Observability for a Class of Nonlinear Systems

t - N m and sufficient computable conditions are obtained for the obsemabii of systems with linear state equations and polgwmIal outputs. Based on these, initial state reconstmctors are also described.

Optimization of an ammonia reactor using regression analysis

This paper presents an optimization algorithm for an ammonia reactor based on a regression model relating the yield to several parameters, control inputs and disturbances. This model is derived from the data generated by hybrid simulation of the steady-state equations describing the reactor behaviour. The simplicity of the optimization program along with its ability to take into account constraints on flow variables make it best suited in supervisory control applications.

Study of voltage collapse at converter bus in asynchronous MTDC-AC systems

This paper presents the analysis and study of voltage collapse at any converter bus in an AC system interconnected by multiterminal DC (MTDC) links. The analysis is based on the use of the voltage sensitivity factor (VSF) as a voltage collapse proximity indicator (VCPI). In this paper the VSF is defined as a matrix which is applicable to MTDC systems. The VSF matrix is derived from the basic steady state equations of the converter, control, DC and AC networks. The structure of the matrix enables the derivation of some of the basic properties which are generally applicable. A detailed case study of a four-terminal MTDC system is presented to illustrate the effects of control strategies at the voltage setting terminal (VST) and other terminals. The controls considered are either constant angle, DC voltage, AC voltage, reactive current and reactive power at the VST and constant power or current at the other terminals. The effect of the strength of the AC system (measured by short circuit ratio) on the VSF is investigated. Several interesting and new results are presented. An analytical expression for the self VSF at VST is also derived for some specific cases which help to explain the number of transitions in VSF around the critical values of SCR.

On a linear steady-state system of equations in microcontinuum fluid mechanics

Galerkin representations and integral representations are obtained for the linearized system of coupled differential equations governing steady incompressible flow of a micropolar fluid. The special case of 2-dimensional Stokes flows is then examined and further representation formulae as well as asymptotic expressions, are generated for both the microrotation and velocity vectors. With the aid of these formulae, the Stokes Paradox for micropolar fluids is established.

Bayesian parameter identification in dynamic state space models using modified measurement equations

When Markov chain Monte Carlo (MCMC) samplers are used in problems of system parameter identification, one would face computational difficulties in dealing with large amount of measurement data and (or) low levels of measurement noise. Such exigencies are likely to occur in problems of parameter identification in dynamical systems when amount of vibratory measurement data and number of parameters to be identified could be large. In such cases, the posterior probability density function of the system parameters tends to have regions of narrow supports and a finite length MCMC chain is unlikely to cover pertinent regions. The present study proposes strategies based on modification of measurement equations and subsequent corrections, to alleviate this difficulty. This involves artificial enhancement of measurement noise, assimilation of transformed packets of measurements, and a global iteration strategy to improve the choice of prior models. Illustrative examples cover laboratory studies on a time variant dynamical system and a bending-torsion coupled, geometrically non-linear building frame under earthquake support motions. (C) 2015 Elsevier Ltd. All rights reserved.

On the nature of power flow equations in security analysis

The power system network is assumed to be in steady-state even during low frequency transients. However, depending on generator dynamics, and toad and control characteristics, the system model and the nature of power flow equations can vary The nature of power flow equations describing the system during a contingency is investigated in detail. It is shown that under some mild assumptions on load-voltage characteristics, the power flow equations can be decoupled in an exact manner. When the generator dynamics are considered, the solutions for the load voltages are exact if load nodes are not directly connected to each other

A Finite Variable Difference Relaxation Scheme for hyperbolic-parabolic equations

Using the framework of a new relaxation system, which converts a nonlinear viscous conservation law into a system of linear convection-diffusion equations with nonlinear source terms, a finite variable difference method is developed for nonlinear hyperbolic-parabolic equations. The basic idea is to formulate a finite volume method with an optimum spatial difference, using the Locally Exact Numerical Scheme (LENS), leading to a Finite Variable Difference Method as introduced by Sakai [Katsuhiro Sakai, A new finite variable difference method with application to locally exact numerical scheme, journal of Computational Physics, 124 (1996) pp. 301-308.], for the linear convection-diffusion equations obtained by using a relaxation system. Source terms are treated with the well-balanced scheme of Jin [Shi Jin, A steady-state capturing method for hyperbolic systems with geometrical source terms, Mathematical Modeling Numerical Analysis, 35 (4) (2001) pp. 631-645]. Bench-mark test problems for scalar and vector conservation laws in one and two dimensions are solved using this new algorithm and the results demonstrate the efficiency of the scheme in capturing the flow features accurately.

Studies on nonisothermal solid state galvanic cells — effect of gradients on EMF

An expression for the EMF of a nonisothermal galvanic cell, with gradients in both temperature and chemical potential across a solid electrolyte, is derived based on the phenomenological equations of irreversible thermodynamics. The EMF of the nonisothermal cell can be written as a sum of the contributions from the chemical potential gradient and the EMF of a thermocell operating in the same temperature gradient but at unit activity of the neutral form of the migrating species. The validity of the derived equation is confirmed experimentally by imposing nonlinear gradients of temperature and chemical potential across galvanic cells constructed using fully stabilized zirconia as the electrolyte. The nature of the gradient has no effect on the EMF.

Reliability models for existing structures based on dynamic state estimation and data based asymptotic extreme value analysis

The problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations is considered. The study assumes that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements m in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes' theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. In all these studies, the governing stochastic differential equations are discretized using the strong forms of Ito-Taylor's discretization schemes. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplifiedmby considering the reliability analysis of a few low-dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on a limited amount of pertinent Monte Carlo simulations. (C) 2010 Elsevier Ltd. All rights reserved.

Simplified Analysis of Steady-State Performance of a Voltage Controlled Induction Motor Drive

Utilizing a circuit model [1, 2] of an induction motor, a simplified analysis of steady state performance of a voltage controlled induction motor (VCIM) drive is described in this paper. By solving a set of nonlinear algebraic equations which describe the VCIM drive under steady operation, the operating variables such as constant components of torque, rotor flux linkages, fundamental components of stator voltage and current and phase angle are obtained for any given value of slip, triggering angle and supply voltage.

Points-to Analysis as a System of Linear Equations

We propose a novel formulation of the points-to analysis as a system of linear equations. With this, the efficiency of the points-to analysis can be significantly improved by leveraging the advances in solution procedures for solving the systems of linear equations. However, such a formulation is non-trivial and becomes challenging due to various facts, namely, multiple pointer indirections, address-of operators and multiple assignments to the same variable. Further, the problem is exacerbated by the need to keep the transformed equations linear. Despite this, we successfully model all the pointer operations. We propose a novel inclusion-based context-sensitive points-to analysis algorithm based on prime factorization, which can model all the pointer operations. Experimental evaluation on SPEC 2000 benchmarks and two large open source programs reveals that our approach is competitive to the state-of-the-art algorithms. With an average memory requirement of mere 21MB, our context-sensitive points-to analysis algorithm analyzes each benchmark in 55 seconds on an average.

Measurement of Gibbs energy of formation of Ca2PbO4 using a solid-state cell with three electrodes

Phase relations in the system Ca-Pb-O at 1100 K have been determined by equilibrating 18 compositions in the ternary and identifying the phases present in quenched samples by X-ray diffraction and energy dispersive X-ray analysis (EDX). Only one ternary compound Ca2PbO4 was found to be present. The compound coexists with CaO and PbO. The intermetallic compounds Ca2Pb, Ca5Pb3 and CaPb and liquid alloys are in equilibrium with CaO. The standard Gibbs energies of formation of Ca2PbO4 (880 - 1100 K) and Pb3O4 (770 - 910 K) were determined using solid-state cells based on yttria-stabilized zirconia as the solid electrolyte. Pure oxygen gas at 0.1 MPa was used as the reference electrode. For measurements on Ca2PbO4, a novel cell design with three electrodes in series, separated by solid electrolyte membranes, was used to avoid polarization of the electrode containing three solid phases. Two three-phase electrodes were used. The first absorbs the electrochemical flux of oxygen from the reference electrode to the measuring electrode. The other three-phase electrode, which is unaffected by the oxygen flux through the solid electrolyte, is used for electromotive force (EMF) measurement. The results from EMF studies were cross-checked using thermogravimetry (TG) under controlled oxygen partial pressures. The stability of Pb3O4 was investigated using a conventional solid-state cell with RuO2 electrodes. The results can be summarized by the following equations: 2CaO + PbO +1/2O(2) --> Ca2PbO4 Delta(r)G degrees/J mol(-1) = (- 128340 + 93.21 T/K) +/- 200 3PbO + 1/2O(2) --> Pb3O4 Delta(r)G degrees/J mol(-1) = (- 70060 + 77.5 T/K) +/- 150

The steady state nuclear Overhauser effect revisited

The steady state of a two spin system coupled to an isotropic environment and to each other through a dipolar interaction and under irradiation by a monochromatic, circularly polarized radio frequency field is determined ab initio using thermodynamic arguments. This steady state is used to describe the well known nuclear Overhauser effect in liquids. The steady state is also derived from the Solomon-Bloch set of equations used to describe the driven spin. It is shown that in the limit of weak driving, the two solutions coincide. (C) 1999 American Institute of Physics. [S0021-9606(99)71210-9].

Phase relations in the system Sr–Ir–O and thermodynamic measurements on SrIrO3, Sr2IrO4 and Sr4IrO6 using solid-state cells with buffer electrodes

The standard Gibbs energies of formation of SrIrO3, Sr2IrO4 and Sr4IrO6 have been determined in the temperature range from 975 to 1400 K using solid-state cells with (Y2O3) ZrO2 as the electrolyte and pure oxygen gas at a pressure of 0.1 MPa as the reference electrode. For the design of appropriate working electrodes, phase relations in the ternary system Sr–Ir–O were investigated at 1350 K. The only stable oxide detected along the binary Ir–O was IrO2. Three ternary oxides, SrIrO3, Sr2IrO4 and Sr4IrO6, compositions of which fall on the join SrO–IrO2, were found to be stable. Each of the oxides coexisted with pure metal Ir. Therefore, three working electrodes were prepared consisting of mixtures of Ir+SrO+Sr4IrO6, Ir+Sr4IrO6+Sr2IrO4, and Ir+Sr2IrO4+SrIrO3. These mixtures unambiguously define unique oxygen chemical potentials under isothermal and isobaric conditions. Used for the measurements was a novel apparatus, in which a buffer electrode was introduced between reference and working electrodes to absorb the electrochemical flux of oxygen through the solid electrolyte. The buffer electrode prevented polarization of the measuring electrode and ensured accurate data. The standard Gibbs energies of formation of the compounds, obtained from the emf of the cells, can be represented by the following equations: View the MathML sourcem View the MathML source View the MathML source where Δf (ox)Go represents the standard Gibbs energy of formation of the ternary compound from its component binary oxides SrO and IrO2. Based on the thermodynamic information, chemical potential diagrams for the system Sr–Ir–O were developed.

An advanced design of the solid-state cell for accurate thermodynamic measurements on ternary oxides: system Sm–Pd–O

An advanced design of the solid-state cell incorporating a buffer electrode has been developed for high temperature thermodynamic measurements. The function of the buffer electrode, placed between reference and working electrodes, was to absorb the electrochemical flux of the mobile species through the solid electrolyte caused by trace electronic conductivity. The buffer electrode prevented polarization of the measuring electrode and ensured accurate data. The application of the novel design and its advantages have been demonstrated by measuring the standard Gibbs energies of formation of ternary oxides of the system Sm–Pd–O. Yttria-stabilized zirconia was used as the solid electrolyte and pure oxygen gas at a pressure of 0.1 MPa as the reference electrode. For the design of appropriate working electrodes, phase relations in the ternary system Sm–Pd–O were investigated at 1273 K. The two ternary oxides, Sm4PdO7 and Sm2Pd2O5, compositions of which fall on the Sm2O3–PdO join, were found to coexist with pure metal Pd. The thermodynamic properties of the ternary oxides were measured using three-phase electrodes in the temperature range 950–1425 K. During electrochemical measurements a third ternary oxide, Sm2PdO4, was found to be stable at low temperature. The standard Gibbs energies of formation (Δf(ox)Go) of the compounds from their component binary oxides Sm2O3 and PdO, can be represented by the equations: Sm4PdO7: Δf(ox)Go (J mol−1)=−34,220+0.84T(K) (±280); Sm2PdO4: Δf(ox)Go (J mol−1)=−33,350+2.49T(K) (±230); Sm2Pd2O5: Δf(ox)Go (J mol−1)=−59,955+1.80T(K) (±320). Based on the thermodynamic information, three-dimensional P–T–C and chemical potential diagrams for the system Sm–Pd–O were developed.