The Experts below are selected from a list of 108 Experts worldwide ranked by ideXlab platform
Mark L. Nagurka - One of the best experts on this subject based on the ideXlab platform.
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A general theory quantifying the Root sensitivity function
2018Co-Authors: Thomas R. Kurfess, Mark L. Nagurka, Carnegie Mellon University.engineering Design Research Center.Abstract:Abstract: "In this report, we present a geometric method for representing the classical Root sensitivity function of linear time-invariant systems. The method employs gain Plots that expand the information presented in the Root Locus Plot in a manner that permits determination of both the real and imaginary components of the Root sensitivity function by inspection.
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Geometric analysis of multivariable control systems
2018Co-Authors: Mark L. Nagurka, Thomas R. Kurfess, Carnegie Mellon University.engineering Design Research Center.Abstract:Abstract: "This report promotes a new graphical representation of the behavior of linear, time-invariant, multivariable systems highly suited for exploring the influence of closed-loop system parameters. The development is based on the adjustment of a scalar control gain cascaded with a square multivariable plant embedded in an output feedback configuration. By tracking the closed-loop eigenvalues as an explicit function of gain, it is possible to visualize the multivariable Root loci in a set of 'gain Plots' consisting of two graphs: (i) magnitude ofsystem eigenvalues vs. gain, and (ii) argument (angle) of system eigenvalues vs. gain.By depicting unambiguously the polar coordinates of each eigenvalue in the complex plane, the gain Plots complement the standard multi-input, multi-output Root Locus Plot. Two example problems demonstrate the utility of gain Plots for interpreting linear multivariable system behavior.
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A Geometric Representation of Root Sensitivity
Journal of Dynamic Systems Measurement and Control, 1994Co-Authors: Thomas R. Kurfess, Mark L. NagurkaAbstract:In this paper, we present a geometric method for representing the classical Root sensitivity function of linear time-invariant dynamic systems. The method employs specialized eigenvalue Plots that expand the information presented in the Root Locus Plot in a manner that permits determination by inspection of both the real and imaginary components of the Root sensitivity function. We observe relationships between Root sensitivity and eigenvalue geometry that do not appear to be reported in the literature and hold important implications for control system design and analysis
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Geometric links among classical controls tools
IEEE Transactions on Education, 1994Co-Authors: Thomas R. Kurfess, Mark L. NagurkaAbstract:This paper develops a geometric perspective that ties together a number of graphically based techniques from classical control theory. In particular, in the frequency domain, a connection between the Nyquist diagram and the Bode Plots is unfolded via a sequence of three-dimensional representations. A parallel development in the "gain-domain" begins with the Evans Root Locus Plot and leads to a set of gain Plots that portray eigenvalue behavior as an explicit function of forward gain. The gain Plots extend the standard Root Locus Plot by depicting explicitly the influence of gain (or any system parameter) on the closed-loop system eigenvalues. This is similar to the way the Bode Plots embellish the information of the Nyquist diagram by exposing frequency explicitly. The gain Plots enable direct determination of gain values for which the closed-loop system is stable or unstable. By exposing the correspondence of gain values to specific eigenvalues, the Plots serve as a pole-placement tool for identifying closed-loop designs meeting performance specifications. Furthermore, the gain Plots reveal by inspection information about the closed-loop Root sensitivity. The authors have found the gain Plots as well as the underlying geometric development in both the frequency and gain domains invaluable in undergraduate and graduate controls education. >
S.r. Weller - One of the best experts on this subject based on the ideXlab platform.
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Bifurcations in iterative decoding and Root Locus Plots
IET Control Theory & Applications, 2008Co-Authors: Christopher M. Kellett, S.r. WellerAbstract:A class of error correction codes called dasialow-density parity-check (LDPC)dasia codes have been the subject of a great deal of recent study in the coding community as a result of their ability to approach Shannondasias fundamental capacity limit. Crucial to the performance of these codes is the use of an dasiaiterativedasia decoder. These iterative decoders are effectively high-dimensional, nonlinear dynamical systems and, consequently, control-theoretic tools are useful in analysing such decoders. The authors describe LDPC codes and the decoding algorithm and make a connection between the fixed points of the decoding algorithm and the well-known Root Locus Plot. Through two examples of LDPC codes, the authors show that the Root Locus Plot visually captures the bifurcation behaviour of iterative decoding that occurs at the signal-to-noise ratio predicted by Shannondasias noisy channel coding theorem.
Thomas R. Kurfess - One of the best experts on this subject based on the ideXlab platform.
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A general theory quantifying the Root sensitivity function
2018Co-Authors: Thomas R. Kurfess, Mark L. Nagurka, Carnegie Mellon University.engineering Design Research Center.Abstract:Abstract: "In this report, we present a geometric method for representing the classical Root sensitivity function of linear time-invariant systems. The method employs gain Plots that expand the information presented in the Root Locus Plot in a manner that permits determination of both the real and imaginary components of the Root sensitivity function by inspection.
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Geometric analysis of multivariable control systems
2018Co-Authors: Mark L. Nagurka, Thomas R. Kurfess, Carnegie Mellon University.engineering Design Research Center.Abstract:Abstract: "This report promotes a new graphical representation of the behavior of linear, time-invariant, multivariable systems highly suited for exploring the influence of closed-loop system parameters. The development is based on the adjustment of a scalar control gain cascaded with a square multivariable plant embedded in an output feedback configuration. By tracking the closed-loop eigenvalues as an explicit function of gain, it is possible to visualize the multivariable Root loci in a set of 'gain Plots' consisting of two graphs: (i) magnitude ofsystem eigenvalues vs. gain, and (ii) argument (angle) of system eigenvalues vs. gain.By depicting unambiguously the polar coordinates of each eigenvalue in the complex plane, the gain Plots complement the standard multi-input, multi-output Root Locus Plot. Two example problems demonstrate the utility of gain Plots for interpreting linear multivariable system behavior.
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A Geometric Representation of Root Sensitivity
Journal of Dynamic Systems Measurement and Control, 1994Co-Authors: Thomas R. Kurfess, Mark L. NagurkaAbstract:In this paper, we present a geometric method for representing the classical Root sensitivity function of linear time-invariant dynamic systems. The method employs specialized eigenvalue Plots that expand the information presented in the Root Locus Plot in a manner that permits determination by inspection of both the real and imaginary components of the Root sensitivity function. We observe relationships between Root sensitivity and eigenvalue geometry that do not appear to be reported in the literature and hold important implications for control system design and analysis
-
Geometric links among classical controls tools
IEEE Transactions on Education, 1994Co-Authors: Thomas R. Kurfess, Mark L. NagurkaAbstract:This paper develops a geometric perspective that ties together a number of graphically based techniques from classical control theory. In particular, in the frequency domain, a connection between the Nyquist diagram and the Bode Plots is unfolded via a sequence of three-dimensional representations. A parallel development in the "gain-domain" begins with the Evans Root Locus Plot and leads to a set of gain Plots that portray eigenvalue behavior as an explicit function of forward gain. The gain Plots extend the standard Root Locus Plot by depicting explicitly the influence of gain (or any system parameter) on the closed-loop system eigenvalues. This is similar to the way the Bode Plots embellish the information of the Nyquist diagram by exposing frequency explicitly. The gain Plots enable direct determination of gain values for which the closed-loop system is stable or unstable. By exposing the correspondence of gain values to specific eigenvalues, the Plots serve as a pole-placement tool for identifying closed-loop designs meeting performance specifications. Furthermore, the gain Plots reveal by inspection information about the closed-loop Root sensitivity. The authors have found the gain Plots as well as the underlying geometric development in both the frequency and gain domains invaluable in undergraduate and graduate controls education. >
Manisha K Bhole - One of the best experts on this subject based on the ideXlab platform.
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a new and simple method to construct Root Locus of general fractional order systems
Isa Transactions, 2014Co-Authors: Mukesh D Patil, Vishwesh A Vyawahare, Manisha K BholeAbstract:Recently fractional-order (FO) differential equations are widely used in the areas of modeling and control. They are multivalued in nature hence their stability is defined using Riemann surfaces. The stability analysis of FO linear systems using the technique of Root Locus is the main focus of this paper. Procedure to Plot Root Locus of FO systems in s-plane has been proposed by many authors, which are complicated, and analysis using these methods is also difficult and incomplete. In this paper, we have proposed a simple method of Plotting Root Locus of FO systems. In the proposed method, the FO system is transformed into its integer-order counterpart and then Root Locus of this transformed system is Plotted. It is shown with the help of examples that the Root Locus of this transformed system (which is obviously very easy to Plot) has exactly the same shape and structure as the Root Locus of the original FO system. So stability of the FO system can be directly deduced and analyzed from the Root Locus of the transformed IO system. This proposed procedure of developing and analyzing the Root Locus of FO systems is much easier and straightforward than the existing methods suggested in the literature. This Root Locus Plot is used to comment about the stability of FO system. It also gives the range for the amplifier gain k required to maintain this stability. The reliability of the method is verified with analytical calculations.
Christopher M. Kellett - One of the best experts on this subject based on the ideXlab platform.
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Bifurcations in iterative decoding and Root Locus Plots
IET Control Theory & Applications, 2008Co-Authors: Christopher M. Kellett, S.r. WellerAbstract:A class of error correction codes called dasialow-density parity-check (LDPC)dasia codes have been the subject of a great deal of recent study in the coding community as a result of their ability to approach Shannondasias fundamental capacity limit. Crucial to the performance of these codes is the use of an dasiaiterativedasia decoder. These iterative decoders are effectively high-dimensional, nonlinear dynamical systems and, consequently, control-theoretic tools are useful in analysing such decoders. The authors describe LDPC codes and the decoding algorithm and make a connection between the fixed points of the decoding algorithm and the well-known Root Locus Plot. Through two examples of LDPC codes, the authors show that the Root Locus Plot visually captures the bifurcation behaviour of iterative decoding that occurs at the signal-to-noise ratio predicted by Shannondasias noisy channel coding theorem.
