Exact algebraic pole-zero cancellation using symbolic mathematical computation

• Published in: IEE conference publication pp. 117 - 122
• Main Authors: Larcombe, P.J, Woodham, C.A, Brown, I.C
• Format: Conference Proceeding
• Language: English
• Published: London IEE 1998
• Subjects: Algebra; Applied sciences; Computer science; control theory; systems; Control system analysis and synthesis methods; Control system design and analysis; Control system synthesis; Control theory. Systems; Exact sciences and technology; Mathematics computing; Mechanical variables control; controllability; process algebra; pendulums; symbolic manipulation; inverted pendulum; symbol manipulation; control system analysis computing; damping; transfer functions; poles and zeros; multivariable polynomials; pole-zero cancellation; System design; Controllability; Control system; Pole zero method
• ISBN: 085296708X; 9780852967089
• ISSN: 0537-9989
• DOI: 10.1049/cp:19980212

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.