the Doppler width, the author has calculated the shift of maxima caused by mutual overlapping of intensity patterns of very close spectral lines for a number of spectroscopic instruments. A table, which may be used to correct for shrinkage effect has been given for Fabry Perot ctalon. The value of the resolving power of Fabry Perot etalon according to Abbe’s criterion has also boon refined taking into account the shrinkage effect

Parametric Study of Orthogonal Pantographic Lattice with Non-Linear Torsional Resistance at Pivots

Pantographic lattices are cellular solids comprised of continuous beam fibers intersecting at periodically spaced pivots. The pivots are simulated in the discrete finite element beam model as torsional springs with varied torsional stiffness across orders of magnitude. An important functional performance feature of pantographic lattices is their ability to undergo large deformation without inducing large stresses at the pivots. There is a need for predictive models of this nonlinear behavior. In this study, parameter studies on the order of magnitude and nonlinear material behavior of the torsional stiffness at the pivots, combined with and without nonlinear geometric beam kinematic behavior is investigated. In this study, the mechanical response of pantographic lattice is analyzed for a series of elongation tests based on a set of kinematic assumptions. Finite element numerical results are presented for the axial bias test for in-plane stretch along the bisector of the beam fiber orientations. Strain energy distributions are used to analyze the stiffness of the deformed geometry behavior. Geometric nonlinearity is introduced to study the response for large deformation while a non-linear torsional spring expressed as a cubic polynomial function of relative beam rotations at connection nodes is utilized to model local pivot softening and stiffening effects. One use of the discrete frame model presented in the study is to serve as a validation tool for homogenized pantographic sheet models based on second gradient field theory in the case of light spring stiffness relative to the beam lengths and section properties, of order epsilon squared, where epsilon is a small-scale parameter measuring the ratio of a repeating unit cell size to the overall lattice size. For epsilon of order one, the discrete beam model serves to validate homogenized models based on the first gradient classical elasticity theory. The discrete beam model of an orthogonally oriented lattice is constituted by torsional springs at intersection points which dictate the internal moments. At a joint, displacements of the nodes are rigidly constrained while rotational degrees of freedom are proportional to a local torsional stiffness for the lattice pivots. The torsional stiffness of the spring is varied from (perfect) zero to infinite limits to replicate a free and rigid connection respectively between the intersecting beams joints. For the nonlinear torsional pivot spring model, the torsional stiffness is not constant, instead of being a function of the magnitude of pivot rotations. The linear torsional springs are generated at the lattice pivots in the discrete mathematical model using constraints setup using Lagrange multipliers. Geometric nonlinearity has been introduced using the large deformation beam kinematics implemented within ABAQUS finite element software. The pantographic lattice is constituted by Euler Bernoulli beams connecting nodes along the designated fibers. A nonlinear relationship between moment and angle of rotation is utilized in Abaqus python scripting to develop nonlinear torsional spring behavior at the pivots. The effective material non-linearity considered is a function of two parameters and is driven by the relative angle of rotation of two beams connecting at the pivot. A predictive model for the total energy of the lattice during a small stretch is also developed and verified in the case of the nonlinear material spring model at the pivots.In order to help understand the effects of different aspects of nonlinearity during lattice stretch, including, deformed shape, reaction force resultant, total strain, and energy distribution, several combinations are studied; small stretch, comparing linear vs. nonlinear torsional spring stiffness at pivots, with and without beam geometric nonlinear kinematics, and large stretch, comparing linear vs. nonlinear pivot stiffness, with and without geometric nonlinearity. The analysis has also been extended to a 3D pantographic lattice where each pivot is constituted by three torsional springs connecting the three combinations of beam fiber pairs at each intersection joint

Effect of Background Intensity on Resolution

The paper discusses the effect of background intensity on the resolving power tables, illustrated by graphs, have been given for the variation of resolving power with background intensity in case of Fabry-Perot etalon, prism, grating and reflecting echelon, and when the instrumental width is negligible