# Two Stage Fractional Order Control Approach to Design an Optimal Controller for A Small Size Rotor Having Internal Dissipation

01 Mar 2019-

TL;DR: This approach not only eases out the implementation of digital/analog realization of a Fractional Order PID (FOPID) controller with its integer order but at the same time it also preserves the advantages of fractional order controller.

Abstract: Rotating machines and its applications directly affect the basic economic issues and deals very closely with human life. Its safe operation is hence an absolute necessity. Rotors with speed higher than a specific threshold value become unstable due to rotating damping forces produced by the dissipation in rotor material, couplings or due to friction in tool-tips and splines. Some techniques do exist for stabilizing rotors however they are not well suited for small, micro and mini rotor systems. Orbital response function and 2-stage sub-optimal controller tuning methodology in rotor system actuated by a piezo actuator for providing adequate damping force has been used to keep the rotor stable. The approximated integer order PID gains thus obtained from conformal mapping-based FO method of stage 2 tuning pushes the closed loop poles of the system towards greater damping as compared to stage 1. This approach not only eases out the implementation of digital/analog realization of a Fractional Order PID (FOPID) controller with its integer order but at the same time it also preserves the advantages of fractional order controller. Simulation is done on MATLAB & SIMULINK. The analysis of the performances for both the cases are discussed.

Topics: Rotor (electric) (60%), PID controller (57%), Control theory (56%), Helicopter rotor (52%), Closed-loop pole (52%)

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01 Jun 2011-

Abstract: When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ordinary differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls. The normal physical laws like, transport theory, electrodynamics, equation of motions, elasticity, viscosity, and several others of are based on ordinary calculus. In this book these physical laws are generalized in fractional calculus contexts; taking, heterogeneity effect in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, physics of random delay in computer network; and several others; mapping the reality of nature closely. The concept of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically with examples. The practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function is deliberated. Practical results of viscoelastic experiments, fractional order controls experiments, design of fractional controller and practical circuit synthesis for fractional order elements are elaborated in this book. The book also maps theory of classical integer order differential equations to fractional calculus contexts, and deals in details with conflicting and demanding initialization issues, required in classical techniques. The book presents a modern approach to solve the solvable system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving approximately exact series solutions.Historically, Sir Isaac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J.von Neumann remarked, the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking.This XXI century has thus started to think-exactly for advancement in science & technology by growing application of fractional calculus, and this century has started speaking the language which nature understands the best.

597 citations

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19 Dec 2002-

TL;DR: This chapter discusses Dynamical Systems and Modeling, a Treatise on Modeling Equations and its Applications to Neural Networks, and its applications to Genetic and Evolutionary Algorithms.

Abstract: 1. Dynamical Systems and Modeling 2. Analysis of Modeling Equations 3. Linear Systems 4. Stability 5. Optimal Control 6. Sliding Modes 7. Vector Field Methods 8. Fuzzy Systems 9. Neural Networks 10. Genetic and Evolutionary Algorithms 11. Chaotic Systems and Fractals Index

362 citations

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Abstract: A mathematical model of an unloaded symmetric rotor supported by one rigid and one fluid lubricated bearing is proposed. The rotor model is represented by generalized (modal) parameters of its first bending mode. The rotational character of the bearing fluid force is taken into account. The model yields synchronous vibrations due to rotor unbalance as a particular solution of the equations of motion, rotor/bearing system natural frequencies and corresponding self-excited vibrations known as “oil whirl” and “oil whip”. The stability analysis yields rotative speed threshold of stability. The model also gives the evaluation of stability of the rotor synchronous vibrations. In the first balance resonance speed region two more thresholds of stability are encountered. The width of this stability region is directly related to the amount of rotor unbalance. The results of the analysis based on this model stand with very good agreement with field observations of rotor dynamic behavior and the experimental data.

257 citations

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21 Jun 2001-

TL;DR: Preface Acknowledgments Introduction: Modeling, Identification, Optimization, and Control Mathematical Model Developments Modeling of Dynamic Systems using Matlab and SIMULINK Analysis and Control of Linear Dynamic Systems Analysis, identification, and control of Nonlinear Dynamic Systems.

Abstract: Preface Acknowledgments Introduction: Modeling, Identification, Optimization, and Control Mathematical Model Developments Modeling of Dynamic Systems using Matlab and SIMULINK Analysis and Control of Linear Dynamic Systems Analysis, Identification, and Control of Nonlinear Dynamic Systems References Index

104 citations