Graphical Method for Robust Stability Analysis for Time Delay Systems: A Case of Study
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This chapter presents a tool for analysis of robust stability, consisting of a graphical method based on the construction of the value set of the characteristic equation of an interval plant that is obtained when the transfer function of the mathematical model is connected with a feedback controller. The main contribution presented here is the inclusion of the time delay in the mathematical model. The robust stability margin of the closed-loop system is calculated using the zero exclusion principle. This methodology converts the original analytic robust stability problem into a simplified problem consisting on a graphic examination; it is only necessary to observe if the value-set graph on the complex plane does not include the zero. A case of study of an internal combustion engine is treated, considering interval uncertainty and the time delay, which has been neglected in previous publications due to the increase in complexity of the analysis when this late is considered.Cite
A transfer function identification method is provided. In combination of nonlinear least squares curve fitting and choosing the initial parameter based on the transfer function model, this method implements curve fitting for different sections with different frequency characteristics. With this method the frequency characteristic of complex control system can be converted to accurate transfer function, thus ±1dB magnitude and ±1degree phase measurement accuracy of transfer function can be obtained in low and middle frequency range. The digital compensator based on the identified transfer function not only effectively eliminates the mechanical resonance but also expands the closed loop bandwidth of the system. The identification of transfer function can facilitate the design of a digital compensator to get rid of manual debugging and provide complex digital compensator for a high performance control system.
Closed-loop pole
Closed-loop transfer function
Identification
Describing function
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This book has four chapters. In the first chapter interval bistructures (biinterval structures) such as interval bisemigroup, interval bigroupoid, interval bigroup and interval biloops are introduced. Throughout this book we work only with the intervals of the form [0, a] where a \in Zn or Z+ \cup {0} or R+ \cup {0} or Q+ \cup {0} unless otherwise specified. Also interval bistructures of the form interval loop-group, interval groupgroupoid so on are introduced and studied. In chapter two n-interval structures are introduced. n-interval groupoids, n-interval semigroups, n-interval loops and so on are introduced and analysed. Using these notions n-interval mixed algebraic structure are defined and described. Some probable applications are discussed. Only in due course of time several applications would be evolved by researchers as per their need. The final chapter suggests around 295 problems of which some are simple exercises, some are difficult and some of them are research problems.
Interval arithmetic
Algebraic structure
Tolerance interval
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Abstract The purpose of an Original Possible Solution (IFS) of an integer transportation interval problematic constructions an essential part of finding a minimum total transportation interval cost solution. Better initial feasible interval solution will result in fewer iterations achieving the minimum total cost solution for the interval. Various methods are obtainable in the fiction to achieve a better original possible result to the problem of interval transport. A new, effective method with row penalties is proposed in this paper to find an initial feasible interval solution to an interval transport problem. One numerical illustration demonstrates the new process. Thus, our new approach can be regarded as an alternate technique for achieving an original possible interval solution to a problem of integral interval transport.
Interval arithmetic
Transportation theory
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This paper is concerned with the robust stabilizability for single-input single-output plants. Robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency-dependent uncertainty band function around the transfer function of a nominal model. A necessary and sufficient condition for robust stabilizability is derived based on the well-known Nevanlinna-Pick theory in classical analysis. It is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model, in order for the class to be robustly stabilizable. A procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown.
Parametrization (atmospheric modeling)
Robustness
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Robustness
Digital Control
Basis (linear algebra)
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Being able to discern the robust stability of a polynomial with coefficients that depend on parameters, is of fundamental importance in control systems analysis. Not only does this allow one to verify the robust stability of some feedback loop, but also confirm other important performance characteristics. Consequently, the development of efficient robust stability tests is of high priority. In this paper, we focus attention on the problem of robust stability of polynomial families with real parameter uncertainty. Several families are considered, with coefficients that depend on parameters in a polynomic fashion. We show that for these families, one can provide efficient finite frequency tests for robust stability.
Robustness
Kharitonov's theorem
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Presents a method to obtain room transfer functions for applications in the design of intelligent systems for video conferencing. In these applications the acoustical dynamics, for example, affects the quality of the recorded speech signal and the ability to achieve accurate source localization. The first part of the paper gives results on the identification of parameterized room transfer functions. The second part presents a method to extrapolate room transfer functions from the identified models. The extrapolation is achieved by getting a functional form of the transfer function parameters which depends on the speaker and the microphone locations.
SIGNAL (programming language)
Identification
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Abstract The sections in this article are Continuous Time Transfer Functions Transfer Function Models of First‐ and Second‐Order Linear Systems Cascading Transfer Functions and the Loading Assumption Block Diagrams Properties of Transfer Functions State‐Space Methods Simulation of Linear Dynamic Systems Control System Design and Analysis Experimental Identification of Discrete Transfer Functions
Closed-loop pole
Block diagram
Identification
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This book has four chapters. In the first chapter interval bistructures (biinterval structures) such as interval bisemigroup, interval bigroupoid, interval bigroup and interval biloops are introduced. Throughout this book we work only with the intervals of the form [0, a] where a \in Zn or Z+ \cup {0} or R+ \cup {0} or Q+ \cup {0} unless otherwise specified. Also interval bistructures of the form interval loop-group, interval groupgroupoid so on are introduced and studied. In chapter two n-interval structures are introduced. n-interval groupoids, n-interval semigroups, n-interval loops and so on are introduced and analysed. Using these notions n-interval mixed algebraic structure are defined and described. Some probable applications are discussed. Only in due course of time several applications would be evolved by researchers as per their need. The final chapter suggests around 295 problems of which some are simple exercises, some are difficult and some of them are research problems.
Interval arithmetic
Algebraic structure
Tolerance interval
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