Abstract: In this study the regional stability of a rotor system which is supported on rolling bearings with radial clearance is studied. The rotor is assumed to be rigid. Due to radial clearance of bearings and dynamic configuration of system, each rolling elements of bearings has the possibility to be in contact with both of the races (under compression) or lose its contact. As a result, this change in dynamic of the system makes it to be known as switching system which is a type of Hybrid systems. In this investigation by adopting Multiple Lyapunov Function theorem and using Hamiltonian function as a candidate Lyapunov function, the stability of the system is studied. The purpose of this study is to inspect the regional stability of rotor-roller bearing and rotor-ball bearing systems.
Abstract: In the past decade, because of wide applications of
hybrid systems, many researchers have considered modeling and
control of these systems. Since switching systems constitute an
important class of hybrid systems, in this paper a method for optimal
control of linear switching systems is described. The method is also
applied on the two-tank system which is a much appropriate system
to analyze different modeling and control techniques of hybrid
systems. Simulation results show that, in this method, the goals of
control and also problem constraints can be satisfied by an
appropriate selection of cost function.