Thermal Diffusivity of High-Density Polyethylene Samples of Different Crystallinity Evaluated by Indirect Transmission Photoacoustics

In this work, thermal diffusivity of crystalline high-density polyethylene samples of various thickness, and prepared using different procedures, was evaluated by transmission gas-microphone frequency photoacoustics. The samples’ composition analysis and their degree of crystallinity were determined from the wide-angle X-ray diffraction, which confirmed that high-density polyethylene samples, obtained by slow and fast cooling, were equivalent in composition but with different degrees of crystallinity. Structural analysis, performed by differential scanning calorimetry, demonstrated that all of the used samples had different levels of crystallinity, depending not only on the preparing procedure, but also on sample thickness. Therefore, in order to evaluate the samples’ thermal diffusivity, it was necessary to modify standard photoacoustic fitting procedures (based on the normalization of photoacoustic amplitude and phase characteristics on two thickness levels) for the interpretation of photoacoustic measurements. The calculated values of thermal diffusivity were in the range of the expected literature values. Besides that, the obtained results indicate the unexpected correlation between the values of thermal diffusivity and thermal conductivity with the degree of crystallinity of the investigated geometrically thin samples. The results indicate the necessity of additional investigation of energy transport in macromolecular systems, as well as the possible employment of the photoacoustic techniques in order to clarify its mechanism.     

A unified framework for input-to-state stability in systems with two time scales

This paper develops a unified framework for studying robustness of the input-to-state stability (ISS) property and presents new results on robustness of ISS to slowly varying parameters, to rapidly varying signals, and to generalized singular perturbations. The common feature in these problems is a time-scale separation between slow and fast variables which permits the definition of a boundary layer system like in classical singular perturbation theory. To address various robustness problems simultaneously, the asymptotic behavior of the boundary layer is allowed to be complex and it generates an average for the derivative of the slow state variables. The main results establish that if the boundary layer and averaged systems are ISS then the ISS bounds also hold for the actual system with an offset that converges to zero with the parameter that characterizes the separation of time-scales. The generality of the framework is illustrated by making connection to various classical two time-scale problems and suggesting extensions.     

Detection of foliage conditions and disturbance from multi-angular high spectral resolution remote sensing

Disturbance of forest ecosystems, an important component of the terrestrial carbon cycle, has become a focus of research over recent years, as global warming is about to increase the frequency and severity of natural disturbance events. Remote sensing offers unique opportunities for detection of forest disturbance at multiple scales; however, spatially and temporally continuous mapping of non-stand replacing disturbance remains challenging. First, most high spatial resolution satellite sensors have relatively broad spectral ranges with bandwidths unsuitable for detection of subtle, stress induced, features in canopy reflectance. Second, directional and background reflectance effects, induced by the interactions between the sun-sensor geometry and the observed canopy surface, make up-scaling of empirically derived relationships between changes in spectral reflectance and vegetation conditions difficult. Using an automated tower based spectroradiometer, we analyse the interactions between canopy level reflectance and different stages of disturbance occurring in a mountain pine beetle infested lodgepole pine stand in northern interior British Columbia, Canada, during the 2007 growing season. Directional reflectance effects were modelled using a bidirectional reflectance distribution function (BRDF) acquired from high frequency multi-angular spectral observations. Key wavebands for observing changes in directionally corrected canopy spectra were identified using discriminant analysis and highly significant correlations between canopy reflectance and field measured disturbance levels were found for several broad and narrow waveband vegetation indices (for instance, r²_NDVI = 0.90; r²_CHL3 = 0.85; p < 0.05). Results indicate that multi-angular observations are useful for extraction of disturbance related changes in canopy reflectance, in particular the temporally and spectrally dense data detected changes in chlorophyll content well. This study will help guide and inform future efforts to map forest health conditions at landscape and over increasingly coarse scales.     

A Lyapunov Proof of an Improved Maximum Allowable Transfer Interval for Networked Control Systems

Simple Lyapunov proofs are given for an improved (relative to previous results that have appeared in the literature) bound on the maximum allowable transfer interval to guarantee global asymptotic or exponential stability in networked control systems and also for semiglobal practical asymptotic stability with respect to the length of the maximum allowable transfer interval     

Controllability of structured polynomial systems

Two algorithms, based on the Grobner basis method, which facilitate the controllability analysis for a class of polynomial systems are presented. The authors combine these algorithms with some results on output dead-beat controllability in order to obtain sufficient, as well as necessary, conditions for complete and state dead-beat controllability for a surprisingly large class of polynomial systems. Our results are generically applicable to the class of polynomial systems in strict feedback form     

Dead beat controllability of polynomial systems: symboliccomputation approaches

State and output dead beat controllability tests for a very large class of polynomial systems with rational coefficients may be based on the quantifier elimination by partial cylindrical algebraic decomposition (QEPCAD) symbolic computation program. The method is unified for a very large class of systems and can handle one- or two-sided control constraints. Families of minimum time state/output dead beat controllers are obtained. The computational complexity of the test is prohibitive for general polynomial systems, but by constraining the structure of the system we may beat the curse of complexity. A computationally less expensive algebraic test for output dead beat controllability for a class of odd polynomial systems is presented. Necessary and sufficient conditions are given. They are still very difficult to check. Therefore, a number of easier-to-check sufficient conditions are also provided. The latter are based on the Grobner basis method and QEPCAD. It is shown on a subclass of odd polynomial systems how it is possible to further reduce the computational complexity by exploiting the structure of the system     

Output feedback stabilization of a class of Wiener systems

A globally stabilizing output feedback controller is designed for a class of continuous-time Wiener systems. The Wiener systems we consider consist of a linear dynamical block and an output polynomial nonlinearity connected in series. The (hybrid) controller consists of three modes of operation which are periodically applied to the system. The controller achieves a dead-beat response of the closed-loop system     

A unified approach to controller design for achieving ISS and related properties

A unified approach to the design of controllers achieving various specified input-to-state stability (ISS) like properties is presented. Both full state and measurement feedback cases are considered. Synthesis procedures based on dynamic programming are given using the recently developed results on controller synthesis to achieve uniform l/sup /spl infin// bound. Our results provide a link between the ISS literature and the nonlinear H/sup /spl infin// design literature.     

Input-to-State Stabilization of Linear Systems With Quantized State Measurements

We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with linear dynamics and quantized state measurements. Quantizers considered in this paper take finitely many values and have an adjustable "zoom" parameter. Building on an approach applied previously to systems with no disturbances, we develop a control methodology that counteracts an unknown disturbance by switching repeatedly between "zooming out" and "zooming in." Two specific control strategies that yield ISS are presented. The first one is implemented in continuous time and analyzed with the help of a Lyapunov function, similarly to earlier work. The second strategy incorporates time sampling, and its analysis is novel in that it is completely trajectory-based and utilizes a cascade structure of the closed-loop hybrid system. We discover that in the presence of disturbances, time-sampling implementation requires an additional modification which has not been considered in previous work     

Influence of Thermal Memory on Thermal Piston Model of Photoacoustic Response

In this study, a model of thermoconducting components of the transmission photoacoustic response is analyzed, which includes thermal memory properties of both the examined solid sample and its fluid environment. It is shown that, at low modulation frequencies, lower than minimum among the inverse thermal relaxation time of air, the inverse thermal relaxation time of the sample, and the certain frequency at which the sample is thinner than one-quarter of the wavelength of time-varying temperature perturbation, thermal memory does not affect the photoacoustic response, while, at high frequencies, noticeable effects are observed. These results indicate the possibility of evaluating thermal memory properties of solid samples using classical, transmission, high frequency photoacoustic measurements.