Deepyaman Maiti

Tuning PID and PI /λ D δ Controllers using the Integral Time Absolute Error Criterion

Particle swarm optimization (PSO) is extensively used for real parameter optimization in diverse fields of study. This paper describes an application of PSO to the problem of designing a fractional-order proportional-integral-derivative (PIlambdaDdelta) controller whose parameters comprise proportionality constant, integral constant, derivative constant, integral order (lambda) and derivative order (delta). The presence of five optimizable parameters makes the task of designing a PIiquestDiquest controller more challenging than conventional PID controller design. Our design method focuses on minimizing the integral time absolute error (ITAE) criterion. The digital realization of the deigned system utilizes the Tustin operator-based continued fraction expansion scheme. We carry out a simulation that illustrates the effectiveness of the proposed approach especially for realizing fractional-order plants. This paper also attempts to study the behavior of fractional PID controller vis-a-vis that of its integer-order counterpart and demonstrates the superiority of the former to the latter.

Design of a fractional-order self-tuning regulator using optimization algorithms

The self-tuning regulators form an important sub-class of adaptive controllers. This paper introduces a novel scheme for designing a fractional order self-tuning regulator. Original designs for all the sub-modules of the self-tuning regulator are proposed. The particle swarm optimization algorithm is utilized for online identification of the parameters of the dynamic fractional order process while the subsequent tuning of the controller parameters is performed by differential evolution. Results show that the proposed self-tuning regulator is both precise and robust.

Complete Identification of a Dynamic Fractional Order System Under Non-ideal Conditions Using Fractional Differintegral Definitions

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as opposed to the ideal integral order models. A simple and elegant scheme of estimating the parameters for such a fractional order process is proposed. This method employs fractional calculus theory to find equations relating the parameters that are to be estimated, and then estimates the process parameters after solving the simultaneous equations. The data used for the calculations are intentionally corrupted to simulate real-life conditions. Results show that the proposed scheme offers a very high degree of accuracy even for erroneous data.

A Study of the Grunwald-Letnikov Definition for Minimizing the Effects of Random Noise on Fractional Order Differential Equations

Of the many definitions for fractional order differintegral, the Grunwald-Letnikov definition is arguably the most important one. The necessity of this definition for the description and analysis of fractional order systems cannot be overstated. Unfortunately, the Fractional Order Differential Equation (FODE) describing such a systems, in its original form, highly sensitive to the effects of random noise components inevitable in a natural environment. Thus direct application of the definition in a real-life problem can yield erroneous results. In this article, we perform an in-depth mathematical analysis the Grunwald-Letnikov definition in depth and, as far as we know, we are the first to do so. Based on our analysis, we present a transformation scheme which will allow us to accurately analyze generalized fractional order systems in presence of significant quantities of random errors. Finally, by a simple experiment, we demonstrate the high degree of robustness to noise offered by the said transformation and thus validate our scheme.

A novel approach for complete identification of dynamic fractional order systems using stochastic optimization algorithms and fractional calculus

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as opposed to the ideal integral order models. A simple and elegant scheme of estimating the parameters for such a fractional order process is proposed. This method employs fractional calculus theory to find equations relating the parameters that are to be estimated, and then estimates the process parameters after solving the simultaneous equations. The said simultaneous equations are generated and updated using particle swarm optimization (PSO) technique, the fitness function being the sum of squared deviations from the actual set of observations. The data used for the calculations are intentionally corrupted to simulate real-life conditions. Results show that the proposed scheme offers a very high degree of accuracy even for erroneous data.

An artificial Ant based novel and efficient approach of regular geometric shape detection from digital image

The paper presents a novel and efficient method of regular geometric shape detection from gray scale images. Artificial ant based methods have not been used much in the field of image processing. This paper demonstrates how artificial ants can be used effectively to extract regular geometric shapes from images. We propose here ant regeneration and recombination system (ARRS), an entirely new approach developed by ourselves. Our scheme of detection of shapes comprises of three steps. Firstly, MATLAB edge detection operator converts a gray scale image into a binary one. Ant regeneration and recombination system algorithm is then applied on this binary image to detect closed loops. Finally, these closed loops are tested for different geometric shapes like circle, ellipse, rectangle and square. The most important aspect of the scheme is it can detect both intersecting as well as non intersecting regular shapes from images consisting of different open and closed loop configurations. It is the incredible time and memory efficiency of the scheme that makes it useful in real time applications where decisions have to be taken within a very small time interval by observing an image.

Extension of Max-Min Ant System with Exponential Pheromone Deposition Rule

The paper presents an exponential pheromone deposition approach to improve the performance of classical ant system algorithm which employs uniform deposition rule. A simplified analysis using differential equations is carried out to study the stability of basic ant system dynamics with both exponential and constant deposition rules. A roadmap of connected cities, where the shortest path between two specified cities are to be found out, is taken as a platform to compare max-min ant system model (an improved and popular model of ant system algorithm) with exponential and constant deposition rules. Extensive simulations are performed to find the best parameter settings for non-uniform deposition approach and experiments with these parameter settings revealed that the above approach outstripped the traditional one by a large extent in terms of both solution quality and convergence time.

Parameter identification of a fractional order dynamical system using particle swarm optimization technique

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Accurate estimation is particularly important for systems having varying parameters, which is the usual case with physical processes. Real processes are usually of fractional order as opposed to the ideal integral order models. A simple and elegant scheme of estimating the parameters for such a fractional order process is proposed in this paper. A population of process models is generated and updated by PSO technique, the fitness function being the sum of squared deviations from the actual set of observations. Results show that the proposed scheme offers a high degree of accuracy.

A partly deterministic and partly stochastic scheme for the identification of fractional-order processes

This contribution proposes a simple yet elegant scheme for identifying a fractional-order dynamic system based on its observed response to a standard excitation. If the fractional powers in the transfer function are precisely known, a set of simultaneous linear equations connecting the unknown coefficient values is obtained and then solved deterministically to yield the desired estimates. In case the fractional powers are uncertain, these are estimated by formulating an optimisation problem and employing a stochastic search algorithm. Results show that the proposed method offers a high degree of accuracy even for data that are intentionally corrupted to simulate real-life conditions.

A Novel Parser Design Algorithm Based on Artificial Ants

This article presents a unique design for a parser using the ant colony optimization algorithm. The paper implements the intuitive thought process of human mind through the activities of artificial ants. Traditional methods of designing parser involve calculation of different sets like FIRST, FOLLOW, GOTO, CLOSURE and parsing or precedence relation tables. Calculation of these tables and sets are both memory and time consuming. Moreover, the grammar concerned has to be converted into a context-free, non-redundant and unambiguous one. The scheme presented here uses a bottom-up approach and the parsing program can directly use ambiguous or redundant grammars. We allocate a node corresponding to each production rule present in the given grammar. Each node is connected to all other nodes (representing other production rules), thereby establishing a completely connected graph susceptible to the movement of artificial ants. Ants are endowed with some memory that they use to carry the sentential form derived from the given input string to the parser. Each ant tries to modify this sentential form by the production rule present in the node and upgrades its position until the sentential form reduces to the start symbol S. Successful ants deposit pheromone on the links that they have traversed through in inverse proportion of the number of hops required to complete a successful tour. Eventually, the optimum path is discovered by the links carrying maximum amount of pheromone concentration. The design is simple, versatile, robust and effective and obviates the calculation of the above mentioned sets and precedence relation tables. Further advantages of our scheme lie in i) ascertaining whether a given string belongs to the language represented by the grammar, and ii) finding out the shortest possible path from the given string to the start symbol S in case multiple routes exist.