Stability robustness bounds for discrete-time linear regulators

Stability robustness analysis and design for linear multivariable discrete-time systems with bounded uncertainties are discussed. Robust stability of the full-state feedback linear quadratic (LQ) regulator in the presence of perturbations (modelling errors) of the system matrices is investigated. These results are based on a recently developed bound on elemental (structured) time-varying perturbations of an asymptotically stable linear time-invariant discrete-time system. Lyapunov theory and singular value decomposition techniques are employed in deriving these bounds. Extensions of these results to linear stochastic systems with the Kalman filter as the stale estimator (LQG regulators) and to reduced-order dynamic compensator feedback are described. A state feedback control design method is presented for LQ regulators, using a quantitative measure called the Stability Robustness Index. Simple examples illustrate these new results.     

A differential-difference equations model of a dynamic aquatic ecosystem†

This paper presents a differential-difference equations model of a dynamic aquatic ecosystem. This paper departs from other models by considering : (a) specific phyla of phytoplankton, zooplankton and nekton ; (b) their prey—predation relationships ; (c) both allelochemic and antotoxic effects of algae upon zooplankton and other algae ; (d) inter-phyla competition for nutrients. Other factors included are : limiting effects of phosphates, nitrates, silicates, photoperiod, turbidity, temperature, and time lag, as they affect growth and reproduction of the biota. The model uses the western basin of Lake Erie as a test example, but any shallow basin that does not experience thermoclines could be used.     

Optimal placement of phasor measurement systems for enhancing on-line protection and control of large-scale power systems

Microprocessor-based real-time phasor measurements, i.e. measurement of fundamental frequency, positive sequence, complex three phase voltages and currents, for enhancing on-line protection and control of interconnected electric power systems are described. The proposed research demonstrates that real-time monitoring of key system states, in the bulk power transfer problem, can be identified. It also provides the means for determining which states are the key states for that problem, and that phasor measurements can be used to improve the protection and/or control of the system. The procedure is applied to a realistic system, where such a control problem exists in practice, for confirmation of the developed technique.     

Convergence of a class of Padé approximations for delay systems

This paper concerns the convergence of a class of rational approximations for delay systems of the form exp (— sT) M(s), where M(s) is a strictly proper rational transfer matrix. The rationale for reducing the order of G(s) is to replace exp (— sT) in G(s) by the class of all-pass/low-pass Pade approximations. The L₂ and L_m convergence in the frequency domain are established under mild conditions on M(s) (and hence impulse response in the L₂ case). For scalar M(s), the convergence is achieved at an optimal rate. Error bounds for the approximants are obtained which provide a priori estimates for the errors.     

Satellite derived estimates of the normal and tangential components of near-surface flow

Abstract

The determination of both the normal and tangential components of the total velocity is important in the study of cross- and along-isopycnal transport processes in the ocean. A pattern-matching method is used to determine objectively the total velocity. Sensitivity of this method to pattern and search tile sizes and to correlation threshold also is examined. Three methods for estimating the cross-isopycnal or normal component of the total flow are compared and discussed: Marr-Ullman, optical flow and minimum norm. It is also shown that optical flow and minimum norm are equivalent when the parameter a in the optical flow formulation is set to zero. The direct computation of the tangential component is not possible because it lies in the null-space of the solution set of the basic constraint equations used in velocity estimation methods which are based on the rate of change of image brightness (or temperature). A new method for indirectly estimating the tangential component of the total flow based on vector subtracting of the total flow and the normal component of flow is introduced. Several sequences of satellite images are analysed and the resulting total flow, normal component of flow, and the tangential component determined using this new method are consistent with motion inferred from edge maps. Recommendations are then made for the best normal component of flow to use in the determination of the tangential component.     

The slightly-rough facet model in radar imaging of the ocean surface

Abstract

The slightly-rough facet model of the ocean surface, an extension of the two-scale radar scattering model, is well suited for investigating synthetic aperture radar (SAR) imaging of the surface. We derive several statistical properties of the facets that are important in an imaging model. The two-scale scattering model is extended to include both first-order and second-order large-scale effects (tilt and curvature) using physical optics, showing that a spectrum of small-scale ripples, rather than a single ripple given by the Bragg resonance condition, contributes to the backscatter from a facet. The bandwidth of the resonant ripple spectrum depends on the radar wavelength, large-scale curvature and illumination widths. The properties of the facets are deduced from this dependence. The large-scale curvature of the surface determines the size of the facets. The expected facet size depends directly on the radar wavelength and is much smaller than the resolution of realistic radars. The resonant ripple spectra of adjacent facets overlap, so the backscatter from adjacent facets is correlated. The backscatter from individual facets temporally decorrelates due to dispersion of the ripples in the resonant spectrum. Depending on the conditions, the decorrelation time may be on the order of the integration times of SAR processors.     

Shoot growth on de-fruited grapevines: a physiological indicator for irrigation scheduling

A simple and inexpensive but biologically meaningful way of gauging grapevine water status that can guide irrigation scheduling is described. The growth rate of shoots on grapevines from which all fruit has been removed (de-fruited shoot growth) is presented as a sensitive indicator of vine and soil water status and we propose a procedure for irrigation scheduling based on monitoring de-fruited shoot growth and soil moisture. These guidelines were derived from corresponding measurements of de-fruited shoot growth and soil moisture potential that were undertaken at frequent intervals (generally 1 to 2 days). De-fruited shoot growth rate between 48 and 71 days after anthesis was linearly correlated with the mean moisture potential of the soil at depths of 60 cm and 90 cm in the centre of the drip-irrigated zone (r = 0.94). De-fruited shoot growth effectively ceased when soil moisture potential at these points had decreased to -70 kPa, although much of the root zone would have been even drier. De-fruited shoot growth thus shows an integrated and dynamic response to vine-available soil water that could aid irrigation scheduling.     

Viscosity and Thermal Expansion of Mixed-Alkali Sodium-Potassium Borate Glasses

The transformation-range viscosity and thermal expansion be-havior of sodium-potassium borate glasses were studied. The results indicate that negative deviations from additivity in the viscosity of these glasses are a function of the Na²O to K²O ratio and that the magnitude of these deviations increases with alkali oxide content. The thermal expansion coefficient exhibits a maximum deviation from additivity as a function of the Na²o to K²O ratio. The magnitude of this deviation increases with increasing total alkali oxide content. The results indicate that there is little, if any, interaction between the factors which lead to the mixed-alkali effect and the changes in the structure of the vitreous network which occur as the alkali oxide content of the glasses increases.     

Synthesis and Characterization of Alkyl-Bridged Bicycloheptanes as Traction Fluids

The traction fluid is a critical component of a toroidal-continuously variable transmission (T-CVT). As the medium that transmits power through the toroids, the traction fluid needs to provide a high traction coefficient and retain low dynamic viscosity at cold temperatures; this is a challenging combination of properties. A comparison of a variety of fluids shows a broad correlation between the traction coefficient and the fluid's low temperature viscosity, or pour point. This work investigated a series of novel compounds as traction fluids through chemical synthesis and the measurement of their relevant physical properties. Specifically, four new alkyl-bridged bicycloheptane fluids have been synthesized and refined to high purity. Their traction coefficients, measured with a ball-on-disc traction apparatus, are comparable to those of commercial fluids over the relevant range of temperature and pressure. Their dynamic viscosities at low temperature, however, are higher than the viscosity of commercial fluids and exceed the value of 3 × 10 ⁴ cP at ?40°C. These bridged bicycloheptanes also exhibit a correlation between their low-temperature viscosity and traction coefficient. The reasons for this correlation are discussed, and the effect of the molecular structure on viscosity and traction coefficient is investigated. This analysis finds semi-quantitative relationships between fluid properties and the molecule's volume, stiffness, and ring structure.