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The Use of Mathematica in Control System Engineering
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1999 Mathematica Developer Conference
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Champaign, IL
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This talk will present several new facilities that have been developed in the framework of Mathematica's Control System Professional. In particular, some alternative, attractive, and fully editable data formats for systems described by state-space equations and transfer functions, or transfer-function matrices, will be introduced, along with some new model data-formats such as matrix-fraction forms and Rosenbrock's system matrix in polynomial form and state-space form. The necessary new transformations to manipulate system descriptions between these new formats have been implemented and will be demonstrated. Additional system analysis tools to extend the existing controllability and observability tests to the more general polynomial system matrix description will be presented. An alternative, simple algorithm for generating minimal state-space realizations will be introduced, and algorithms to reduce polynomial matrix descriptions of a system to least-order (or minimal-order) form will be presented, along with an algorithm to extract the greatest left- or right-matrix common divisor from two polynomial matrices. The Smith standard form of a polynomial matrix has been implemented, which enables the Smith-McMillan standard form of a rational polynomial matrix to be determined. If time allows, a presentation will be made of some interesting results on the accuracy and computing time of several pole assignment algorithms, when used with system descriptions containing symbols, and a best choice will be suggested. Also, an interesting extension of the optimal control LQR approach to the model reference case will be discussed.
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| Munro.ppt (1 MB) - Microsoft Powerpoint document |
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