International Journal of applied mathematics and computer science

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Paper details

Number 3 - September 1995
Volume 5 - 1995

On multipurpose control systems synthesis for non-square discrete-time multivariable plants

Stanisław Bańka

The paper is devoted to the synthesis of multipurpose control systems for linear m-input l-output (m ≥ I) discrete-time models of plants defined by proper right-invertible rational transfer matrices in z ∈ ℂ. The under consideration control systems simultaneously ensure: (i) complete dynamic decoupling, (ii) arbitrary dosed-loop pole placement and (iii) steady-state output rejection of deterministic part of disturbances and zero steady-state regulations (or tracking) errors. Two cases of control systems are considered assuming that the state vector of the plant is either accessible or inaccessible for direct measurement. In the case of inaccessible plant's state vector, a stationary Kalman filter or a Luenberger observer is applied to estimate (to reconstruct) the state vector of the plant, which is then used in a linear state variable feedback. In a stochastic case with the inaccessible state vector, two control system structures can be designed with the filtered output ŷ(k) or the original output y(k) which are then used to define the error signal vectors e(k) = y0 - ŷ(k) or e(k) = y0 - y(k),respectively. The idea of the method and the algorithm for the synthesis of the proposed control systems as well as a short analysis of control system properties are presented.