POLYNOMIAL DESIGN OF LOW-ORDER CONTROLLERS FOR SISO DESCRIPTOR SYSTEMS
A.V. Chekhonadskikh
Novosibirsk State Technical University, Novosibirsk, Russia
Keywords: descriptor system, differential-algebraic equations, low-order controller, pole location, maximum relative stability, critical root diagram, root polynomial, polynomial equations, impulse response
Abstract
We apply a polynomial approach to low-order optimal controller design for linear stationary SISO systems described by differential-algebraic equations. Critical root diagrams and root polynomials are explored in low-order controller design in classical control systems. The method is illustrated on an unstable controlled plant defined by an improper transfer fraction with a 6th-degree numerator and a 4th-degree denominator. We find the settings of a few stabilizing PI3-controllers and select the optimal one providing the maximum relative stability; the impulse response calculation confirms that the close loop system is astatic and impulse-free. The method scheme remains the same as that for the classical control systems; however, the arising polynomial systems turn out to be of a higher degree and more difficult for numerical solving.
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