Exact Algebraic Pole-Zero cancellation using Symbolic Mathematical Computation.

Larcombe, P; Woodham, C A; Brown, I C

Abstract

Modern symbolic computational systems which perform automated manipulation of mathematical variables offer insights during modelling and problem solving which remain otherwise partially or wholly obscured to the analyst. The classic inverted pendulum model is re-visited, and previous work concerning the systems controllability is investigated. In particular, the ability of the software to factorise complicated multivariable polynomials is exploited to identify, in fully general form, the anticipated pole-zero term cancelling throughout the transfer functions of the system when it is in a state of un-controllability. All three balancing problems associated with the two link pendulum are treated, and the phenomenon of non-controllability is examined in this way along the entire `curve of non-controllability' which, within the approximation of linearity, theoretically exists for each when damping is present

Citation

Larcombe, P., Woodham, C. A., & Brown, I. C. (1998). Exact Algebraic Pole-Zero cancellation using Symbolic Mathematical Computation. . https://doi.org/10.1049/cp%3A19980212

• Conference Name: Control '98. UKACC International Conference on (Conf. Publ. No. 455)
• Start Date: Sep 1, 1998
• End Date: Sep 4, 1998
• Publication Date: Sep 1, 1998
• Deposit Date: Jun 1, 2015
• Electronic ISSN: 0537-9989
• Peer Reviewed: Peer Reviewed
• Volume: 1
• Pages: 117-122
• DOI: https://doi.org/10.1049/cp%3A19980212
• Keywords: control system analysis computing; controllability; damping; inverted pendulum; multivariable polynomials; pole-zero cancellation; symbolic manipulation; transfer functions
• Public URL: http://researchrepository.napier.ac.uk/id/eprint/8287
• Publisher URL: http://dx.doi.org/10.1049/cp:19980212