Behavioral Realizations using Companion Matrices and the Smith Form

Carrier compensation for servomechanisms

A fairly new type of compensator for carrier control systems consists of a passive electric network that contains one or more periodically-conducting branches. This type of compensator (referred to as a demodulating compensating network) is superior to other types, used previously, in terms of size, weight, cost, and sensitivity to variations in carrier frequency. Although a detailed analysis of the operation of a demodulating compensating network is usually very tedious, it is possible to describe the effect of such a network in a feedback control system very simply by the use of an equivalent time-invariant passive electric network. A procedure for designing a phase-lead demodulating compensating network to meet specifications on system performance is presented in this paper. In essence, this procedure consists of the following steps. First, the uncompensated frequency response of the system is examined. Then an acceptable and realizable phase and/or gain characteristic is selected. Finally, by the use of design curves, the parameters of the demodulating compensator required to provide the desired frequency response are determined. Numerical examples are included to illustrate the application of the design procedure, and experimental results are reported to reveal the value of the procedure.

A recently found solution to the problem of a random walk over a lattice with reflecting boundaries is used to evaluate the resistances of several passive electrical networks. The solutions are particularly simple for rectangular planar networks and various types are considered. The extension of the solution to the corresponding three-dimensional array, the simple cubic lattice, is given.

In electromechanical measurement techniques, passive transducers and passive electrical networks often interact. In some applications, continua are part of the system, in which fields are formed and waves are propagated. If networks, continua and electromechanical transducers feature sufficient amplitude linear behavior in their environment (e.g., in a small region around the operating point) and all elements of the system having constant parameters during the measurement period, the skillful application of the inherent reciprocity of these systems can lead to surprisingly useful benefits. This is shown by actual examples from metrology. Although the facts of the matter are well known, its potential is often overlooked or disregarded in measurement technique.

Passive damping of structural dynamics using piezoceramic electromechanical energy conversion and passive electrical networks is a relatively recent concept with little implementation experience base. This paper describes an implementation case study, starting from conceptual design and technique selection, through detailed component design and testing to simulation on the structure to be damped. About 0.5 kg. of piezoelectric material was employed to damp the ASTREX testbed, a 5000 kg structure. Emphasis was placed upon designing the damping to enable high bandwidth robust feedback control. Resistive piezoelectric shunting provided the necessary broadband damping. The piezoelectric element was incorporated into a steel flextensional device in order to concentrate damping into the 30 to 40 Hz frequency modes at the rolloff region of the proposed compensator. The effective stiffness and damping of the flextensional device was experimentally verified.

A novel method is presented for the solution of the one-dimensional continuous Kalman filter equations implemented on a digital computer. The Kalman filter is implemented in an unusual way as a transmission line circuit. Estimated variables are regarded as discrete pulses bouncing to and from the nodes in the transmission line network at each time step. This approach is tested on a problem of voltage estimation in a passive electrical network in the presence of voltmeter errors. The transmission line method is compared with the results that are obtained using the Gear first- and third-order methods, the fourth-order Runge-Kutta method and the application of the discrete Kalman filter. It is found that the transmission line method has a tendency to yield less biased estimates than the other algorithms as well as providing smoother estimates for sampling times approaching the time constant of the circuit.

The paper presents a new method based on the Electromagnetic Time-Reversal (EMTR) for locating faults in power systems. The applicability of the EMTR to electromagnetic transients associated with traveling waves in transmission lines originated by the fault is theoretically demonstrated. A new fault location technique is then proposed and illustrated for a simple case of a single-conductor transmission line, for which the performance of the proposed technique in terms of location accuracy is discussed. The use of the EMTR technique appears to be particularly promising for locating faults in passive and active electrical distribution networks in view of their radial structure.

This paper has three contributions. The first involves polytopes of matrices whose characteristic polynomials also lie in a polytopic set (e.g. companion matrices). We show that this set is Hurwitz or Schur invariant if there exist multiaffinely parameterized positive definite Lyapunov matrices which solve an augmented Lyapunov equation. The second result concerns uncertain transfer functions with denominator and numerator belonging to a polytopic set. We show all members of this set are strictly positive real if the Lyapunov matrices solving the equations featuring the Kalman-Yakubovic-Popov Lemma are multiaffinely parameterized. Moreover, under an alternative characterization of the underlying polytopic sets, the Lyapunov matrices for both of these results admit affine parameterizations. Finally, we apply the Lyapunov equation results to derive stability conditions for a class of linear time-varying systems. >

This paper has three contributions. The first involves polytopes of matrices whose characteristic polynomials also lie in a polytopic set (e.g. companion matrices). We show that this set is Hurwitz or Schur invariant if there exist multiaffinely parameterized positive definite, Lyapunov matrices that solve an augmented Lyapunov equation. The second result concerns uncertain transfer functions with denominator and numerator belonging to a polytopic set. We show all members of this set are strictly positive real if the Lyapunov matrices solving the equations featuring in the Kalman-Yakubovic-Popov Lemma are multiaffinely parameterized. Moreover, under an alternative characterization of the underlying polytopic sets, the Lyapunov matrices for both of these results admit affine parameterizations. Finally, we apply the Lyapunov equation results to derive stability conditions for a class of linear time varying systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new method of solving electrical networks is described which is more rapid than the classical determinant method. The new method is based on the properties of certain sub-networks termed "trees" and "2-trees.". It is shown that, with suitable algebraic representations, the required sets of trees and 2-trees can be evaluated with the aid of equations in which the terms are networks. Functions known as linkages are defined in terms of sets of trees and 2-trees, and it is shown that these functions obey laws analogous to Kirchhoff's laws for voltages and currents. Hence relations involving voltages and currents can be expressed in terms of linkages. In particular, the transfer admittance of a network can be expressed as the ratio of the set of all trees on the network to an appropriate linkage. Network theorems can be rapidly deduced with the aid of trees and 2-trees. Since the method gives results in terms of admittances, a rule is given whereby admittance functions can be transformed into the corresponding impedance functions.

This paper studies linear passive electrical networks with ideal switches. We employ the so-called linear switched systems framework in which these circuits can be analyzed for any given switch configuration. After providing a complete characterization of admissible inputs and consistent initial states with respect to a switch configuration, the paper introduces a new state reinitialization rule that is based on energy minimization at the time of switching. This new rule is proven to be equivalent to the classical methods of Laplace transform and charge/flux conservation principle. Also we illustrate the new rule on typical examples that have been treated in the literature.

This review focuses on the spark plasma sintering (SPS) of Ti-based MAX phases, particularly those with Al and Si at the A-site, emphasizing their role in composite materials. The general properties and detailed oxidation behavior of the MAX phases (especially Ti2AlC, Ti3AlC2 and Ti3SiC2) are investigated. The production review is structured under two main categories: first, binary composites using spark plasma sintered MAX phases as the matrix are examined, and an in-depth analysis of their microstructural and mechanical properties is presented. Secondly, composites in which MAX phases are used as additives to enhance the properties of other matrices via the SPS method are reviewed, paying consideration to the impact of the inclusion of the MAX phase on overall performance. Important aspects such as sintering kinetics, phase stability, and property optimization are also discussed for both MAX phases and composites, based on comparisons of findings reported in the literature. This review aims to provide a comprehensive understanding of the role of SPS in tailoring MAX phase-based composites for advanced applications by integrating findings from recent studies.

BackgroundThe ability to compose biological systems from smaller elements that act independently of the other upon assembly may help make the forward engineering of biological systems practical. Engineering biology in this manner is made difficult by the inherent nonlinear response of organisms to genetic devices. Devices are inevitably coupled to one another in the cell because they share the same transcriptional machinery for expression. Thus, new properties can emerge when devices that had been characterized in isolation are expressed concurrently. We show in this report that, similar to physical systems, the Escherichia coli (E. coli) transcriptional system can exhibit linear behavior under "small" perturbation conditions. This, in turn, allows devices to be treated as independent modules.ResultsWe developed a framework and model system consisting of three devices to investigate linear system behavior in E. coli. Our framework employed the transfer curve concept to determine the amount of nonlinearity elicited by the E. coli transcriptional system in response to the devices. To this effect, the model system was quantitatively characterized using real-time quantitative PCR to produce device transfer curves (DTCs). Two of the devices encoded the bacterial neomycin phosphotransferase II (nptII) and chloramphenicol acetyl transferase (cat), while the third encoded the jellyfish-originating green fluorescent protein (gfp). The gfp device was the most nonlinear in our system, with nptII and cat devices eliciting linear responses. Superposition experiments verified these findings, with independence among the three devices having been lost when gfp was present at copy numbers above the lowest one used.ConclusionsWe show that linear system behavior is possible in E. coli. Elucidation of the mechanism underlying the nonlinearity observed in gfp may lead to design rules that ensure linear system behavior, enabling the accurate prediction of the quantitative behavior of a system assembled from individually characterized devices. Our work suggests that biological systems follow principles similar to physical ones, and that concepts borrowed from the latter (such as DTCs) may be of use in the characterization and design of biological systems.

In recent years, the DSP group at the University of Manchester has developed a range of DSP platforms for realtime filtering and processing of acoustic signals. These include Signal Wizard 2.5, Signal Wizard 3 and Vsound. These incorporate processors operating at 100 million multiplication-accumulations per second (MMACs) for SW 2.5 and 600 MMACS for SW 3 and Vsound. SW 3 features six input and eight output analogue channels, digital input/output in the form of S/PDIF and a USB interface. For all devices, The software allows the user, with no knowledge of filter theory or programming, to design and run standard or completely arbitrary FIR, IIR and adaptive filters. Processing tasks are specified using the graphical icon based interface. In addition, the system has the capability to emulate in real-time linear system behavior such as sensors, instrument bodies, string vibrations, resonant spaces and electrical networks. Tests have confirmed a high degree of fidelity between the behavior of the physical system and its digitally emulated counterpart. In addition to the supplied software, the user may also program the system using a variety of commercial packages via the JTAG interface.

Recent advancements in power electronics, storage and renewable technologies have led to a proliferation of distributed energy resources. While the emergence of distributed energy resources provides improved control over the grid, it becomes necessary to analyze the stability of these devices in grid connected mode. It is desirable to provide a simple, robust stability criterion that can be checked locally, without the information of the entire grid. Passivity based stability criterion is well-suited for this purpose as the electrical transmission and distribution network to which these devices are connected is primarily made up of passive components. It is necessary to examine the passivity behavior of synchronous generators, which comprise a large part of the generation in modern grids. This paper presents the passivity behavior of a synchronous machine and the effect of its closed loop controllers on the passivity behavior. It has been observed that the non-passivity can be minimized if the controllers are tuned properly, but the generator is not passive over the entire frequency range. However, it has been observed that passivity can be achieved by encapsulating the generator with a portion of the passive network. Case studies have been carried out using detailed models of the synchronous generators and their controllers.