A homotopy approach for stabilizing single-input systems with control structure constraints

A linear state feedback gain vector used in the control of a single input dynamical system may be constrained because of the way feedback is realized. Some examples of feedback realizations which impose constraints on the gain vector are: static output feedback, constant gain feedback for several operating points of a system, and two-controller feedback. We consider a general class of problems of stabilization of single input dynamical systems with such structural constraints and give a numerical method to solve them. Each of these problems is cast into a problem of solving a system of equalities and inequalities. In this formulation, the coefficients of the quadratic and linear factors of the closed-loop characteristic polynomial are the variables. To solve the system of equalities and inequalities, a continuous realization of the gradient projection method and a barrier method are used under the homotopy framework. Our method is illustrated with an example for each class of control structure constraint.

An Approach Toward Homocalystegines and Silyl-homocalystegines. Acid-Mediated Migrations of Acetates in Seven-Membered Ring Systems

A short access to homocalystegine analogues silylated at C7 is described. The synthesis involves the desymmetrization of a (phenyldimethylsilyl)methylcycloheptatriene using osmium-mediated dihydroxylation, followed by the diol protection and a cycloaddition involving the remaining diene moiety and an acylnitroso reagent. Additions of the osmium and acylnitroso reagents were shown, through X-ray diffraction studies of the resulting major isomers, to occur anti and syn, respectively, relative to the SiCH2 substituent. N-O bond cleavage on the resulting cycloadduct then produces the aminopolyol having a silylmethyl substituent. Oxidation of the C-Si bond also afforded an access to unusual amino-heptitols having five contiguous stereogenic centers. In the course of this work, we finally observed a unusual rearrangement taking place on cycloheptanone 18 substituted by two acetyl groups and a neighboring Boc-protected amine. A profound reorganization of the substituents on the seven-membered ring effectively took place under acidic conditions (TFA) leading to the thermodynamically more stable homocalystegine-type compound., DFT calculations of the conformational energy of isomeric silyl homocalystegines indicated that the product observed upon the acid-mediated rearrangement was the most stable of a series of analogues with various distributions of substituents along the seven-membered ring backbone. A tentative mechanism is proposed to rationalize the acetate migrations and inversions of the stereochemistry at various stereocenters.

An optimal dynamic inversion approach for controlling a class of one-dimensional nonlinear distributed parameter systems

Combining the principles of dynamic inversion and optimization theory, a new approach is presented for stable control of a class of one-dimensional nonlinear distributed parameter systems, assuming the availability a continuous actuator in the spatial domain. Unlike the existing approximate-then-design and design-then-approximate techniques, here there is no need of any approximation either of the system dynamics or of the resulting controller. Rather, the control synthesis approach is fairly straight-forward and simple. The controller formulation has more elegance because we can prove the convergence of the controller to its steady state value. To demonstrate the potential of the proposed technique, a real-life temperature control problem for a heat transfer application is solved. It has been demonstrated that a desired temperature profile can be achieved starting from any arbitrary initial temperature profile.

Hybrid systems through natural product leads: An approach towards new molecular entities

Hybrid systems are constructs of different molecular entities, natural or unnatural, to generate functional molecules in which the characteristics of various components are modulated, amplified or give rise to entirely new properties. These hybrids can be designed from carefully selected components either through domain intergration of key structural/functional features or via straightforward covalent linkages. Some of the recently reported hybrid systems based on steroid, carbohydrate, C-60-fullerene platforms, amongst others, mainly crafted with the object of enhancement of the therapeutical spectrum, will be discussed.

Integrated Reservoir Operation Modeling for Irrigation Systems - A Multi-Objective Approach

An integrated reservoir operation model is presented for developing effective operational policies for irrigation water management. In arid and semi-arid climates, owing to dynamic changes in the hydroclimatic conditions within a season, the fixed cropping pattern with conventional operating policies, may have considerable impact on the performance of the irrigation system and may affect the economics of the farming community. For optimal allocation of irrigation water in a season, development of effective mathematical models may guide the water managers in proper decision making and consequently help in reducing the adverse effects of water shortage and crop failure problems. This paper presents a multi-objective integrated reservoir operation model for multi-crop irrigation system. To solve the multi-objective model, a recent swarm intelligence technique, namely elitist-mutated multi-objective particle swarm optimisation (EM-MOPSO) has been used and applied to a case study in India. The method evolves effective strategies for irrigation crop planning and operation policies for a reservoir system, and thereby helps farming community in improving crop benefits and water resource usage in the reservoir command area.

Average variation L2-stability criteria for time-varying feedback systems-A unified approach

The problem of developing L2-stability criteria for feedback systems with a single time-varying gain, which impose average variation constraints on the gain is treated. A unified approach is presented which facilitates the development of such average variation criteria for both linear and nonlinear systems. The stability criteria derived here are shown to be more general than the existing results.

Approach to the problem of ferroresonance in e.h.v. systems

An analytical analysis of ferroresonance with possible cases of its occurrence in series-and shunt-compensated systems is presented. A term `percentage unstable zoneÿ is defined to compare the jump severity of different nonlinearities. A direct analytical method has been shown to yield complete information. An attempt has been made to find all four critical points: jump-from and jump-to points of ferroresonance jump phenomena. The systems considered for analysis are typical 500 kV transmission systems of various lengths.

Representation of evidence: An approach to uncertainty handling in knowledge-based systems

Many knowledge based systems (KBS) transform a situation information into an appropriate decision using an in built knowledge base. As the knowledge in real world situation is often uncertain, the degree of truth of a proposition provides a measure of uncertainty in the underlying knowledge. This uncertainty can be evaluated by collecting `evidence' about the truth or falsehood of the proposition from multiple sources. In this paper we propose a simple framework for representing uncertainty in using the notion of an evidence space.

Intelligent Approach for Fault Diagnosis in Power Transmission Systems Using Support Vector Machines

This paper presents an approach for identifying the faulted line section and fault location on transmission systems using support vector machines (SVMs) for diagnosis/post-fault analysis purpose. Power system disturbances are often caused by faults on transmission lines. When fault occurs on a transmission system, the protective relay detects the fault and initiates the tripping operation, which isolates the affected part from the rest of the power system. Based on the fault section identified, rapid and corrective restoration procedures can thus be taken to minimize the power interruption and limit the impact of outage on the system. The approach is particularly important for post-fault diagnosis of any mal-operation of relays following a disturbance in the neighboring line connected to the same substation. This may help in improving the fault monitoring/diagnosis process, thus assuring secure operation of the power systems. In this paper we compare SVMs with radial basis function neural networks (RBFNN) in data sets corresponding to different faults on a transmission system. Classification and regression accuracy is reported for both strategies. Studies on a practical 24-Bus equivalent EHV transmission system of the Indian Southern region is presented for indicating the improved generalization with the large margin classifiers in enhancing the efficacy of the chosen model.

An invariant subspace-based approach to the random eigenvalue problem of systems with clustered spectrum

The repeated or closely spaced eigenvalues and corresponding eigenvectors of a matrix are usually very sensitive to a perturbation of the matrix, which makes capturing the behavior of these eigenpairs very difficult. Similar difficulty is encountered in solving the random eigenvalue problem when a matrix with random elements has a set of clustered eigenvalues in its mean. In addition, the methods to solve the random eigenvalue problem often differ in characterizing the problem, which leads to different interpretations of the solution. Thus, the solutions obtained from different methods become mathematically incomparable. These two issues, the difficulty of solving and the non-unique characterization, are addressed here. A different approach is used where instead of tracking a few individual eigenpairs, the corresponding invariant subspace is tracked. The spectral stochastic finite element method is used for analysis, where the polynomial chaos expansion is used to represent the random eigenvalues and eigenvectors. However, the main concept of tracking the invariant subspace remains mostly independent of any such representation. The approach is successfully implemented in response prediction of a system with repeated natural frequencies. It is found that tracking only an invariant subspace could be sufficient to build a modal-based reduced-order model of the system. Copyright (C) 2012 John Wiley & Sons, Ltd.

A pseudobinary approach to study interdiffusion and the Kirkendall effect in multicomponent systems

Interdiffusion studies become increasingly difficult to perform with the increasing number of elements in a system. It is rather easy to calculate the interdiffusion coefficients for all the compositions in the interdiffusion zone in a binary system. The intrinsic diffusion coefficients can be calculated for the composition of Kirkendall marker plane in a binary system. In a ternary system, however, the interdiffusion coefficients can only be calculated for the composition where composition profiles from two different diffusion couples intersect. Intrinsic diffusion coefficients are possible to calculate when the Kirkendall markers are also present at that composition, which is a condition that is generally difficult to satisfy. In a quaternary system, the composition profiles for three different diffusion couples must intersect at one particular composition to calculate the diffusion parameters, which is a condition that is almost impossible to satisfy. To avoid these complications in a multicomponent system, the average interdiffusion coefficients are calculated. I propose a method of calculating the intrinsic diffusion coefficients and the variation in the interdiffusion coefficients for multicomponent systems. This method can be used for a single diffusion couple in a multicomponent pseudobinary system. The compositions of the end members of a diffusion couple should be selected such that only two elements diffuse into the interdiffusion zone. A few hypothetical diffusion couples are considered in order to validate and explain our method. Various sources of error in the calculations are also discussed.

State estimation in power systems using linear model infinity norm-based trust region approach

State estimation is one of the most important functions in an energy control centre. An computationally efficient state estimator which is free from numerical instability/ill-conditioning is essential for security assessment of electric power grid. Whereas approaches to successfully overcome the numerical ill-conditioning issues have been proposed, an efficient algorithm for addressing the convergence issues in the presence of topological errors is yet to be evolved. Trust region (TR) methods have been successfully employed to overcome the divergence problem to certain extent. In this study, case studies are presented where the conventional algorithms including the existing TR methods would fail to converge. A linearised model-based TR method for successfully overcoming the convergence issues is proposed. On the computational front, unlike the existing TR methods for state estimation which employ quadratic models, the proposed linear model-based estimator is computationally efficient because the model minimiser can be computed in a single step. The model minimiser at each step is computed by minimising the linearised model in the presence of TR and measurement mismatch constraints. The infinity norm is used to define the geometry of the TR. Measurement mismatch constraints are employed to improve the accuracy. The proposed algorithm is compared with the quadratic model-based TR algorithm with case studies on the IEEE 30-bus system, 205-bus and 514-bus equivalent systems of part of Indian grid.