A perturbation approach to the stabilization of nonlinear cascade systems with time-delay

The effect of bounded input perturbations on the stability of nonlinear globally asymptotically stable delay differential equations is analyzed. We investigate under which conditions global stability is preserved and if not, whether semi-global stabilization is possible by controlling the size or shape of the perturbation. These results are used to study the stabilization of partially linear cascade systems with partial state feedback.

Delayed control of a Moore-Greitzer axial compressor model

Several feedback control laws have appeared in the literature concerning the stabilization of the nonlinear Moore-Greitzer axial compression model. Motivated by magnitude and rate limitations imposed by the physical implementation of the control law, Larsen et al. studied a dynamic implementation of the S-controller suggested by Sepulchre and Kokotović. They showed the potential benefit of implementing the S-controller through a first-order lag: while the location of the closed-loop equilibrium achieved with the static control law was sensitive to poorly known parameters, the dynamic implementation resulted in a small limit cycle at a very desirable location, insensitive to parameter variations. In this paper, we investigate the more general case when the control is applied with a time delay. This can be seen as an extension of the model with a first-order lag. The delay can either be a result of system constraints or be deliberately implemented to achieve better system behavior. The resulting closed-loop system is a set of parameter-dependent delay differential equations. Numerical bifurcation analysis is used to study this model and investigate whether the positive results obtained for the first-order model persist, even for larger values of the delay.

Liquid crystal based continuous phase retarder: From optically neutral to a quarter waveplate in 200 microseconds

Liquid crystal variable phase retarders have been incorporated into prototype devices for optical communications system applications, both as endless polarization controllers 1,2,3, and as holographic beam steerers 4. Nematic liquid crystals allow continuous control of the degree of retardation induced at relatively slow switching speeds, while ferroelectric liquid crystal based devices allow fast (sub millisecond) switching, but only between two bistable states. The flexoelectro-optic effect 5,6 in short-pitch chiral nematic liquid crystals allows both fast switching of the optic axis and continuous, electric field dependent control of the degree of rotation of the optic axis. A novel geometry for the flexoelectro-optic effect is presented here, in which the helical axis of the chiral nematic is perpendicular to the cell walls (grandjean texture) and the electric field is applied in the plane of the cell. This facilitates deflection of the optic axis of the uniaxial negatively birefringent material from lying along the direction of propagation to having some component in the polarization plane of the light. The device is therefore optically neutral at zero field for telecommunications wavelengths (1550nm), and allows a continuously variable degree of phase excursion to be induced, up to 2π/3 radians achieved so far in a 40μm thick cell. The retardation has been shown both to appear, on application of the field, and disappear on removal, at speeds of 100-500 μs. The direction of deflection of the optic axis is also dependent on the direction of the field, allowing the possibility, in a converging electrode "cartwheel cell", of endless rotation of the liquid crystal waveplate at a higher rate than achievable through dielectric coupling to plain nematic materials.

Retinal adaptation of visual processing time delays.

A significant proportion of the processing delays within the visual system are luminance dependent. Thus placing an attenuating filter over one eye causes a temporal delay between the eyes and thus an illusion of motion in depth for objects moving in the fronto-parallel plane, known as the Pulfrich effect. We have used this effect to study adaptation to such an interocular delay in two normal subjects wearing 75% attenuating neutral density filters over one eye. In two separate experimental periods both subjects showed about 60% adaptation over 9 days. Reciprocal effects were seen on removal of the filters. To isolate the site of adaptation we also measured the subjects' flicker fusion frequencies (FFFs) and contrast sensitivity functions (CSFs). Both subjects showed significant adaptation in their FFFs. An attempt to model the Pulfrich and FFF adaptation curves with a change in a single parameter in Kelly's [(1971) Journal of the Optical Society of America, 71, 537-546] retinal model was only partially successful. Although we have demonstrated adaptation in normal subjects to induced time delays in the visual system we postulate that this may at least partly represent retinal adaptation to the change in mean luminance.

Neuro-Fuzzy genetic system for selection of construction project managers

Choosing a project manager for a construction project—particularly, large projects—is a critical project decision. The selection process involves different criteria and should be in accordance with company policies and project specifications. Traditionally, potential candidates are interviewed and the most qualified are selected in compliance with company priorities and project conditions. Precise computing models that could take various candidates’ information into consideration and then pinpoint the most qualified person with a high degree of accuracy would be beneficial. On the basis of the opinions of experienced construction company managers, this paper, through presenting a fuzzy system, identifies the important criteria in selecting a project manager. The proposed fuzzy system is based on IF-THEN rules; a genetic algorithm improves the overall accuracy as well as the functions used by the fuzzy system to make initial estimates of the cluster centers for fuzzy c-means clustering. Moreover, a back-propagation neutral network method was used to train the system. The optimal measures of the inference parameters were identified by calculating the system’s output error and propagating this error within the system. After specifying the system parameters, the membership function parameters—which by means of clustering and projection were approximated—were tuned with the genetic algorithm. Results from this system in selecting project managers show its high capability in making high-quality personnel predictions

Differential Dynamic Microscopy: a High-Throughput Method for Characterizing the Motility of Microorganism

We present a fast, high-throughput method for characterizing the motility of microorganisms in 3D based on standard imaging microscopy. Instead of tracking individual cells, we analyse the spatio-temporal fluctuations of the intensity in the sample from time-lapse images and obtain the intermediate scattering function (ISF) of the system. We demonstrate our method on two different types of microorganisms: bacteria, both smooth swimming (run only) and wild type (run and tumble) Escherichia coli, and the bi-flagellate alga Chlamydomonas reinhardtii. We validate the methodology using computer simulations and particle tracking. From the ISF, we are able to extract (i) for E. coli: the swimming speed distribution, the fraction of motile cells and the diffusivity, and (ii) for C. reinhardtii: the swimming speed distribution, the amplitude and frequency of the oscillatory dynamics. In both cases, the motility parameters are averaged over \approx 10^4 cells and obtained in a few minutes.

Proposal for a novel and simple WDM NRZ-DPSK system

A novel and simple non-return-to-zero differential phase shift keying (NRZ-DPSK) wavelength division multiplexing (WDM) system, which can simultaneously demultiplex and demodulate multiple wavelengths, is proposed and investigated in this paper. The phase-to-intensity demodulation principle is based on detuned filtering, which is achieved by using a single commercial array waveguide grating (AWG) in our scheme. By properly choosing appropriate AWG channels at the transmitter, the AWG at the receiver can act as both the demultiplexer and the demodulator of the DPSK signals. Simulations at 10, 20, and 40 Gbit/s show good flexibility and performance for the proposed system. © 2009 Higher Education Press and Springer-Verlag GmbH.

Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach

We apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic system: a Rijke tube containing a hot wire. We calculate how the growth rate and frequency of small oscillations about a base state are affected either by a generic passive control element in the system (the structural sensitivity analysis) or by a generic change to its base state (the base-state sensitivity analysis). We illustrate the structural sensitivity by calculating the effect of a second hot wire with a small heat-release parameter. In a single calculation, this shows how the second hot wire changes the growth rate and frequency of the small oscillations, as a function of its position in the tube. We then examine the components of the structural sensitivity in order to determine the passive control mechanism that has the strongest influence on the growth rate. We find that a force applied to the acoustic momentum equation in the opposite direction to the instantaneous velocity is the most stabilizing feedback mechanism. We also find that its effect is maximized when it is placed at the downstream end of the tube. This feedback mechanism could be supplied, for example, by an adiabatic mesh. We illustrate the base-state sensitivity by calculating the effects of small variations in the damping factor, the heat-release time-delay coefficient, the heat-release parameter, and the hot-wire location. The successful application of sensitivity analysis to thermo-acoustics opens up new possibilities for the passive control of thermo-acoustic oscillations by providing gradient information that can be combined with constrained optimization algorithms in order to reduce linear growth rates. © Cambridge University Press 2013.

On the time delay in continuous in-cylinder sampling from IC engines

When gas sample is continuously drawn from the cylinder of an internal combustion engine, the sample that appears at the end of the sampling system corresponds to the in-cylinder content sometime ago because of the finite transit time which is a function of the cylinder pressure history. This variable delay causes a dispersion of the sample signal and makes the interpretation of the signal difficult An unsteady flow analysis of a typical sampling system was carried out for selected engine loads and speeds. For typical engine operation, a window in which the delay is approximately constant may be found. This window gets smaller with increase in engine speed, with decrease in load, and with the increase in exit pressure of the sampling system.

Designing and testing an advanced pneumatic braking system for heavy vehicles

Heavy goods vehicles exhibit poor braking performance in emergency situations when compared to other vehicles. Part of the problem is caused by sluggish pneumatic brake actuators, which limit the control bandwidth of their antilock braking systems. In addition, heuristic control algorithms are used that do not achieve the maximum braking force throughout the stop. In this article, a novel braking system is introduced for pneumatically braked heavy goods vehicles. The conventional brake actuators are improved by placing high-bandwidth, binary-actuated valves directly on the brake chambers. A made-for-purpose valve is described. It achieves a switching delay of 3-4 ms in tests, which is an order of magnitude faster than solenoids in conventional anti-lock braking systems. The heuristic braking control algorithms are replaced with a wheel slip regulator based on sliding mode control. The combined actuator and slip controller are shown to reduce stopping distances on smooth and rough, high friction (μ = 0.9) surfaces by 10% and 27% respectively in hardware-in-the-loop tests compared with conventional ABS. On smooth and rough, low friction (μ = 0.2) surfaces, stopping distances are reduced by 23% and 25%, respectively. Moreover, the overall air reservoir size required on a heavy goods vehicle is governed by its air usage during an anti-lock braking stop on a low friction, smooth surface. The 37% reduction in air usage observed in hardware-in-the-loop tests on this surface therefore represents the potential reduction in reservoir size that could be achieved by the new system. © 2012 IMechE.

Differential equation based length scales to improve DES and RANS simulations

Surprisingly expensive to compute wall distances are still used in a range of key turbulence and peripheral physics models. Potentially economical, accuracy improving differential equation based distance algorithms are considered. These involve elliptic Poisson and hyperbolic natured Eikonal equation approaches. Numerical issues relating to non-orthogonal curvilinear grid solution of the latter are addressed. Eikonal extension to a Hamilton-Jacobi (HJ) equation is discussed. Use of this extension to improve turbulence model accuracy and, along with the Eikonal, enhance Detached Eddy Simulation (DES) techniques is considered. Application of the distance approaches is studied for various geometries. These include a plane channel flow with a wire at the centre, a wing-flap system, a jet with co-flow and a supersonic double-delta configuration. Although less accurate than the Eikonal, Poisson method based flow solutions are extremely close to those using a search procedure. For a moving grid case the Poisson method is found especially efficient. Results show the Eikonal equation can be solved on highly stretched, non-orthogonal, curvilinear grids. A key accuracy aspect is that metrics must be upwinded in the propagating front direction. The HJ equation is found to have qualitative turbulence model improving properties. © 2003 by P. G. Tucker.