Switching Curve Research Articles

Generation scheduling and the switching curve law

The switching curve law is an analytic procedure derived from the dual of the Lagrangian relaxation approach to the static unit commitment (SUC) problem. It is argued here that this analytic result provides a new understanding of the general unit commitment problem not otherwise possible from numerical methods. Moreover, the SUC problem and the analytic results presented here have direct applications in the scheduling of hydro generation in power plants and in the interpretation of the pricing rules of the England and Wales Power Pool.

Optimal control problems in the theory of smart structures

The methods of optimal control are applied to the problems of the theory of smart structures. Two optimization problems in the theory of smart structures are formulated and solved. These problems are concerned with the damping of mechanical oscillations by controlling the rigidity of the structure and applied force. The optimal controls are obtained in the form of optimal syntheses. In the first problem, the optimization criterion is to minimize the time required to transfer the system to a required state. The recurrent formula for the segments constituting the switching curve is derived. The second optimization problem is concerned with reduction of energy of oscillations by controlling the coefficient of rigidity of the structure. The objective of optimal control is to transfer the system to a given lower energy level in a minimal time. An explicit expression for all the segments of the switching curve is obtained.

Matteucci effect as exhibited by cylindrical CoP amorphous multilayers

CoP amorphous samples, electrodeposited on copper wires and exhibiting a longitudinal magnetic anisotropy, show a spontaneous Matteucci effect once the substrate has been subjected to torque. This induces an easy axis to allow for magnetization to occur, breaking away from its original longitudinal direction. The magnetic domain structures, as observed by the Bitter technique, revealed that the anisotropy changes direction, rotating gradually from its initial longitudinal position to a 45° helix, as the torque was increased. The reversible part of the circular magnetization switching curves, set against the longitudinal magnetic field, was fitted by assuming a magnetization rotation model in which constant anisotropic magnitude values were hardly modified, while allowing changes in direction.

Solution of Fixed Final State Optimal Control Problems via Simple Cell Mapping

A strategy is proposed to solve the fixed final state optimal control problem using the simple cell mapping method. A non-uniform time step simple cell mapping is developed to create a general database from which solutions of various optimal control problems can be obtained. A two-stage backward search algorithm is proposed to eliminate degenerated paths often associated with the simple cell mapping. The proposed method can accurately delineate the switching curves and eliminate false limit cycles in the solution. The method is applied to two optimal control problems with bang-bang control. The well-known minimum time control problem of moving a point mass from any initial condition to the origin of the phase plane is studied first. This example has exact solutions available which provide a yardstick to examine the accuracy of the method. The cell size dependence of the solution accuracy is studied numerically. The second example is a variable stiffness feedback control problem with tuning range saturation. The strategy proposed is able to provide the switching curves in the phase plane. This result has not been obtained before.

Self-switching with a nonlinear birefringent loop mirror

We investigate switching characteristics of the nonlinear birefringent loop mirror which consists of a symmetric directional coupler, a birefringent fiber, and a symmetry-breaking element that converts linearly polarized light to circularly polarized light, and vice versa. The condition for total reflection in the linear regime is obtained using the Jones matrix formalism, The switching curves have been obtained through numerical computations both in the nondispersive pulse regime and in the soliton-like pulse regime. Parameter values suitable for practical applications of our device as an intensity filter are obtained.

On "Evaluating the bounded-input-bounded-output stability integral for second-order systems"

It is shown that the value of this integral is easily calculated by using the nastiest disturbance switch curve in spiral coordinates.

A closed analytic form for the disturbance switch curve of some second-order linear systems

It is shown that the time-maximum disturbance switch curve for some second-order linear systems with the most stressful bounded disturbance has a closed analytic form. This enables a simple state-feedback synthesis for the bounded disturbance stress.

Analytical synthesis of time-optimal control in a third-order system

A time-optimal control that steers the phase point for a third-order linear system to the origin is constructed in an explicit analytical form. It is assumed that the characteristic exponents are zero, and the constraints on the control function are non-symmetric. The system simulates the dynamics of a point mass driven by a force whose rate of change can be regulated. An optimal control is constructed both in the feedback and open-loop forms. In the latter case, the optimal control is a function of time. Relations are derived for the switching curve and surface and for the time intervals of the motion; optimal phase trajectories are constructed; the feedback control portrait is investigated. The influence of a parameter characterizing the degree of asymmetry of the constraints is studied. “Near-optimal” control modes, which are much simpler to implement, are constructed.

A Random Approach to Time-Optimal Control

This paper concerns the time-optimal control for objects described by a random differential inclusion with discontinous right-hand side, representing the second law of Newtonian mechanics and taking into account a complex model of resistance to motion. Such a task has broad technical applications, especially in robotics. By generalizing the concept of the classic switching curve to the switching region, it is possible to construct in practice a range of convenient suboptimal control structures that provide many advantages, especially in respect to robustness.

Effect of cobalt nanoclusters on magnetization processes in CoB amorphous alloys

The magnetization processes in Co 80B 20 and Co 75B 25 amorphous alloys have been studied by means of their hysteresis loops and switching curves at room temperature. This analysis is correlated with the structural characterization made by HRTEM which showed different microstructure in both compositions. In particular, it is proposed that the presence of cobalt nanoclusters in the composition with stoichiometry departing from Co 3B, plays a main role in the magnetic behavior.

Ferroelectricity of lanthanum-modified lead titanate thin films obtained by a diol-based sol-gel method

Lanthanum-modified lead titanate thin films have been prepared by a diol-based sol-gel method from precursor solutions with a growing excess of PbO. The films were crystallized with thermal treatments at 650 °C and heating rates of 10 °C min-1 and higher than 500 °C min-1 by direct insertion in a pre-heated furnace. The structure, microstructure, and composition of the films were studied by grazing-incidence X-ray diffraction, electron microscopies, and energy-dispersive X-ray spectroscopy. A 20 mole % excess of PbO must be included in the precursor solution in order to compensate PbO volatilization occurring during the thermal treatment and, thus, obtain single-phase perovskite-type structure films. Non-textured porous films were obtained when a 10 °C min-1 rate is used, whereas [001]/[100] oriented films without porosity were obtained when rapid heating was used. Dielectric permittivity, ac current density, hysteresis loops, and switching curves were measured in the films. Values of remanent polarization and coercive field are comparable to those reported for similar films. The effects on the ferroelectric properties of an electrical and a post-crystallization thermal treatments were characterised.

Optimal control structure of an unreliable manufacturing system with random demands

This paper considers an unreliable manufacturing system with random processing times and random product demands. The system can produce many part types and its total capacity is constrained by a fixed constant. The objective is to find an optimal service-rate allocation policy between different part types by minimizing the expected discounted inventory and backlog cost. Structural properties of the optimal control policy are investigated. It is shown that the optimal policy is of a switching structure. For producing a one part type case, the optimal control is a threshold policy. For producing a two part types case, the optimal control can be described by three monotone switching curves and its asymptote properties are derived. Numeric examples are given to illustrate the results.

Effect of curing progress on the electrooptical and switching properties of PDLC system

Experimental studies on the morphology and thermal and electrooptical behavior of PDLC films consisting droplets of nematic LC (6CB) up to a 40% weight fraction in a polyester resin matrix crosslinked by diacrylane are presented. The PDLC samples were prepared by LC separation from a solution in a UV-polymerizing oligoester resin between TIO-coated glass plates. The electrooptical and switching results depending on the UV curing time of the polyester matrix are shown. The curing process of the polymer binder leading to phase separation of the LC causes increasing polymer stiffness affected by the boundary condition on the LC droplets. The reorientational dynamics of LC in PDLC, which reflects the character of switching curves for varying voltage and with progressing curing (varying from 40 s to 15 min), is discussed on the basis of the kinetic analysis of light scattering by the system. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 455–463, 1999

Analysis of Ferroelectric Switching Process in VDF/Trfe Copolymers

AbstractThe ferroelectric switching curve of vinylidene fluoride / trifluoroethylene copolymer exhibits a characteristic time evolution consisting of two processes; an initial gradual increase in proportion to t0 5 followed by a rapid increase according to an exponential function with particularly large exponent 6. Such a switching curve was analyzed by means of computer simulation based on a modified nucleation-growth mechanism. It was found that the initial gradual increase is attributed to generation of considerably large nuclei that grow according to a random-walk scheme. Once such nuclei gain a critical size, they start to grow automatically either one or two dimensionally. The time required to generate critical nuclei serves as an incubation time for the later growth process to result in the large exponent.

Quantitative modelling of HDPE spurt experiments using wall slip and generalised Newtonian flow

A quantitative model to describe capillary rheometer experiments is presented. The model can generate `two-branched' discontinuous flow curves and the associated pressure oscillations. Polymer compressibility in the barrel, incompressible axisymmetric generalised Newtonian flow in the die, and a switch curve that defines a stick-slip boundary condition are key elements in the model. Well defined experimental results of high density polyethylene are used to validate the model. The calculations compare well with the experiments. The only fit parameters are those related to the slip law. The present model can be made fully predictive by relating the slip law to fundamental polymer-wall interaction properties. The model offers a mathematical framework to validate potential slip laws.

DISTURBANCE STRESS FOR STABILIZED SECOND ORDER CONTROL SYSTEMS

It is shown that the nastiest bounded disturbance stress for the stable second order oscillator is bang–bang with switching set by the state. A quadratic index and a time-distance index are used to evaluate the severity of the stressing. A procedure is suggested to construct a switching curve which synthesizes the disturbance stress in feedback form. Examples illustrating the results and the possible extension to third and higher order systems are given.

Beyond the cμ rule: Dynamic scheduling of a two-class loss queue

We consider scheduling a single server in a two-class M/M/1 queueing system with finite buffers subject to holding costs and rejection costs for rejected jobs. We use dynamic programming to investigate the structural properties of optimal policies. Provided that the delay of serving a job is always less costly than rejecting an arrival, we show that the optimal policy has a monotonic threshold type of switching curve; otherwise, numerical analysis indicates that the threshold structure may not be optimal.

Suppression of switchable polarization in KDP by ionizing radiation

Switching curves were obtained from ${\mathrm{KH}}_{2}{\mathrm{PO}}_{4}$ single crystals exposed to x-ray radiation for various time intervals, up to 8 h. The applied electric field was varied between 370 and 740 V/cm, as well. The temperature was held constant at 99 K. The switching curves were fit to a three-parameter nucleation and growth model based on the original works by Johnson and Mehl, and independently by Avrami. The two dynamic parameters, characteristic time ${t}_{c},$ and effective domain wall dimensionality $n,$ produced values consistent with unirradiated studies, however, they did not show any clear dependancy on exposure time. The switchable polarization $P$ decreased with increasing exposure time. A simple exponential decay is used to describe $P$ as a function of exposure time. The rate coefficient $k$ for the exponential, decreases with increasing electric field.

Switching curve controller for FES-assisted standing up and sitting down.

A low-level, closed-loop controller for FES-assisted standing up and sitting down is described. If, for able-bodied individuals, when standing up and sitting down, the knee angular velocity is plotted against knee angle, consistent phase-plane trajectories are produced. The bang-bang controller uses a model of this trajectory as a switching curve. The design rationale for the controller was the desire to avoid injuries that might occur if knee-locking on standing up and seat-contact on sitting down are not adequately controlled. This switching curve controller (SCC) was incorporated within a hierarchical, finite state control scheme, with electrical stimulation applied bilaterally to the knee extensors. The SCC was tested in a pilot study on a female volunteer with paraplegia (T5/6 ASIA A) and evaluated against an unramped, open-loop controller (OLC). The vertical hand forces and knee angles were measured. The subject was able to achieve standing up and sitting down safely using both controllers. For standing up, the SCC was not found to offer any quantifiable advantages over the OLC and was found to increase the hand force by 8.4%. In contrast, for sitting down the SCC was found to reduce the knee angular velocities as the subject approached the seat by 27%, demonstrating a safer, softer landing.

Wavelength switching and routing using absorption and resonance

A resonator side coupled to a pair of waveguides can switch an optical signal between two ports by means of absorption. The absorptive mechanism is used to suppress the resonant power transfer, rather than to promote loss. Thus, the input signal only suffers small attenuation, provided that the mode volumes of the resonators can be made small enough. Multiply-coupled resonators lead to improved crosstalk performance for both the ON and OFF switched states. The performance of such devices are analyzed analytically, and universal switching curves are derived.