A Note on Robust Stability Analysis of Fractional Order Interval Systems by Minimum Argument Vertex and Edge Polynomials

By using power mapping(s =v^m),stability analysis of fractional order polynomials was simplified to the stability analysis of expanded degree integer order polynomials in the first Riemann sheet.However,more investigation is needed for revealing properties of power mapping and demonstration of conformity of Hurwitz stability under power mapping of fractional order characteristic polynomials.Contributions of this study have two folds: Firstly,this paper demonstrates conservation of root argument and magnitude relations under power mapping of characteristic polynomials and thus substantiates validity of Hurwitz stability under power mapping of fractional order characteristic polynomials.This also ensures implications of edge theorem for fractional order interval systems.Secondly,in control engineering point of view,numerical robust stability analysis approaches based on the consideration of minimum argument roots of edge and vertex polynomials are presented.For the computer-aided design of fractional order interval control systems,the minimum argument root principle is applied for a finite set of edge and vertex polynomials,which are sampled from parametric uncertainty box.Several illustrative examples are presented to discuss effectiveness of these approaches.

Towards Earthquake Shields: A Numerical Investigation of Earthquake Shielding with Seismic Crystals

Authors numerically demonstrate that the seismic surface waves from an earthquake can be attenuated by a seismic crystal structure constructed on the ground. In the study, seismic crystals with a lattice constant of kilometer are investigated in the aspect of band gaps (Stop band), and some design considerations for earthquake shielding are discussed for various crystal configurations in a theoretical manner. Authors observed in their FDTD based 2D wave simulation results that the proposed earthquake shield can provide a decreasing in magnitude of surface seismic waves. Such attenuation of seismic waves might reduce the damage in an earthquake.

Theoretical demonstration of the hybrid focusing points of sonic crystal flat lenses and possible applications

We demonstrate the hybrid focusing points of sonic crystals for a multi-source array applied to flat sonic crystal lenses. The contributions of different point source couples form hybrid focusing points. Ray-trace analyses are conducted for acoustic flat lenses with multi-source configurations. The finite-difference time-domain （FDTD） simulation of flat lenses with multi-source configurations demonstrates the establishment of pure and hybrid focusing points in a pyramidal constellation. The number of focusing points in the pyramidal constellation depends on the number of point sources. We propose an acoustic device for fine-tuning the location of a far-field hybrid focusing point and discuss its benefits for acoustic energy focusing application.

Time-domain identification of One Noninteger Order Plus Time Delay models from step response measurements

Practical performances of controller design methods strongly depend on relevancy of identified models.Fractional order system models promise advantage of more accurate modeling of real systems.This study presents a discussion on utilization of two fundamental numerical solution methods of fractional calculus in identification problems of One Noninteger Order Plus Time Delay with one pole(NOPTD-I)models.The identification process is carried out by estimating parameters of a NOPTD-I type transfer function template so that the step response of the NOPTD-I model can sufficiently fit experimental step response data.In the study,step responses of NOPTD-I models are numerically calculated according to two fundamental methods,which are Mittag-Leffler(ML)function and Grunwald-Letnikov(GL)definition.Particle swarm optimization(PSO)algorithm is used to perform data fitting.Illustrative examples are presented to evaluate model parameter estimation performances of these two methods for synthetically generated noisy test data.An experimental study is conducted for modeling pitch rotor of TRMS to compare experimental performances.