Fractional Order Chaotic Model Based Enhanced Equilibrium Optimization Algorithm for Controller Design of 3 DOF Hover Flight System

In this study, the K feedback gain vector parameters that are used for the control of three degree of freedom four rotor quadcopter system (3 DOF Hover) are optimized with the Enhanced Equilibrium Optimization Algorithm (E2O). The E2O algorithm is proposed with using parameters obtained from fractional order chaotic oscillator models instead of random variables. The Basic EO algorithm is inspired by volume-mass balance. In EO algorithm, each particle is called a motion that searches a parameter vector space. However, random coefficients derived from uniform distribution are used in the parameters updating process or in the generation of the initial population. The E2O algorithm was proposed by using vectors obtained from fractional order chaotic oscillators instead of stochastic coefficients in the basic Equilibrium optimization algorithm. Genesio Tesi, Rössler, Lotka Volterra fractional-order chaotic oscillator models were used in the E2O algorithm to optimize K feedback gain vector of 3 DOF Hover. The order and initial conditions the fractional chaotic oscillator models were experimentally adjusted for the control of 3 DOF problem. Thus, suitable fractional-order chaotic models for the problem were obtained. The E2O algorithm results are compared with the Stochastic Multi Parameter Optimization (SMDO) and Discreet Stochastic Optimization (DSO) algorithms for the system’s pitch, roll and yaw angles.

Random Response of Wake-Oscillator Excited by Fluctuating Wind

Many wake-oscillator models applied to study vortex-induced vibration (VIV) are assumed to be excited by ideal wind that is assumed to be uniform flow with constant velocity. While in the field of wind engineering, the real wind generally is described to be composed of mean wind and fluctuating wind. The wake-oscillator excited by fluctuating wind should be treated as a randomly excited and dissipated multi-degree of freedom (DOF) nonlinear system. The involved studies are very difficult and so far there are no exact solutions available. The present paper aims to carry out some study works on the stochastic dynamics of VIV. The stochastic averaging method of quasi integrable Hamiltonian systems under wideband random excitation is applied to study the Hartlen-Currie wake-oscillator model and its modified model excited by fluctuating wind. The probability and statistics of the random response of wake-oscillator in resonant or lock-in case and in non-resonant case are analytically obtained, and the theoretical results are confirmed by using numerical simulation of original system. Finally, it is pointed out that the stochastic averaging method of quasi integrable Hamiltonian systems under wideband random excitation can also be applied to other wake-oscillator models, such as Skop-Griffin model and Krenk-Nielsen model excited by fluctuating wind.

On the Direct Limit from Pseudo Jacobi Polynomials to Hermite Polynomials

In this short communication, we present a new limit relation that reduces pseudo-Jacobi polynomials directly to Hermite polynomials. The proof of this limit relation is based upon 2F1-type hypergeometric transformation formulas, which are applicable to even and odd polynomials separately. This limit opens the way to studying new exactly solvable harmonic oscillator models in quantum mechanics in terms of pseudo-Jacobi polynomials.