Controllability of heterogeneous interdependent group systems under undirected and directed topology

The controllability problem of heterogeneous interdependent group systems with undirected and directed topology is investigated in this paper. First, the interdependent model of the heterogeneous system is set up according to the difference of individual characteristics. An extended distributed protocol with the external sliding-mode control is designed, under which it is shown that a heterogeneous interdependent group system is controllable when the corresponding communication topology is controllable. Then, using the network eigenvalue method, the driving individuals are determined for a heterogeneous system with undirected topology. Under directed topology, the maximum match method is utilized to confirm the driving individuals. Some sufficient and necessary conditions are presented to assure that the heterogeneous interdependent group system is structurally controllable. Via theoretical analysis, the controllability of heterogeneous interdependent systems is related to the interdependent manner and the structure of the heterogeneous system. Numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

A comparative study of the role of solute,potent particles and ultrasonic treatment during solidification of pure Mg,Mg-Zn and Mg-Zr alloys

Ultrasonic treatment(UST)applied during the solidification of pure Mg,eutectic(Mg-Zn)and peritectic(Mg-Zr)alloys was investigated in order to explore the grain refinement mechanisms.Temperature dependent grain refinement is observed in pure Mg where decreasing the superheat temperature(at which UST is applied from above the melting temperature,TM)from 100℃to 40℃produces significant refinement with a uniform grain structure.The presence of solute reduces the temperature dependence of the UST refinement and excellent grain refinement is obtained regardless of the superheat temperature(100℃or 40℃)and even with the use of preheated sonotrode in the Mg-6 wt.%Zn alloy.A further improvement in grain refinement is achieved when the alloy contains potent particles that introduce additional nucleation of grains in Mg-0.5 and 1.0 wt.%Zr alloys(producing an average grain size of≤100μm).At 40℃superheat,UST of Mg-Zn alloys produces excellent refinement(average grain size<200μm)with non-dendritic grains,which is normally achieved only with the addition of grain refining master alloy in the as-cast condition.The enhanced refinement observed in the eutectic alloy is explained through the undercooling imposed by a relatively cold sonotrode combined with high frequency vibrations and acoustic streaming.The advantages of using a cold sonotrode,a low superheat and solute are demonstrated for achieving significant refinement during solidification of Mg alloys under UST without or with a lower addition of grain refining master alloys.