Implementation of fractioanl order filters by particle swarm optimization method

Fractional order systems can be implemented in digital system by designing approximate equivalent discrete filters. In this thesis, fundamental approximate equivalent discrete filter design methods, which are proposed for the implementation of fractional order filters in the literature, are investigated and Infinite Impulse Response (IIR) filter structures are used for implementation of fractional order transfer function in digital systems. These IIR filter designs are optimized by using Particle Swarm Optimization (PSO) method. For this purpose, a cost function, which is expressed in the form of a weighed multi-objective function to improve magnitude and phase response approximations, is defined. This cost function can provide improvement of the magnitude and phase responses of discrete filter approximations. To allow PSO algorithm that yield stable approximate filter solutions, the particles that are representing instable filter solutions are assigned to maximum cost values. With this modification, the objective function is dynamically shaped and this allows searching of particles in the region of stable filter solutions. For computer-aided computation and easy-use of these methods, Matlab Graphical User Interfaces (GUI) are designed. With this GUI programs, approximate equivalent discrete filter design of fractional order filters can be carried out by using fundamental analytical methods in the literature, this filter design can be improved to reach a targeted phase and magnitude response performance by means of PSO, for the analyses of designed filter solutions, Bode diagram, unit step responses, pole placements in complex plane are plotted. By means of this GUI, approximate equivalent discrete filter design of fractional order systems in Matlab is facilitated.