Phase limitations of Zames-Falb multipliers

Phase limitations of both continuous-time and discrete-time Zames-Falb multipliers and their relation with the Kalman conjecture are analysed. A phase limitation for continuous-time multipliers given by Megretski is generalised and its applicability is clarified; its relation to the Kalman conjecture is illustrated with a classical example from the literature. It is demonstrated that there exist fourth-order plants where the existence of a suitable Zames-Falb multiplier can be discarded and for which simulations show unstable behavior. A novel phase-limitation for discrete-time Zames-Falb multipliers is developed. Its application is demonstrated with a second-order counterexample to the Kalman conjecture. Finally, the discrete-time limitation is used to show that there can be no direct counterpart of the off-axis circle criterion in the discrete-time domain

Method of remotely characterizing thermal properties of a sample

A sample in a wind tunnel is radiated from a thermal energy source outside of the wind tunnel. A thermal imager system, also located outside of the wind tunnel, reads surface radiations from the sample as a function of time. The produced thermal images are characteristic of the heat transferred from the sample to the flow across the sample. In turn, the measured rates of heat loss of the sample are characteristic of the flow and the sample

Thermal Diffusivity Measurements in Carbon-Carbon Composites

In recent years, carbon-carbon composite materials have come into widespread use in aerospace industries. These materials are particularly attractive for high temperature applications due to their thermal and mechanical behavior. Few quantitative measurements, however, have been made to characterize these materials. One problem encountered with carbon-carbon composites is porosity. Materials engineers have determined that degree of porosity is correlated to inter-laminar shear strength in carbon-carbon composites. Since repetition of the carbon-carbon processing cycle reduces porosity, a technique for assessing porosity between processing cycles that is non-contacting and does not contaminate the material would be of value. A material property which is related to density and therefore to porosity, is thermal diffusivity. Thermal diffusivity is easily measured non-contactingly and remotely with infrared techniques and is therefore an attractive candidate measurement for assessing porosity between processing cycles of carbon-carbon composites

Spontaneous patterning of quantum dots at the air-water interface

Nanoparticles deposited at the air-water interface are observed to form circular domains at low density and stripes at higher density. We interpret these patterns as equilibrium phenomena produced by a competition between an attraction and a longer-ranged repulsion. Computer simulations of a generic pair potential with attractive and repulsive parts of this kind, reproduce both the circular and stripe patterns. Such patterns have a potential use in nanoelectronic applications

Stability Analysis of Piecewise Affine Systems with Multi-model Model Predictive Control

Constrained model predictive control (MPC) is a widely used control strategy, which employs moving horizon-based on-line optimisation to compute the optimum path of the manipulated variables. Nonlinear MPC can utilize detailed models but it is computationally expensive; on the other hand linear MPC may not be adequate. Piecewise affine (PWA) models can describe the underlying nonlinear dynamics more accurately, therefore they can provide a viable trade-off through their use in multi-model linear MPC configurations, which avoid integer programming. However, such schemes may introduce uncertainty affecting the closed loop stability. In this work, we propose an input to output stability analysis for closed loop systems, consisting of PWA models, where an observer and multi-model linear MPC are applied together, under unstructured uncertainty. Integral quadratic constraints (IQCs) are employed to assess the robustness of MPC under uncertainty. We create a model pool, by performing linearisation on selected transient points. All the possible uncertainties and nonlinearities (including the controller) can be introduced in the framework, assuming that they admit the appropriate IQCs, whilst the dissipation inequality can provide necessary conditions incorporating IQCs. We demonstrate the existence of static multipliers, which can reduce the conservatism of the stability analysis significantly. The proposed methodology is demonstrated through two engineering case studies.Comment: 28 pages 9 figure

Convex searches for discrete-time Zames-Falb multipliers

In this paper we develop and analyse convex searches for Zames--Falb multipliers. We present two different approaches: Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) multipliers. The set of FIR multipliers is complete in that any IIR multipliers can be phase-substituted by an arbitrarily large order FIR multiplier. We show that searches in discrete-time for FIR multipliers are effective even for large orders. As expected, the numerical results provide the best $\ell_{2}$-stability results in the literature for slope-restricted nonlinearities. Finally, we demonstrate that the discrete-time search can provide an effective method to find suitable continuous-time multipliers.Comment: 12 page