PARAMETERS ESTIMATION OF FRACTIONAL ORDER SYSTEM WITH DOMINANT POLE USING CO-EVOLUTIONARY PARTICLE SWARM OPTIMIZZATION (CPSO) ALGORITHM

ABSTRACT This paper deals with fractional order systems parameters estimation by use of Co-evolutionary Particle Swarm Optimization (CPSO) method. in some cases such as fractional order systems identification in spite of existing different methods, it is difficult to obtain estimation of model structure parameters and generally it leads to solving the with constrained complex non-linear optimization problems and this topic is one of the identification challenges of these systems. Since some of systems are inherently fractional order and because of having special behavior in these systems which in its similar integer order systems are not found. There for necessity of fractional modeling is double for such systems. In this paper, at first, we assume that the measured out-input data exists and for approximation to reality is considered that these data has been corrupted with noise. Then considering model structure as the linear combination of fractional orthogonal basis functions by use of CPSO suitable algorithm leads to estimation of fractional order system parameters and related to the complexity level of master system, suitable or acceptable approximation is obtained. In finally, by simulating of physical-typical sample system in noisy conditions leads to system identification which gained results shows the effectiveness of presented method. KEYWORDS: Fractional Order Systems, Parameter Estimation, System Identification, Co-Evolutionary Particle Swarm Optimization (Cpso) Algorithms Although the mathematics of fractional calculations has a few hundred years old, but in the two decades ago, it has been attracted in research and applicable fields of various sciences. Also, it was seen that some of the real systems have inherent fractional order behaviour and for example we can refer to real systems such as: viscoelastic materials, cell diffusion processes, transmission of signals via strong magnetic fields and some systems with disturbance characteristics that they have inherent fractional order behaviour One of the features of behaviour of fractional order systems is presence of non-periodic modes that they are decay in polynomial form and also a behaviour that it is called long memory that we can't find its similarity in integer order rational systems . So, if modelling, identification, controlling and other studies on these systems want to be accurate and close to reality, it should be based on fractional order model of these systems. Even in integer order systems, modelling in the form of fractional order mode or controller design with fractional model is also more effective, because of its more degrees of freedom and also the systems with integer order are special state of fractional order systems. This topic has been shown in several researches, therefore, the importance of fractional models and their synthesis is clear in practic

Minimal symmetric Darlington synthesis

We consider the symmetric Darlington synthesis of a p x p rational symmetric Schur function S with the constraint that the extension is of size 2p x 2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically given by the number of zeros of odd multiplicity of I-SS*. A constructive characterization of all such extensions is provided in terms of a symmetric realization of S and of the outer spectral factor of I-SS*. The authors's motivation for the problem stems from Surface Acoustic Wave filters where physical constraints on the electro-acoustic scattering matrix naturally raise this mathematical issue

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Automatic Flight Control Systems

The history of flight control is inseparably linked to the history of aviation itself. Since the early days, the concept of automatic flight control systems has evolved from mechanical control systems to highly advanced automatic fly-by-wire flight control systems which can be found nowadays in military jets and civil airliners. Even today, many research efforts are made for the further development of these flight control systems in various aspects. Recent new developments in this field focus on a wealth of different aspects. This book focuses on a selection of key research areas, such as inertial navigation, control of unmanned aircraft and helicopters, trajectory control of an unmanned space re-entry vehicle, aeroservoelastic control, adaptive flight control, and fault tolerant flight control. This book consists of two major sections. The first section focuses on a literature review and some recent theoretical developments in flight control systems. The second section discusses some concepts of adaptive and fault-tolerant flight control systems. Each technique discussed in this book is illustrated by a relevant example

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Significant effort has been directed towards improving computational efficiency in calculating radiated or scattered fields from a complex structure over a broad frequency band. The formulation and solution of boundary integral equation methods in commercial and scientific software has seen considerable attention; methods presented in the literature are often abstract, “curve-fits” or lacking a sound foundation in the underlying physics of the problem. Anomalous results are often characterized incorrectly, or require user expertise for analysis, a clear disadvantage in a computer-aided design tool. This dissertation documents an investigation into the motivating theory, limitations and integration into SuperNEC of a technique for the analytical, continuous, wideband description of the response of a complex conducting body to an electromagnetic excitation. The method, referred to by the author as Transfer Function Estimation (TFE) has its foundations in the Singularity Expansion Method (SEM). For scattering and radiation from a perfect electric conductor, the Electric-Field Integral Equation (EFIE) and Magnetic-Field Integral Equation (MFIE) formulations in their Stratton-Chu form are used. Solution by spectral representation methods including the Singular Value Decomposition (SVD), the Singular Value Expansion (SVE), the Singular Function Method (SFM), Singularity Expansion Method (SEM), the Eigenmode Expansion Method (EEM) and Model-Based Parameter Estimation (MBPE) are evaluated for applicability to the perfect electric conductor. The relationships between them and applicability to the scattering problem are reviewed. A common theoretical basis is derived. The EFIE and MFIE are known to have challenges due to ill-posedness and uniqueness considerations. Known preconditioners present possible solutions. The Modified EFIE (MEFIE) and Modified Combined Integral Equation (MCFIE) preconditioner is shown to be consistent with the fundamental derivations of the SEM. Prony’s method applied to the SEM poleresidue approximation enables a flexible implementation of a reduced-order method to be defined, for integration into SuperNEC. The computational expense inherent to the calculation of the impedance matrix in SuperNEC is substantially reduced by a physically-motivated approximation based on the TFE method. iv Using an adaptive approach and relative error measures, SuperNEC iteratively calculates the best continuous-function approximation to the response of a conducting body over a frequency band of interest. The responses of structures with different degrees of resonant behaviour were evaluated: these included an attack helicopter, a log-periodic dipole array and a simple dipole. Remarkable agreement was achieved

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