An Integrated CMOS Front-End for Optical Absolute Rotary Encoders

This paper presents a front-end circuit for optical rotary encoders. The light pulses modulated by the encoder disc are transduced into current signals, which are pre-processed and converted into digital waveforms related to the disc angular position information. The proposed front-end circuit is compensated against temperature drifts. Digitally programmable calibration is provided to account for spreads in impinging light pulse power. Measurement results on integrated prototypes are shown, demonstrating correct operation of the front-end with an optical input power from 0.5 W to 3 W up to a signal frequency of 500 kHz in a temperature range from 0 °C to 80 °C.     

Optimisation of the throttling system in a CO2 refrigerating machine

This paper is an answer to the need of finding the optimal solution for the throttling system in refrigerating machines using CO₂ as working fluid; such a solution must combine reliability, low installation cost and high energy efficiency. To this purpose, different expansion systems are compared by means of a simulation programme, including a new one, operating with a differential valve, a liquid receiver and a thermostatic valve. The typical compression refrigerating cycle performed by CO₂ involves transcritical operations and therefore the upper pressure needs to be adjusted to the optimal value, that, unlike the traditional cycle, is not determined by heat transfer. The innovative system here proposed shows an intrinsic self-adjusting capability that leads to COP values quite close to the maximum ones when a fixed suitable value of the differential pressure is chosen, even if the temperature of the secondary fluid varies to a large extent.     

Squaring down LTI systems: A geometric approach

In this paper, the problem of reducing a given LTI system into a left or right invertible one is addressed and solved with the standard tools of the geometric control theory. First, it will be shown how an LTI system can be turned into a left invertible system, thus preserving key system properties like stabilizability, phase minimality, right invertibility, relative degree and infinite zero structure. Moreover, the additional invariant zeros introduced in the left invertible system thus obtained can be arbitrarily assigned in the complex plane. By duality, the scheme of a right inverter will be derived straightforwardly. Moreover, the squaring down problem will be addressed. In fact, when the left and right reduction procedures are applied together, a system with an unequal number of inputs and outputs is turned into a square and invertible system. Furthermore, as an example it will be shown how these techniques may be employed to weaken the standard assumption of left invertibility of the plant in many optimization problems.     

Simulation of the St. Francis Dam-Break Flood

A two-dimensional (2D) simulation of flooding from the 1928 failure of St. Francis Dam in southern California is presented. The simulation algorithm solves shallow-water equations using a robust unstructured grid Godunov-type scheme designed for wetting and drying and achieves good results. Flood extent and flood travel time are predicted within 4 and 10% of observations, respectively. Representation of terrain by the mesh is identified as the dominant factor affecting accuracy, and an iterative process of mesh refinement and convergence checks is implemented to minimize errors. The most accurate predictions are achieved with a uniformly distributed Manning n = 0.02. A 50% increase in n increases travel time errors to 25% but has little effect on flood extent predictions. This highlights the challenge of a priori travel time prediction but robustness in flood extent prediction when topography is well resolved. Predictions show a combination of subcritical and supercritical flow regimes. The leading edge of the flood was supercritical in San Francisquito Canyon, but due to channel tortuosity, the wetting front reflected off canyon walls causing a transition to subcritical flow, considerably larger depths, and a standing wave in one particular reach that accounts for a 30% fluctuation in discharge. Elsewhere, oblique shocks locally increased flood depths. The 2D dam-break model is validated by its stability and accuracy, conservation properties, ability to calibrate with a physically realistic and simple resistance parametrization, and modest computational cost. Further, this study highlights the importance of a dynamic momentum balance for dam-break flood simulation.     

Skew product cycles with rich dynamics: From totally non-hyperbolic dynamics to fully prevalent hyperbolicity

We introduce a two-parameter family of ‘partially hyperbolic’ skew products (G_{a, t})_{a > 0, t ∈ [ ? ε, ε]} maps with one dimensional centre direction. In this family, the parameter a models the central dynamics and the parameter t the unfolding of cycles (that occurs for t = 0). The parameter a also measures the ‘central distortion’ of the systems: for small a, the distortion of the systems is small and it increases and goes to infinity as a → ∞. The family (G_{a, t}) displays some of the main characteristic properties of the unfolding of heterodimensional cycles as intermingled homoclinic classes of different indices and secondary bifurcations via collision of hyperbolic homoclinic classes. For a ∈ (0, log?2), the dynamics of (G_{a, t}) is always non-hyperbolic after the unfolding of the cycle. However, for a > log?4 intervals of t-parameters corresponding to hyperbolic dynamics appear and turn into totally prevalent as a → ∞ (the density of ‘hyperbolic parameters’ goes to 1 as a → ∞). The dynamics of the maps G_{a, t} is described using a family of iterated function systems modelling the dynamics in the one-dimensional central direction.     

Optimizing a remotely sensed proxy for plankton biomass in Lake Kivu

Many regions of the world, including inland lakes, present with suboptimal conditions for the remotely sensed retrieval of optical signals, thus challenging the limits of available satellite data-processing tools, such as atmospheric correction models (ACM) and water constituent-retrieval (WCR) algorithms. Working in such regions, however, can improve our understanding of remote-sensing tools and their applicability in new contexts, in addition to potentially offering useful information about aquatic ecology. Here, we assess and compare 32 combinations of two ACMs, two WCRs, and three binary categories of data quality standards to optimize a remotely sensed proxy of plankton biomass in Lake Kivu. Each parameter set is compared against the available ground-truth match-ups using Spearman’s right-tailed ρ. Focusing on the best sets from each ACM–WCR combination, their performances are discussed with regard to data distribution, sample size, spatial completeness, and seasonality. The results of this study may be of interest both for ecological studies on Lake Kivu and for epidemiological studies of disease, such as cholera, the dynamics of which has been associated with plankton biomass in other regions of the world.     

The generalised discrete algebraic Riccati equation in linear-quadratic optimal control

This paper investigates the properties of the solutions of the generalised discrete algebraic Riccati equation arising from the classic infinite-horizon linear quadratic (LQ) control problem. In particular, a geometric analysis is used to study the relationship existing between the solutions of the generalised Riccati equation and the output-nulling subspaces of the underlying system and the corresponding reachability subspaces. This analysis reveals the presence of a subspace that plays an important role in the solution of the related optimal control problem, which is reflected in the generalised eigenstructure of the corresponding extended symplectic pencil. In establishing the main results of this paper, several ancillary problems on the discrete Lyapunov equation and spectral factorisation are also addressed and solved.     

Analytical and graphical design of lead–lag compensators

In this article an approach based on inversion formulae is used for the design of lead–lag compensators which satisfy frequency domain specifications on phase margin, gain margin and phase (or gain) crossover frequency. An analytical and graphical procedure for the compensator design on the Nyquist and Nichols planes is presented with some numerical examples.