Adaptive Edge Detectors for Piecewise Smooth Data Based on the minmod Limiter

We are concerned with the detection of edges—the location and amplitudes of jump discontinuities of piecewise smooth data realized in terms of its discrete grid values. We discuss the interplay between two approaches. One approach, realized in the physical space, is based on local differences and is typically limited to low-order of accuracy. An alternative approach developed in our previous work [Gelb and Tadmor, Appl. Comp. Harmonic Anal., 7, 101–135 (1999)] and realized in the dual Fourier space, is based on concentration factors; with a proper choice of concentration factors one can achieve higher-orders—in fact in [Gelb and Tadmor, SIAM J. Numer. Anal., 38, 1389–1408 (2001)] we constructed exponentially accurate edge detectors. Since the stencil of these highly-accurate detectors is global, an outside threshold parameter is required to avoid oscillations in the immediate neighborhood of discontinuities. In this paper we introduce an adaptive edge detection procedure based on a cross-breading between the local and global detectors. This is achieved by using the minmod limiter to suppress spurious oscillations near discontinuities while retaining high-order accuracy away from the jumps. The resulting method provides a family of robust, parameter-free edge-detectors for piecewise smooth data. We conclude with a series of one- and two-dimensional simulations.To David Gottlieb, on his 60th birthday, with friendship and appreciation.     

On Geometric and Analytic Constraints in the H∞ Fixed-Lag Smoothing

Limiting factors on achievable performance in the continuous- and discrete-time fixed-lag smoothing problems are shown to include geometric constraints, inherited from the fixed-interval (L^infin) problem, and analytic constraints, affected by the preview interval. Thus, the fixed-lag problem is viewed as a constrained version of its fixed-interval counterpart. The analysis sheds light on the dependence of achievable performance on the preview length and, in particular, on the generic presence of performance saturation at a finite preview interval.     

Model-based low-level control in flexible manufacturing systems

Low-level (supervisory) control of flexible manufacturing systems (FMS) assures conflict-free operation and enforces production requirements such as priorities. It forms a crucial link between medium and higher-level decision making, on the one hand, and the various machine-controllers and servomechanisms on the other. In the absence of a suitable control methodology, ad hoc development is the current practice and compromised results at high cost are far too common. Here we described a model-based framework for a new, systematic approach to supervisory control.     

Quantitative characterization of extruded film texture

Quantitative characterization of the texture of extruded low density polyethylene films was attempted with the aid of concepts such as the scale and intensity of segregation. The scale of segregation defined along a line and the profile of the scale of segregation were found to be useful modifications of the originally defined scale of segregation. The former, which is obtained by taking concentration points along a line, was needed because the film texture is non-isotropic, while the latter, which is obtained by repeated calculations of the scale of segregation over a varying size sample was needed, for a more accurate representation of this texture. The profile of the scale of segregation leads to a few typical values, which perhaps, can be related to particular features of the mixing mechanisms in the extruder.     

Fourier transform infrared-probed O(3P) microreactor: demonstration with ethylene reactions in argon matrix

To demonstrate the development of an oxygen atom microreactor in the form of liquid-helium-cooled solid argon matrix deposited on an infrared (IR) window, the oxidation of ethylene by mobile O atoms has been investigated. O atom diffusion through the argon matrix is confirmed and used to examine ethylene-oxygen atom reactions. In a bench-scale matrix isolation system probed with a Fourier transform infrared (FT-IR) spectrometer, matrices of solid Ar at 8-10 K doped with NO2 and ethylene have been prepared on a ZnSe window within an evacuated cryostat. The matrices have been photolyzed using 350-450 nm photons, and the reaction products resulting from the reaction of O(3P), one of the photolysis products of NO2, with ethylene have been identified using FT-IR and a Gaussian 98W simulation program. These products include oxirane, acetaldehyde, ethyl nitrite radical, and ketene. The temperature effect in the range of 10-30 K on the products formed has also been investigated. The reaction mechanisms are discussed and the viability of the solid Ar matrix being a low temperature microreactor to examine reaction mechanisms of mobile oxygen atoms is elaborated.     

Adaptive torque-ripple minimization in switched reluctance motors

This paper addresses torque-ripple reduction in current-fed switched reluctance motors (SRMs). Ripple-free torque production in SRMs requires an accurate model that is often too complex for practical implementation. The algorithm proposed here combines the use of a simplified model with adaptation. Explicitly, it includes dynamic estimation of low harmonics of the combined unknown load torque and the ripple in the produced torque (due to model simplification), and adds appropriate terms to the commanded current to cancel these harmonics. Several simulations are presented first, suggesting that our method is effective for constant-speed reference commands, even when a very simple model is used in control design. Experimental results are included next to demonstrate that the algorithm performs well in reducing the torque ripple. Finally, limitations of the adaptive algorithm are explored and quantified     

Factorization and the Nehari theorem in time-varying systems

The Nehari Theorem and related results on operator interpolation play an important role in modern system theory. These results are embedded in a function-theoretic conceptual framework and therefore restricted to LTI systems. We give a state space oriented extension of the Nehari Theorem to a time-varying system-theoretic setting. In that setting the theorem addresses the issue of measuring the distance between a noncausal bounded I/O operator and the family of causal I/O operators in stable linear systems. The analysis is based on the recent time-domain LQ optimization approach to robust control. The discussion includes a geometrical analysis of stable and antistable invariant subspaces, a short study of certain types of co-prime factorizations of I/O operators in time-varying systems, and a parametrization of all suboptimal solutions.The research was supported in part by the National Science Foundation under Grant ECS 9108927 and by the U.S. Army Research Office under Contract DAALO3 92 G 0015.The research was supported by NSERC, Canada.     

Solids conveying in screw extruders part I: A modified isothermal model

An improved theoretical model was derived for the solids conveying zone of a plasticating extruder. The model makes possible calculations in variable channel depth section. It also allows for a bulk density which is a function of pressure and for the non-isotropic pressure distribution in the solid plug. An expression for maximum flow rate was also derived. Results simulated by the model on a computer indicate the effect of variables on extruder performance. The power consumption terms in the solids conveying zone of a plasticating extruder were also derived. Total power consumption is the sum of power consumptions on the barrel surface, screw surfaces and those due to pressure rise. Their relative importance was analyzed by computations. The effect of operating conditions and coefficients of friction on the various power terms was also analyzed.     

Optimal controls and their discontinuities in quadratic problems of delay systems

We construct and study quadratic optimal controls in delay systems of neutral type. In these systems we allow functional lags in the derivative, the state, the control, and in the cost index. We point out that, typically, optimal controls of time lag systems are discontinuous: discontinuities might occur as a consequence of delays in the control action and of the neutrality of the system. We exhibit computed examples of jumps in optimal controls whose origins are in each of the two types. Our techniques are based on the method of steps which we generalize to fit systems with functional lags. The work includes an analysis ofR^{n-}controllability in time lag systems.