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Polynomial Control Systems Adds Practical Solutions for Multivariable Control to Control System Professional Suite

Published July 27, 2006

July 27, 2006–The new Polynomial Control Systems from Wolfram Research further expands the functionality of Control System Professional Suite (CSPS), an extensible framework of tightly integrated Mathematica application packages that provides an object-oriented environment for solving the common control problems that arise in engineering, science, economics, and finance.

Polynomial Control Systems offers new tools for modeling, analysis, and design of linear control systems described by polynomial matrix equations or by matrices with rational polynomial elements. For multivariable systems, these polynomial-based algorithms often provide designers with more informative and meaningful answers than established state-space-based methods. It is the third package in CSPS, joining the award-winning Control System Professional and Advanced Numerical Methods, the latter of which provides state-of-the-art numerical algorithms for systems and control.

Unlike MATLAB and other software packages in this area, Polynomial Control Systems‘ tight integration with the Mathematica engine enables it to utilize both symbolic and exact computation methods. A shared user interface and consistent data structures and function names throughout CSPS make it easier and more transparent to use, while Mathematica‘s professional typesetting capabilities let control engineers display and work with input in traditional textbook formats.

Polynomial Control Systems provides new features for practical control system design, such as the following:

  • Extensive tools for system analysis, such as the Smith and McMillan standard forms and the Luenberger controllable and observable canonical forms
  • Facilities for the computation of controllability and observability indices, invariant and transmission zeros, and detection and removal of input and output decoupling zeros
  • Computation of the relative gain array (RGA) and RGA number plot
  • Direct and inverse Nyquist arrays for analyzing input-output interaction and diagonal dominance using Gershgorin and Ostrowski circles, as well as row and column dominance ratio plots
  • Frequency-domain design methods using the Perron-Frobenius eigenvalue and eigenvector plots, characteristic value plots, and the characteristic locus method
  • Design of constant and dynamic scaling compensators, pseudo-diagonalizing compensators, and aligning compensators

With the addition of Polynomial Control Systems, the Control System Professional library of pole assignment methods is extended to include spectral and mapping dyadic algorithms and the full-rank algorithms for state and output feedback. New objects for system matrices in polynomial and state-space forms, as well as left- and right-matrix-fraction descriptions that are seamlessly incorporated with state-space and transfer-function objects in Control System Professional, add another dimension to the proven CSPS environment.

Polynomial Control Systems is the result of the collaboration of Wolfram Research with the late Professor Neil Munro–a Fellow of the IEEE and the IEE, and head of the Control Systems Centre at the University of Manchester. A pioneering expert in the field, Dr. Munro made critical contributions to the control research community over the course of nearly 40 years.

Polynomial Control Systems can be immediately downloaded from the Wolfram Research web store and is available for all Mathematica platforms. It requires Mathematica 5.0 or higher and Control System Professional 2.0.3, and includes 225 pages of online documentation that provide a concise introduction to the implemented constructs and algorithms, as well as many worked examples.

More information is available on the Polynomial Control Systems website.