Exact algebraic pole-zero cancellation using symbolic mathematical computation
Exact algebraic pole-zero cancellation using symbolic mathematical computation
- Author(s): P.J. Larcombe ; C.A. Woodham ; I.C. Brown
- DOI: 10.1049/cp:19980212
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- Author(s): P.J. Larcombe ; C.A. Woodham ; I.C. Brown Source: UKACC International Conference on Control (CONTROL '98), 1998 p. 117 – 122
- Conference: UKACC International Conference on Control (CONTROL '98)
- DOI: 10.1049/cp:19980212
- ISBN: 0 85296 708 X
- Location: Swansea, UK
- Conference date: 1-4 Sept. 1998
- Format: PDF
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.
Inspec keywords: symbol manipulation; pendulums; damping; controllability; poles and zeros; control system analysis computing; process algebra
Subjects: Mathematics computing; Algebra; Control system analysis and synthesis methods; Mechanical variables control; Algebra; Control system design and analysis
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