ROOT COORDINATES IN THE DESIGN OF SISO CONTROL SYSTEMS
A. V. Chekhonadskikh
Novosibirsk State Technical University, pr. Karla Marksa 20, Novosibirsk, 630073 Russia
Keywords: линейные одноканальные системы управления, регулятор пониженного порядка, оптимальное расположение полюсов, R-градуировка, критические корневые диаграммы, корневые многочлены, SISO linear control systems, low-order controller, optimal pole placement, R-graduation, critical root diagrams, root polynomials
Abstract
We study pole placement in SISO linear control systems with low-order controllers is studied. A method for finding critical (including optimal and suboptimal) pole placement in closedloop systems is theoretically justified and demonstrated on an example. Using critical root diagrams and root polynomials, it is possible to analytically express the parameters of a suboptimal controller in terms of root coordinates, in particular, the real and imaginary parts of characteristic roots. The resulting algebraic equations and inequalities allow specifying the left-most shift of the pole placement domain and the greatest relative stability (possibly taking into account oscillation) without cumbersome calculations.
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