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Control System Analysis with Mathematica

H. A. Barker
P. Grant
M. Zhuang
Journal / Anthology

IEE Colloquium on Symbolic Computation and Control
Year: 1996
Volume: 78
Page range: 2/1-2/5

Although symbolic computation software has been available for many years, its application to control engineering has been rather limited, possibly because the early software was not particularly user-friendly. It was possible to solve particular problems of considerate complexity using first-generation software such as MACSYMA, but for the development of general tools the facilities of second-generation software such as Mathematica were required. These facilities now include linkages to software more familiar to the control engineer, such as MATLAB, which opens up interesting possibilities of combined symbolic and numeric software for control. In this presentation, it is shown that the linkage between Mathematica and MATLAB also allows the graphical user interface of the associated simulation software SIMULINK to be used as a graphical user interface for Mathematica. This facility for defining the dynamic system models to be analyzed by Mathematica has several significant advantages. In particular, the models are constructed by means of a comprehensive and well-developed graphical interface familiar to the control engineer, and the results of analysis obtained with Mathematica can be compared directly with the results of simulation obtained with SIMULINK. A Mathematica-based toolbox for the analysis and design of linear control systems is then described. It is shown that both continuous and digital systems may be analyzed by Laplace- and z-transforms and that familiar tools such as root locus- and frequency response-diagrams are also available. Finally, an application of Mathematica to the analysis of nonlinear systems by means of multidimensional transforms is described, and results presented which by manual methods would take an inordinate amount of time to obtain.

*Engineering > Control Theory