Generation of mathematical models of linear dynamic systems given by block diagrams

M. L. Simonov, K. S. Zaytsev, N. P. Popova


The purpose of this work is to develop a method for calculating the mathematical model of a block diagram in the form of equations in the state space. The calculation of the model is built as an iterative process. The initial state of the mathematical model is a model consisting of unconnected elements of the block diagram. The hierarchy of the elements, in the general case, is not established, and is arbitrary, but unchanged during the calculation. The iterative process consists of steps, each of which processes one connection. A connection links the output and input ports of the element(s) in the block diagram. It is useful to implement the algorithm for calculating the current connection without exception and without zeroing the rows and columns of the matrices of state equations corresponding to this connection. This corresponds to obtaining an equivalent, block diagram model with input ports available for signaling and output ports open for observation of all elements that make up the block diagram. It is shown that for a linear dynamical system in the case of the presence of a solvable system of algebraic contours in it, it is possible to obtain a mathematical model of the dynamical system in the form of equations of state. A condition is derived under which the system of algebraic contours can be solvable.

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