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Proper feedback compensators for a strictly proper plant by polynomial equations

Frank CallierFerdinand Kraffer — 2005

International Journal of Applied Mathematics and Computer Science

We review the polynomial matrix compensator equation X_lD_r + Y_lN_r = Dk (COMP), e.g. (Callier and Desoer, 1982, Kučera, 1979; 1991), where (a) the right-coprime polynomial matrix pair (N_r, D_r) is given by the strictly proper rational plant right matrix-fraction P = N_rD_r, (b) Dk is a given nonsingular stable closed-loop characteristic polynomial matrix, and (c) (X_l, Y_l) is a polynomial matrix solution pair resulting possibly in a (stabilizing) rational compensator given by the left fraction...

Parametrization and reliable extraction of proper compensators

Ferdinand KrafferPetr Zagalak — 2002


The polynomial matrix equation X l D r + Y l N r = D k is solved for those X l and Y l that give proper transfer functions X l - 1 Y l characterizing a subclass of compensators, contained in the class whose arbitrary element can be cascaded to a plant with the given strictly proper transfer function N r D r - 1 such that wrapping the negative unity feedback round the cascade gives a system whose poles are specified by D k . The subclass is navigated and extracted through a...

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