Tuning a Fractional Order Controller from a Heat Diffusion System Using a PSO Algorithm
In this paper we use a particle swarm optimization (PSO) algorithm for the tuning of a fractional order controller, applied to a heat diffusion system. PSO is an optimization technique, inspired by social behaviour of bird flocking or fish schooling. It h
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Tuning a Fractional Order Controller from a Heat Diffusion System Using a PSO Algorithm Isabel S. Jesus and Ramiro S. Barbosa
Abstract In this paper we use a particle swarm optimization (PSO) algorithm for the tuning of a fractional order controller, applied to a heat diffusion system. PSO is an optimization technique, inspired by social behaviour of bird flocking or fish schooling. It has the better ability of global searching and has been successfully applied in many areas of engineering and science. Simulations are presented assessing the performance of the proposed fractional algorithms.
37.1
Introduction
Particle swarm optimization (PSO) is one of the latest evolutionary techniques developed by Dr. Eberhart and Dr. Kennedy in 1995, inspired by social behaviour of bird flocking or fish schooling. The PSO scheme optimizes searching by virtue of the swarm intelligence produced by the cooperation and competition among the particles of a species. The social system is discussed through the collective behaviours of simple individuals interacting with their environment and each other. Examples of this are the bird flock or fish school. Some applications of PSOs are found in the field of nonlinear dynamicalsystems, data analysis,electrical engineering, function optimization, artificial neural network training, fuzzy control and many others in real world applications [1, 2]. The concept of differentiation and integration to non-integer order dates to 1695, when Leibniz mentioned it in a letter to L’Hopital. Since then, many scientists developed the area and notable contributions have been made, both in theory and in applications [3, 4]. In fact, fractional calculus (FC) is a generalization of integration and differentiation to a non-integer order a ∈ C, being the fundamental operator a Dat , where a and t are the limits of the operation [3, 4]. These fractional concepts constitute a useful
I.S. Jesus (*) • R.S. Barbosa GECAD – Knowledge Engineering and Decision Support Research Center, Institute of Engineering – Polytechnic of Porto (ISEP/IPP), Porto, Portugal e-mail: [email protected]; rsbisep.ipp.pt A. Madureira et al. (eds.), Computational Intelligence and Decision Making: Trends and 397 Applications, Intelligent Systems, Control and Automation: Science and Engineering 61, DOI 10.1007/978-94-007-4722-7_37, # Springer Science+Business Media Dordrecht 2013
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tool for describing several physical phenomena in almost all areas of science and engineering, such as heat, magnetism, flow, mechanics or fluid dynamics. Presently, the ability of the FC is being recognized for better modelling and control of many dynamical systems. In fact, during the last years FC has been used increasingly to model the constitutive behaviour of materials and physical systems exhibiting hereditary and memory properties. This is the main advantage of fractional derivatives in comparison with the classical integer-order counterpart, where these effects are neglected. It is well known that the fractional operato
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