Symbolic transfer function evaluation by Grassman Algebra




Ahmad, Munawar Baseer

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Symbolic transfer function evaluation means to obtain the overall transfer function with the original symbols preserved. The task is difficult in that (1) it cannot be directly handled by a digital computer with regular languages such as FORTRAN; and (2) it cannot be easily manipulated by hand, if the system is large and the components involved are many. This thesis is concerned with this fundamental problem in systems theory by using Grassmann Algebra. A set of rules of Grassmann Algebra is first systematically derived. The relations among Grassmann Algebra and signal flow graphs of Mason and signal graphs of Coates are investigated. The idea of exterior product is explained in detail. Practical applications in control systems are analyzed and a new method is developed for symbolic matrix inversion by the Grassmann Algebra technique. Finally, a computer program based on PL/C language is developed and several involved cases are tested.