Dynamic of Distributed Parameter Systems; From Infinite to Finite System
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This work focuses on describing the dynamic behavior of distributed parameter systems by means of spatial discretization. In control and system theory literature, distributed parameter systems are simply the systems that are represented mathematically by partial differential equations. Thus, the key notion of this work is representing the dynamic behavior of distributed parameter systems by means of spatial discretization of the dynamics of the system. Spatial discretization, or lumping, aims to transform a partial differential equation to a set of ordinary differential equations. The proposed concept approximates the dynamic behavior of the physical system by lumping it to small tranches and then using the finite differences method to interconnect formally these lumps and simulates the dynamic of the overall system.