State Variable Description Research Articles

Global reliability assessment of coupled transmission tower-insulator-line systems considering soil-structure interaction subjected to multi-hazard of wind and ice

This study aims to assess the global reliability of coupled transmission tower-insulator-line systems considering soil-structure interaction (CTTILSs-SSI) subjected to multi-hazard of wind and ice. Firstly, two simplified models of CTTILSs-SSI under stochastic wind and ice loads are established, and their governing equations are derived through the Lagrange equation. On this basis, a global reliability assessment framework of CTTILSs-SSI is proposed based on the improved maximum entropy method, in which the global performance function of CTTILSs-SSI is defined via the state variable description method. Finally, a practical ultra-high voltage overhead transmission line located on the icing zone is chosen to illustrate the proposed framework. Moreover, to investigate the influence of soil-structure interaction (SSI) and soil types on the global reliability of transmission tower-insulator-line systems (TTILSs), the global reliability of CTTILSs-SSI with various soil types is compared with that of a fixed base system. The results indicate that under the in-plane wind and ice loads, the global failure probability of TTILSs is almost zero, and it is essentially not affected by the SSI effect and soil types. However, under the out-of-plane wind and ice loads, the global failure probability of CTTILSs-SSI is higher than that of the fixed base system, and the global failure probability of CTTILSs-SSI increases as the soil stiffness decreases. Accordingly, it may be more reasonable to consider the SSI effect into the global reliability analysis of TTILSs subjected to ice and out-of-plane wind loads, particularly when the soil is soft.

Double bracket formulation for the distribution function approach to multibead-chain suspensions

A suspension of elastic chains of small beads in a Newtonian fluid is a common model for a viscoelastic polymer solution. The configuration of these multibead chains is described by a distribution function that evolves according to a Liouville or Fokker–Planck equation. The evolution of these multibead-chain suspensions is described using a double bracket formulation with a Hamiltonian functional. The conservative part of the dynamics is described by a Poisson bracket, and the dissipative part by an additional symmetric bracket. We treat the configuration space of multibead chains as a higher order tangent bundle. Lifting the fluid velocity field to the bundle leads naturally to a semidirect product Lie–Poisson bracket for the conservative dynamics. The elastic stress exerted by the multibead chains on the fluid then follows directly from the same Hamiltonian functional that governs the internal dissipative mechanics of the multibead chains. For chains with three or more beads, the possible bending of the chain introduces an angular momentum flux that is absent for chains with two beads. This flux appear as an asymmetric elastic stress whose antisymmetric part is the divergence of a rank-3 tensor, as in the Cosserats’ theory of couple stresses in media with no internal angular momentum density. We investigate the possibility of an exact closure, passing from a distribution function description to a closed internal state variable description of the fluid suspension, and obtain some sufficient conditions for their existence. The resulting exactly closable models are generalisations of the upper-convected Maxwell model to Hookean bead–spring chains instead of Hookean bead–spring pairs.

Transient Stability Assessment of an Alternator Connected to Infinite Bus Through a Series Impedance Using State Space Model

The power angle stability analysis is most important for a grid-connected alternator. This stability may be classified under transient or steady state. The steady state stability may again be classified as static and dynamic. Steady state stability is concerned for slow changes, often in the presence of automatic control systems. Transient stability is the stability of a machine or a group of machines under a sudden impact, e.g., a sudden change in load or a sudden change in generation or in network parameters. The recent practice is to deal with both these problems in terms of state variables for their various advantages. This paper presents the state variable description of an alternator under normal operating conditions and its deviation from normalcy due to a sudden change, e.g., a sudden short-circuit and subsequent operation of the breakers. Then, the power angle swing ( $$\delta ,\omega$$ ) has been computed using state variables. Infinite bus idealization has been made for the alternator as the capacity of the set (s) is small compared to that of the regional power grid. The classical model based on Park–Gorev transformation has been used to represent the machines. The state space models have been developed from it. The next task is to include the effect of exciter.

On optimal control theory in marine oil spill management: A Markovian decision approach

Most evaluations of ecological effects of petroleum contamination have related impacts to effects on the supply of products and services of importance to human cultures. In order to facilitate the decision making process in the event of crude oil spills into marine environments, this paper treats marine oil spill problem from a system-theoretic point of view using the state variable description of Markovian decision process and operational research formalism.

A non-IQ sampling controller in low level RF system**Supported by SSRF Project

This paper describes a non-IQ controller for digital Low Level RF (LLRF) feedback control. Based on this non-IQ sampling method, arbitrary frequency relationship between ADC/DAC sampling clocks and IF signals can be employed. The nonlinearity in digital conversion can be reduced and the system dynamic performance improved. This paper analyzes the nonlinearity in conventional IQ sampling, gives the state variable description of the non-IQ algorithm, presents an implementation and its synchronization, and compares its performances with IQ sampling.

Optical Phase Estimation in an Urban Wireless Communications Enviroment

We evaluate the performance of a sub-optimum optical phase estimator obtained using a state variable description of the optical channel and stochastic estimation techniques. We implement the estimator for an urban wireless communications network.

Costate prediction based optimal control for non-linear hybrid systems

This paper is derived for solving a non-linear discrete-continuous systems optimal control problem by iterating on a sequence of simplified problems in discrete form. A mixed approach with a discrete cost function and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local subsystem problems and a coordinator within a hierarchical framework. The correct optimal solution to a real system in which model-reality difference exists can be obtained from the system model by interconnected costate prediction iterative solution. The algorithm efficiency and convergence properties are demonstrated by simulation study.

An Internal State Variable Constitutive Description for the Deformation of Metals at Elevated Temperatures

In the present investigation, an internal state variable constitutive model for the description of metals that are deformed under hot-working conditions in the range of thermal recovery, where positive work hardening is displayed, is proposed. The flow stress of the material is expressed in terms of the deformation temperature and strain rate, besides the contribution of the mechanical strength of the different obstacles that oppose dislocation motion. The constitutive description is validated employing the flow stress, temperature, strain rate, and strain increment data obtained from tests carried out both on Al-5.5 pct Mg and C-Mn steel. The model thus advanced assumes that the main obstacles to dislocation motion are solute atoms either in substitutional or interstitial solid solution and forest dislocations, although other contributions to the flow stress can also be readily incorporated. The formulation developed describes quite accurately the flow stress and work-hardening rate of the material under the temperature and strain rate conditions investigated. Also, it is able predict the occurrence of significant strain transients when deformation conditions are suddenly changed. Appropriate parameters involved in the model allow the comparison of the contribution of different strengthening mechanisms to the flow stress of different materials

Linear state space model for long-term blood pressure regulation

Abnormal cardiovascular regulation acts as a potential trigger of hypertension, which is one of the main problems in modern societies. The purpose of the present work is to describe the non-linear cardiovascular system in a state variable form, suitable for applying control theory techniques. A linear state variable description of long-term Arterial Blood Pressure (ABP) regulation has been developed for the analysis of the system's properties. The influence of the system's parameters on the stability and dynamic behaviour is analysed using eigen values. The closed loop poles of the system under normal and pathological conditions have been evaluated through the root locus technique, which indicates some applications of prediction and diagnosis. The simulation results show that the linear model yields a performance which is very close to that of the actual non-linear model.

Minimal Multirealization of MIMO Linear Systems

This note explores the minimal multirealization problem, which is the determination of a minimal degree, parameter-dependent, state variable description to express a finite set of linear multivariable systems. The form of the parameter-dependent state variable description is selected as a feedback form to implement "state sharing" and "bumpless transfer," which are possible ways to improve poor transient responses for switching control. The problem is solved by finding a special kind of minimal multiplier for a finite set of polynomial matrices.

Dynamics analysis of a single-stage isolated high power factor converter with a magnetic switch

The dynamics analysis of a single-stage isolated high power factor correction (PFC) converter is presented. In the single-stage PFC converter, the boost converter is operating in discontinuous conduction mode to exhibit an inherent gift of high power factor. It is integrated with a flyback converter that is operating in continuous conduction mode to achieve tight output voltage regulation. In addition, a magnetic switch is added to effectively reduce the high stress voltage across the bulk capacitor. Based on the averaging method, a nonlinear state-variable description of the converter is established. The small-signal model linearised around the operating point is then derived. The average power balance method, IsSpice simulation and experimental results successfully verify the dynamics and performances of the converter.

A coupling procedure of FE and SBFE for soil–structure interaction in the time domain

AbstractA coupling procedure of finite element (FE) and scaled boundary finite element (SBFE) is presented for three‐dimensional (3D) dynamic analysis of unbounded soil–structure interaction in the time domain. The procedure is implemented with the following efficient techniques: (1) Based on the concepts of linear system theory, the acceleration unit‐impulse response matrix of the unbounded soil calculated by the SBFE method is converted into a group of time‐independent matrices; thus, the time history of the unit‐impulse response function of the unbounded medium can be replaced by an equivalent state‐variable description. (2) The interaction forces between the unbounded soil and the structure are evaluated by a system of linear equations instead of time‐consuming convolution integrals. (3) Since only the partial information of the unit‐impulse response function is sufficient to capture the main character of the unbounded medium and the history of response function can be truncated at the cut‐off time tc, the computational effort spent in the SBFE method can be further reduced. In addition, the accuracy of the procedure can be controlled with prescribed parameters, thus the main advantage of the SBFE method as a highly accurate procedure is retained. Three numerical examples of foundation response demonstrate that good agreement can be achieved when compared with previous results, and high efficiency is also evident compared with the direct convolution integral method. Copyright © 2004 John Wiley & Sons, Ltd.

Modeling the evolution in microstructure and properties during plastic deformation of f.c.c.-metals and alloys – an approach towards a unified model

A new approach to the modeling of work hardening during plastic deformation of f.c.c.-metals and alloys has been recently proposed by the present authors. The model is based on a statistical approach to the problem of athermal storage of dislocations. By combining the solution for the dislocation storage problem with models for dynamic recovery of network dislocations and sub-boundary structures, a general internal state variable description is obtained. The model includes effects due to variations in: (i) stacking fault energy, (ii) grain size, (iii) solid solution content, and (iv) particle size and volume fraction. The result is a work hardening model, which in principle is capable of providing the stress–strain behavior for a given metal or solid solution alloy under condition ranging from deformation in the ambient temperature range to high temperature creep. It will be demonstrated that the model predictions, in terms of microstructure evolution and associated properties, in general, are in good agreement with experimental observations.

Optimal control of a class of discrete–continuous non-linear systems—decomposition and hierarchical structure

A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.

Modelling strain hardening and steady state deformation of Al–Mg alloys

A new approach to the modelling of work hardening during plastic deformation of pure fcc metals has recently been proposed by the present authors. The model is based on a statistical approach to the problem of athermal storage of dislocations. By combining the solution for the dislocation storage problem with models for dynamic recovery of network dislocations and sub-boundary structures, a general internal state variable description is obtained. In the present work this model is further developed by including the effects resulting from grain boundaries, elements in solid solution, and the presence of non-deformable precipitate particles. The result is a work hardening model and associated computer code, capable of providing the stress–strain behaviour for a given solid solution alloy under any combination of constant strain rate and temperature. The model has been applied to the problems of work hardening and flow stress saturation in Al–Mg alloys. It is demonstrated that the model predictions, in terms of microstructure evolution and associated strengthening, are in good agreement with experimental observations.

Dynamic Model of an Airborne Permanent Magnet Direct Telescope Drive

A three axes synchronous torque motor with permanent magnet excitation and solid stator and rotor yokes is used to adjust an air borne telescope for infrared starlight observation. To simulate the nonlinear behaviour of the motor, mainly due to the rising eddy currents in the solid yokes, a dynamic model is presented for MATLAB/SIMULINK using the results from previous FD calculations in frequency domain transfered into state variable description. A comparison between measured and calculated dynamic thrust force is presented.

The <i>ALFLOW</i>-Model - A Microstructural Approach to Constitutive Plasticity-Modelling of Aluminium Alloys

A new approach to the modeling of work hardening during plastic deformation of pure fcc metals has recently been proposed by the present authors. The model is based on a statistical approach to the problem of athermal storage of dislocations. By combining the solution for the dislocation storage problem with models for dynamic recovery of network dislocations and sub-boundary structures, a general internal state variable description is obtained. Effects due to elements in solid solution and the presence of non-deformable precipitate particles are also included. The result is a work hardening model and associated computer code capable of providing the stress strain behavior for a given solid solution alloy under any combination of constant strain rate and temperature. This paper presents a dedicated version of this model (ALFLOW) designed for dealing with the problems of work hardening and flow-stress saturation in aluminium alloys.

Evolution of mechanical state in Carrara marble during deformation at 400° to 700°C

The evolution of the mechanical state of Carrara marble during deformation up to strains of 0.2 at 400° to 700°C and strain rates of 10−4 to 10−6 s−1 has been investigated by applying Hart's [1976] state variable description of inelastic deformation to the results of isothermal, constant displacement rate experiments performed at these conditions. At T⪕600°C the magnitude of the mechanical state increases over the full range of strains investigated even when the deformation occurs at almost constant stress and strain rate, although the rate of increase at given strain decreases with increasing temperature and decreasing strain rate. The deformation microstructures suggest that under these conditions mechanical twinning controls the deformation behavior, with twin boundary migration becoming significant at T⪖450°C. As a dynamic recovery process, twin boundary migration is as efficient as strain‐induced grain boundary migration. At T>600°C the magnitude of the mechanical states attained is difficult to evaluate reliably using the method employed, but the continuing evolution of the deformation microstructures suggests that a steady state is not attained by strains of 0.2. At these conditions, mechanical twinning is replaced by other intracrystalline slip processes and by grain boundary bulge nucleated dynamic recrystallization. Hart's description of inelastic deformation, as previously evaluated for Carrara marble at T⪕400°C, may be extrapolated to 600°C provided the mechanical state evolution equation is modified to accommodate twin boundary migration and the influence of annealing‐type recovery processes. Extrapolation to higher temperatures may require modifications to the equation of state in that description. Although at the conditions investigated steady state appears to be a poor approximation, steady state flow laws of exponential and power law type do provide a good empirical description of the data. However, the observation that steady state is not attained indicates that any microphysical interpretation of the magnitude of the material parameters in such steady state flow law fits should be treated with caution.

Optimal Control of Non-Linear Hybrid Systems Under Model-Reality Differences - Decomposition and Hierarchical Structure

A technique is described for solving a non-linear optimal problem when the model dynamic equations, model performance index and model terminal constraints are all different from reality. The technique is designed to achieve the correct solution of the real optimal control problem in spite of these model-reality differences. A hybrid approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be composed in local sub-system problems and a co-ordinator within a hierarchical framework.

The high temperature static recovery and recrystallization behaviour of cold-worked Carrara marble

The static recovery and recrystallization behaviour of Carrara marble has been investigated as a function of pre-strain (8–27%) and annealing temperature (500–700 °C). Quantitative estimates of the rate of recovery were obtained by comparing the stress/strain curves generated at a temperature of 426 °C, a confining pressure of 170 MPa, and a strain-rate of 3 × 10 −4s −1 before and after a period of isostatic annealing. Curves of fractional recovery ( r) as a function of log time ( t) show a characteristic sigmoidal shape in which the rate of recovery ( dr/d logt) is initially small, increases rapidly, and finally becomes small again. The acceleration of recovery occurs at shorter times both with increasing pre-strain and with increasing annealing temperature. Microstructural examination of the annealed material shows that the acceleration of recovery corresponds to the onset of recrystallization, and that prior to the onset of recrystallization, recovery is controlled by the development of a subgrain structure, whereas after recrystallization has gone to completion, it is controlled by the intensification and growth of this substructure. The results have been interpreted within the perspective of Hart's state variable description of inelastic deformation. This analysis shows that the decay of the mechanical state of the marble during annealing can be treated as a two stage static recovery process (substructure formation → substructure coarsening), with the recrystallization marking the transition between these two stages.