Discrete dynamics analysis for nonlinear collocated multivariable mass-damper-spring intelligent mechanical vibration systems

A new time-discretization method for the development of nonlinear collocated multivariable mass-damper-spring (MDS) intelligent mechanical vibration systems is proposed. It is based on the Runge-Kutta series expansion method and zero-order hold assumption. In this paper, we show that the mathematical structure of the new discretization scheme is explored and characterized in order to represent the discrete dynamics properties for nonlinear collocated multivariable MDS intelligent mechanical vibration systems. In particular, the decent effects of the time-discretization method on key properties of nonlinear multivariable MDS mechanical vibration systems, such as discrete zero dynamics and asymptotic stability, are examined. The resulting time-discretization provides discrete dynamics behavior for nonlinear MDS mechanical vibration systems, which enabling the application of existing controller design techniques. The ideas presented here generalize well-known results from the linear case to nonlinear plants.