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The fundamental equation that describes limit cycles in nonlinear sampled-data systems was derived. The equivalence of limit cycles with finite pulsed systems having a periodically varying sampling-rate was observed, and the methods of analysis applied to the latter were extended to obtain these limit cycles with the aid of final value theorem. This fundamental equation is modified and simplified under certain assumptions as it can be applied to systems both with and without integrators. The limitation on the longest period of saturated and unsaturated oscillation is investigated and the critical gain for their existence is derived, starting from the modified fundamental equation. Also, the stability of limit cycles and the equilibrium point is considered, based on Neace's method. Various kinds of non-linearities, namely, pulse-width modulation, relay saturating amplifier with linear zone and quantized level amplifier are discussed. Self-excited oscillations are mainly examined, as well as the possible existence and stability of limit cycles, however, the method can be extended to forced oscillations.
Various techniques are available for the analysis of nonlinear sampled-data systems. Most of these methods use either the phase plane approach or the describing function technique. Since the performance of such a system is described, at sampling instants, by means of a difference equation, an approach based on the difference equation would seem to be both natural and direct. The principle of complex convolution for a transform is explained and its geometrical interpretation is given. It is shown how the application of the convolution transform is both direct and simple with respect to solving nonlinear difference equations when the equation is given in scalar form. Dependence of the convergence of the solution on the initial value and the degree of nonlinearity is pointed out. It is concluded that for difference equations of second order and higher, this method involves too much laborious computation to justify its use. A simple method is presented for examining free oscillations in a sampled-data system containing either relay or a saturating amplifier. In addition, a certain analytical technique, analogous to that for differential equations, is developed to investigate the stability of forced oscillations for certain types of nonlinear difference equations. (Author).
Containing papers from the Special Technical Session on Earthquake Geotechnical Engineering, this volume includes coverage of: zonation maps; liquefaction; side effects; ground motions; slope instability; seismic behaviour of slopes; dikes and dams; and warning systems.
This book offers a historical account of the development of the On-X carbon mechanical heart valve, discussing the steps involved in developing the materials, and describes how the design of the valve has evolved over the years. It explores both the scientific and corporate problems researchers have encountered over the years in the journey of making a mechanical heart valve. The chapters provide a detailed description of the design of the mechanical leaflet-based prosthetic valve, with a particular focus on blood flow characteristics. This book includes an overview of the state-of-the-art in the chemistry and physics of carbon, and compiles the advances in carbon-based technology and its applications in cardiac and thoracic surgery. This is an ideal book for bioengineers working on the chemistry and physics of carbon, and other professionals involved with cardiac and thoracic surgery.
The use of concurrent models has become a necessity in embedded system design. This trend is driven by the growing complexity and inherent multitasking of embedded systems. Describing a system as a set of concurrently executed, relatively simple subtasks is more natural than using a single, complicated task. Embedded systems, however, have limited resources. They often have a few processors. This implies that several software subtasks "programs" have to share a CPU. Compile-time scheduling determines a sequential execution order of the program statements that satisfies certain constraint, e.g. bounded memory usage, at compile time. We study compile-time schedulability of concurrent programs based on a Petri net model. We consider concurrent programs that asynchronously communicate with each other and the environment through unbounded first-in first-out "FIFO" buffers. The Petri net represents the control flow and communications of the programs, and models data dependent branches as non-deterministic free choices. A schedule of a Petri net represents a set of firing sequences that can be infinitely repeated within a bounded state space, regardless of the outcomes of the nondeterministic choices. Schedulability analysis for a given Petri net answers the question whether a valid schedule exists in the reachability space of this net. Due to the heuristics nature of existing scheduling algorithms, discovering powerful necessary condition for schedulability is important to gain efficiency in analysis. We propose a novel structural approach to schedulability analysis of Petri nets. Structural analysis often yields polynomial-time algorithms and is applicable for all initial states. We show that unschedulability can be caused by a structural relation among transitions modelling nondeterministic choices. Two methods for checking the existence of the relation are propo.