Smart Systems for Industrial Applications. Группа авторов. Читать онлайн. Newlib. NEWLIB.NET

Автор: Группа авторов
Издательство: John Wiley & Sons Limited
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Жанр произведения: Программы
Год издания: 0
isbn: 9781119762041
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Kdi and are the proportional, integral, and differential coefficient, respectively, where e(t) = yd (t) − y(t) is the system error, yd (t) is the reference input, y(t) is system response, and u(t) is controlled output [6, 9]. The FOPID controller is an extension of the conventional IPID controller with the integral and the differential orders as fractional one [7].

      FOPID controller is represented as

      (2.9)image

      λe indicates integral order.

      µ indicates the differential order.

      Kpf, Kif, and Kdf are fractional-order controller gains.

      Laplace transfer function of the controller is given as

      (2.10)image

      The FOPID has additionally more adjustable parameters, λ and µ, than IPID controller and have five control parameters (Kpf, Kif, Kdf, λe, and μ) to find a better control performance [9]. For optimization, the GA has a possibility to come with five optimum parameter space to achieve best control performance.

      GA is an adaptive empirical search algorithm depends on the mutative concepts of natural selection and genetics. It emphasizes the intellectual manipulation in finding solution to the optimization problems. Based on the historical information, GA searches for random variables through the best performance region of the search space. GA technique resembles the survival of the fittest principle proposed by Charles Darwin. In view of nature’s law, competition or struggle among the individuals results in the fittest predominating the inferior ones.

      Alike chromosomes in DNA, the population in every generation has certain character strings impinged from the parent. In the search space each one of the individual signifies a point and has a feasible solution. The next stage through which the individuals undergo is the evolution process. Every individual in the population strives for the best position and mates. The fittest individual competes and yields offspring, whereas the inferior individuals will not proceed to the successive process. In every generation, the offspring thus produced from the fittest parent will be more suitable for the environment.

      2.5.1 GA Optimization Methodology

Schematic illustration of Phases in genetic algorithm.

      1 Initialization: population of chromosomes are initialized

      2 Selection: reproduce chromosomes

      3 Crossover: produce next generation of chromosomes

      4 Mutation: random mutation of chromosomes in new generation

       2.5.1.1 Initialization

       2.5.1.2 Fitness Function

      Fitness function is the most crucial part of the algorithm. The capability of an individual entity to race with other entities is determined using fitness function. Fitness score is bestowed to every individual and the possibility for the selection of an individual for reproduction is entirely based on this score. It is the function that the algorithm optimizes. The word fitness is taken from evolutionary theory. Fitness is the word coined from evolutionary theory.

       2.5.1.3 Evaluation and Selection

      Population generation is followed by evaluation. It is the process in which the fitness level of the newly generated off springs is estimated using a fitness function. The inferior individuals are eradicated during selection and the best individual proceeds to the next generation.

       2.5.1.4 Crossover

       2.5.1.5 Mutation

Schematic illustration of mutation.

      2.5.2 GA Parameter Tuning

Graph depicts the fitness with crossover probabilities.