In maintaining power system stability; especially that of large interconnected systems, in the face of large disturbances it is desirable to have a non-linear control technique that is simple and inexpensive to implement. This thesis presents a non-linear control technique which relies on angle measurements taken at strategic points in the power system with the aid of the G.P.S. ( Global Positioning System ) timing signal. A method for estimating these bus angles which is faster than previous methods is developed as well as a technique for choosing the locations of these transducers. This transducer placement algorithm aims to place transducers at locations whose bus voltage response to the less well damped inter-area modes is maximised and whose response to the better damped local modes is minimised. Since the control techniques are based on aggregated classical models of coherent generators it is important to be able to estimate the internal voltages of these aggregate machines. The placement algorithm ensures maximally precise angle estimates in the presence of noise by minimising the condition number of the observation matrix relating transducer bus voltages to internal aggregated machine voltages. The non-linear control techniques presented rely on an energy function developed in this thesis which is based on the physical circuit energy of the system. One technique; the Direct Energy technique looks at maximising the negativity of the time rate of change of the energy function, assuming that the energy function is positive during the time frame of interest. It is shown that should the number of controllers be less than the number of modes, excluding the centre of area mode, then sustained oscillations appear which will only be damped by the natural damping of the system. This may be overcome by using techniques which rely on reducing the entire system energy over the time frame of interest. These so-called Lookahead techniques can rely on higher order time derivatives of the energy function or on co-states, the latter being the principal focus of this thesis. The Lookahead control technique developed is based on co-states which are estimated by the using the solution to the time independent Ricatti equation for a LQ model of the system. It is shown to produce good damping in a number of case studies. Furthermore it is shown to perform well in the presence of both static and dynamic load models. Also it is shown that the path dependent terms introduce some ambiguity as to whether or not the system will converge to a stable equilibrium point. It is shown that it is possible to put a bound on the region to which the power system can be assured to converge. Furthermore the addition of the above-mentioned control strategies has the effect of overcoming the effect of the path dependent terms and, should the control action be strong enough, completely swamping them and ensuring system convergence to a stable operating point. In any case the energy function could be directly monitored since all the data needed is being collected anyway for control purposes. / PhD Doctorate

Master of Science (Dentistry) / Dimensional stability was defined by Nicholls (1977) as “the ability (of a material) to maintain accuracy over time”, and the result of loss of accuracy, “distortion”, as “the relative movement of a single point, or group of points, away from some originally specified reference position such that permanent deformation is apparent”. Maintaining dimensional stability of dental impression materials is vital if the impression cannot be cast (in stone) soon after removal from the mouth. Dental irreversible hydrocolloid (alginate) is a major dental impression material used worldwide in many clinical procedures. However, alginate is dimensionally unstable and changes its dimensions (suffers “distortion”) after removal from the mouth. With storage times of more than ten minutes, alginate begins to distort, and after one to three hours (depending on the product and storage conditions) cannot be used for many clinical purposes, especially fixed prosthodontics such as crowns and bridges (Hampson 1955, Skinner & Hoblit 1956, Wilson & Smith 1963, Rudd et al. 1969, Miller 1975, Inohara 1977, Schoen et al. 1978, Coleman et al. 1979, Linke et al. 1985, Habu et al. 1986, Peutfeldt & Asmussen 1989, Mathilde & Peters 1992, Khan & Aziz Sahu 1995, Eriksson et al. 1998, Schleier et al. 2001, and Donovan & Chee 2004). This loss of accuracy, due to dimensional instability, manifests as a time-dependent distortion of the poured stone cast, and thus any prosthesis fabricated will not fit in the mouth. With the introduction of the more stable elastomers in the 1950s (Stackhouse 1970, Glenner 1997, Brown 2003) that could be stored for days if necessary, without loss of accuracy, the alginates fell out of favour for fixed prosthodontics. Recently, there has been a resurgence of interest in alginate for use in dental procedures where dimensional stability is critical (Peutzfeldt and Asmussen 1989, Eriksson et al. 1998). This in part is due to the favourable properties of alginate not found in the elastomers. Of greatest significance is that alginate hydrocolloid is hydrophilic, whereas elastomers are hydrophobic (Phillips & Ito 1958, Glenner 2004). Thus, alginate materials are able to reproduce wet oral areas with greater precision and to produce a superior "fit" of, say, a gold casting produced by the Lost Wax technique (Skinner and Phillips 1982). A number of reports have been published which investigate newer alginate materials that are claimed to be more dimensionally stable than older formulations. Puetzfeldt and Asmussen (1989) found that a newer alginate , if stored at 100% relative humidity, retained accuracy over 24 hours that was equivalent to that of the elastomers. More recently, the manufacturer of another alginate has claimed equivalent dimensional stability to the elastomers for up to 100 hours, and, whilst this claim has not been reported on in the literature, the present thesis will show that, under favourable conditions of storage, the material maintained clinically useful accuracy for up to 100 hours. Another approach to improving the accuracy of alginate impressions has been to combine reversible hydrocolloid with alginate (the “Bilaminar” technique). Frederick and Caputo (1997) confirmed that the new agar reversible hydrocolloids are just as accurate (at the time of removal from the mouth) as the new elastomers. Mathilde et al. (1992) and Eriksson et al. (1998) have shown that several of the “bilaminar” impression techniques for fixed prosthodontics, where alginate is used as a tray material supporting a reversible hydrocolloid (agar) wash, are as accurate and dimensionally stable as elastomers for up to three hours. However, these studies are difficult to interpret due to lack of uniformity in the testing methods, and the fact that there is no regulatory standard available to measure dimensional stability for dental alginates. The International Standard (IS) for alginate impression materials (ISO 1563:1990E) contains no specification for dimensional stability, and thus places no requirement for manufacturers to state dimensional stability properties on their labels. In contrast, ISO 4823:1992(E) specifies the IS for elastomeric dental impression materials, and it does specify a requirement for dimensional stability (less than 1.5% distortion after 24 hours). Further, the IS sets a method for determination of dimensional stability. Briefly, this method (the Optical Method) uses a travelling optical microscope to measure the accuracy of the distance between score lines on an impression of a test grid, at various time periods. The American Dental Association Specification No. 19 for dental elastomeric impression materials is identical to the IS. There is currently no specific Australian Standard (AS) for the dimensional stability of any dental impression material. Overview of Experimental Methods A. The Optical Method The aim of Part A of this investigation was to: 1. Adapt the Optical Method of the IS for elastomers to be reproducible for dental alginates. This was achieved by using a perforated test tray (to simulate clinical conditions), and measuring the grid pattern on a dental stone button after casting the test impression, rather than direct measurement of the impression, as for the IS. 2. To measure and rank the dimensional stability of a number of locally available dental alginates. Measurements of the test stone buttons proved reproducible, and the results were different for each sample, allowing them to be ranked according to dimensional stability after 50 and 100 hours of storage. The results show that the traditional optical method for measuring dimensional stability, as specified in the IS for dental elastomers, can be adapted to measure the dimensional stability of dental alginates However, the Optical Method of measuring dimensional stability of dental alginates is cumbersome and time-consuming. It was hypothesised that dimensional stability of dental alginates could be measured more conveniently by finding a thermal property that is directly proportional to dimensional stability. This method could be useful for the rapid determination of relative performance, and allow comparison with a determined benchmark. B. The Thermal Method Recently, modern methods of Thermal Analysis, Thermal Gravimetric Analysis (TGA) and Differential Scanning Calorimetry (DSC) have been used to rapidly age various polymers, including food alginates (Chinachoti 1996), in order to measure thermal stability. This thesis shows that thermal stability is an indicator of dimensional stability. The aim of Part B of this investigation was therefore to adapt thermal analysis techniques to dental alginates, and develop a method to measure their thermal stability. These results were then compared with those for dimensional stability measured by the Optical Method to determine the relationship between thermal and dimensional stability for dental alginates. The results show that current thermal analysis methods of TGA and DSC can be adapted to measure relative dental alginate dimensional stability, and are both rapid and convenient. This study also provides evidence that commercial products differ as regards the property of dimensional stability, and can be ranked accordingly. C. Practical Application of the Methods The aim of part C of this thesis was to validate the methods (both optical and thermal) developed in this study by using them to investigate the effect of varying the water/powder ratio on the dimensional stability of dental alginates. It was shown that dimensional stability is affected by changes to the recommended water/powder ratio, that both the methods detected and measured the changes, and that the results were proportional, in that any percentage change detected by the optical method, was mirrored by the thermal method, confirming that the more convenient thermal methods can be used to measure dimensional stability.

Thesis (Ph. D. electrical engineering)--Washington State University, December 2007. / Includes bibliographical references (p. 112-116).

<p>This thesis presents the making and the implementation of a roll stability system for a simulator truck. The purpose of the system is to prevent rollover. The making of the system consists of three parts; calculating the roll angle, calculating a rollover index and constructing the control system. The roll angle was calculated using a one degree of freedom model of the truck with the measured lateral acceleration as input signal. Using the roll angle and the roll rate, a rollover index was calculated. The controller made the truck brake to avoid the impending rollover when the rollover index was at a critical point. The benefits of the system were measured by conducting a study in which test persons drove the simulator truck both with the stability system switched on and switched off. The scenario in the study was carefully constructed so that it would test the system thoroughly. The results were not unambiguous, in some situations the roll stability system prevented roll over, but in others it had the opposite effect.</p> / <p>I den här examensarbetesrapporten presenteras ett rollstabiliseringssystem för tunga fordon framtaget på VTIs (Statens väg- och transportforskningsinstitut) begäran. Systemet ska användas i VTIs simulator och det ska förhindra att fordonet välter. Utvecklingen av systemet kan delas in i tre större områden; beräkning av fordonets rollvinkel, framtagandet av ett rolloverindex samt skapandet av en regulator. Rollvinkeln är framtagen utifrån en lastbilsmodell med en frihestgrad, och skattades utifrån den mätta sidoaccelerationen. Rollhastigheten i sin tur skattades utifrån rollvinkeln. Ett rolloverindex som anger risken för vältning i varje ögonblick räknades fram med hjälp av rollvinkeln och rollhastigheten. Då indexet indikerar att vältning är nära aktiveras ett reglersystem. Detta system bromsar in lastbilen för att minska vältrisken. Examensarbetet avslutades med en studie utförd i simulatorn där försökspersoner körde både med och utan stabiliseringssytemet inkopplat. Scenariot i studien var speciellt utformat för att testa stabiliseringssystemet. Resultaten var inte entydiga, stabiliseringssystemet hjälpte i vissa situationer men i andra hade det motsatt effekt och fick lastbilen att välta snarare än att förhindra vältningen. Slutligen utvärderades nyttoeffekterna av det framtagna systemet.</p>

Graduation date: 1995

The spectral radius of a matrix is a widely used concept in linear algebra. It expresses the asymptotic growth rate of successive powers of the matrix. This concept can be extended to sets of matrices, leading to the notion of "joint spectral radius". The joint spectral radius of a set of matrices was defined in the 1960's, but has only been used extensively since the 1990's. This concept is useful to study the behavior of multi-agent systems, to determine the continuity of wavelet basis functions or for expressing the capacity of binary codes. Although the joint spectral radius shares some properties with the usual spectral radius, it is much harder to compute, and the problem of approximating it is NP-hard. In this thesis, we first review theoretical results that lead to basic approximations of the joint spectral radius. Then, we list various specific cases where it is effectively computable, before presenting a specific type of sets of matrices, for which we solve the problem of computing it with a polynomial computational cost.

The influence of periodic vibrations on the granular flow of materials is of great interests to scientists and engineers due to both theoretical and practical reasons. In this paper, the stability of a vertically vibrated granular layer is examined by linear stability analysis. This includes two major steps, firstly, the base state at various values of mass holdup (Mt) and energy input (Qt) is calculated and secondly, small perturbations are introduced to verify the stability of the base state by solving the resultant eigenvalue problem derived from the linearized governing equations and corresponding boundary conditions. Results from the base state solution show that, for a given pair of Mt and Qt, solid fraction tends to increase at first along the layer height and then decrease after a certain vertical position while granular temperature decreases rapidly from the bottom plate to the top surface. This may be due to the existence of inelastic collisions between particles that dissipate the energy input from the bottom. It is also found that more energy input results in a lower solid fraction and a higher granular temperature. The stability diagram is constructed by checking the stability property at different points in the Mt-Qt plane. For a fixed Mt, the base state is stable at low energy inputs, and becomes unstable if Qt is larger than a critical value Qtc1. A higher value of Mt corresponds to a larger Qtc1. There also exists a critical mass holdup (Mtc), for Mt larger than Mtc, the patterns corresponding to the instabilities are standing waves (stationary mode); otherwise the flat layer appears (layer mode). Moreover, the stationary mode turns into the layer mode when Qt is increased beyond a critical value Qtc2. These findings agree with the experimental observations of other researchers (Hsiau and Pan, 1998). The effects of restitution coefficients (ep, ew) and material properties (dp, ρp) on the stability diagram are also investigated. Together with Mt and Qt these variables can be classified into two groups, i.e. the stabilizing factors (Mt, dp, ρp) and the destabilizing factors (Qt, ep, ew). The stability of the system is enhanced with increasing stabilizing factors and decreasing destabilizing factors. / Singapore-MIT Alliance (SMA)

N.H. Frank and R.Q. Twiss. / "February 9, 1948." / Bibliography: p. 27. / Army Signal Corps Contract No. W-36-039 sc-32037.

No description available.

Tool chatter in longitudinal turning is addressed with a new perspective using a complex machining model describing the coupled tool-workpiece dynamics subject to nonlinear regenerative cutting forces, instantaneous depth-of-cut (DOC) and workpiece whirling due to material imbalance. The workpiece is modeled as a system of three rotors: unmachined, being machined and machined, connected by a flexible shaft. The model enables workpiece motions relative to the tool and tool motions relative to the machining surface to be three-dimensionally established as functions of spindle speed, instantaneous DOC, rate of material removal and whirling. Excluding workpiece vibrations from the cutting model is found improper. A rich set of nonlinear behaviors of both the tool and the workpiece including period-doubling bifurcation and chaos signifying the extent of machining instability at various DOCs is observed. Presented numerical results agree favorably with physical experiments reported in the literature. It is found that whirling is non-negligible if the fundamental characteristics of machining dynamics are to be fully understood. The 3D model is explored along with its 1D counterpart, which considers only tool motions and disregards workpiece vibrations. Numerical simulations reveal diverse behaviors for the 3D coupled and 1D uncoupled equations of motion for the tool. Most notably, observations made with regard to the inconsistency in describing stability limits raise the concern for using 1D models to obtain stability charts. The nonlinear 3D model is linearized to investigate the implications of applying linear models to the understanding of machining dynamics. Taylor series expansion about the operating point where optimal machining conditions are desired is applied to linearize the model equations of motion. Modifications are also made to the nonlinear tool stiffness term to minimize linearization errors. Numerical experiments demonstrate inadmissible results for the linear model and good agreement with available physical data in describing machining stability and chatter for the nonlinear model. Effects of tool geometry, feed rate, and spindle speed on cutting dynamics are also explored. It is observed that critical DOC increases with increasing spindle speed and small DOCs can induce cutting instability -- two of the results that agree qualitatively well with published experimental data.