Kumar S. Ray

Application of circle criteria for stability analysis of linear SISO and MIMO systems associated with fuzzy logic controller

The concept of the sector bound nonlinearity has been considered for frequency domain stability analysis of linear single-input single-output (SISO) and decoupled multi-input multi-output (MIMO) systems associated with the fuzzy logic controller. For analysis of the fuzzy logic controller, the systems model is considered to be available in transfer-function form, but for generation of the fuzzy logic controller no model description is necessary. A generalized Nyquist-type stability analysis is presented.

Determination of optimal polygon from digital curve using L1 norm

Abstract A technique to determine optimal polygons of digital curves is proposed. It determines the longest possible line segments with the minimum possible error. The L 1 norm is used to measure the closeness of a polygon to a digital curve. The algorithm runs in linear time. The procedure is applied to several digital curves and promising results are obtained.

An algorithm for detection of dominant points and polygonal approximation of digitized curves

Abstract A new technique for the detection of dominant points and polygonal approximation of digitized curves is proposed. The procedure needs no input parameter and remains reliable even when features of multiple size are present. Unlike the existing algorithms, the present technique introduces the concept of an asymmetric region of support and k - l -cosine. The dominant points are the local maxima of k - l -cosine. The polygon is obtained joining the dominant points successively.

A new split-and-merge technique for polygonal approximation of chain coded curves

Abstract In all split-and-merge techniques the fundamental problem is the initial segmentation. In this paper the initial segmentation is done by introducing the concept of rank of a point. The split-and-merge is done using two criteria functions, namely, the ratio of the arc length to the length of the line segment and the ratio of the distance from a point to the line segment (not the perpendicular distance) to the length of the line segment. The procedure generates polygons that are insensitive to rotation and scales and remains reliable in presence of noise.

Detection of significant points and polygonal approximation of digitized curves

Abstract A new method, based on k -cosine, is proposed for the determination of region of support and detection of significant points of digitized curves. A new measure of significance, based on k -cosine, is introduced. The procedure is parallel and requires no input parameter. A polygonal approximation is suggested by joining the successive significant points.

L 2 -stability and the related design concept for SISO linear system associated with fuzzy logic controller

A hybrid (fuzzy and nonfuzzy) design concept has been proposed for the linear single-input single-output (SISO) system associated with fuzzy logic controllers. In the present design techniques, the concept of L2-stability and its graphical interpretation, i.e. the circle criterion, are used. Thus the use of the classical Nyquist locus and the gain-phase chart are brought into the picture. The drawbacks of the L2-stability/circle criterion are indicated and overcome. In the present design technique, which is graphical in nature, the designer is given a feel for the system. Examples are provided to illustrate the application of hybrid controllers structure for the synthesis of the linear SISO system associated with the fuzzy logic controller.

Similarity-based approximate reasoning: methodology and application

This correspondence elucidates the importance of similarity, as modeled by a measure of similarity, in approximate reasoning. A set of axioms is proposed to compute a reasonable measure of similarity between two imprecise concepts represented as fuzzy sets. For approximate reasoning, a similarity index between the fact and the antecedent of a rule is computed and is used in the reasoning mechanism. Accordingly, the existing reasoning mechanism is modified. A new similarity-based approximate reasoning methodology is proposed. As an illustration of its effectiveness, the proposed mechanism is used to develop a rule-based pattern classifier.

A non-parametric sequential method for polygonal approximation of digital curves

Abstract A non-parametric sequential technique for polygonal approximation of digital curves is proposed. The procedure looks for the longest possible line segments by maximising an objective function which comprises of the length of the line segment and the integral square error along the line segment. The vertices of the polygon are those points where this function attains a local maximum. Though the procedure is sequential and one pass, neither does it round off sharp turnings nor does it dislocate the vertices near the other turnings.

Fuzzy logic control of a nonlinear multivariable steam generating unit using decoupling theory

A nonlinear multivariable steam generating unit (200 MW) has been decoupled using the existing decoupling theory. A set of fuzzy logic controllers, which virtually reduce to nonlinear multilevel relay elements, is designed for the decoupled subsystems to make the closed-loop subsystems asymptotically stable. Subsequently it has been shown, through digital simulation and field simulation, that the closed-loop subsystems track the desired state parameters under different operating conditions. A frequency domain stability analysis has been presented assuming that the decoupled subsystems are linear in nature and decoupling is accurate.

Corner detection using iterative Gaussian smoothing with constant window size

Abstract In contrast to the existing Gaussian smoothing process with varying window size, an iterative Gaussian convolution with constant window size is proposed. The iterative process is shown to converge as the norm of the convolution matrix is less than unity. For a closed digital curve the number of iterations is shown to be related to the number of points on the curve. The Gaussian filter coefficients that are used to smooth the curve are shown to enjoy the scale-space property. A scale-space map showing the location of the maxima of absolute curvature over iterations is proposed. The map is converted into a tree organization on the basis of an analysis of the scale-space behavior of different corner models such as Γ models, END models and STAIR models. Corners are detected in a process of interpreting the tree. The corner detector has been applied successfully on different digital curves even in presence of additive white Gaussian noise and at varying orientations.