For a given linear, shift-invariant, single-input single-output (SISO), m-D discrete system, with real constant coeficients, an input sequence is speczjied such that the system achieves deadbeat behaviour. This means that the system output reaches a steady ualue after a minimum number of steps in the space domain and remains at that value thereafter. In the present paper this steady value is chosen to be zero. No feedback control is applied and the appropriate input sequence, leading to deadbeat response, is found by pure algebraic methodology.
I. Zntmduction
In the present paper linear, shift-invariant, SISO, m-dimensional (m-D), discrete systems with real constant coefficients are examined. Although some work has been done concerning the deadbeat control of 1-D systems, there are very few results for the case of multidimensional systems. Kaczorek (1) has examined a kind of deadbeat behaviour in 2-D systems, in the sense that the output deviation from a reference input and the input vanish after a minimal 2-D space interval. Theodorou and Tzafestas (2) developed a deadbeat controller using output (for m-D systems) and state feedback (for 2-D systems), which results in a steady output, after a minimal space interval, and for an appropriate input sequence. A comparison of the above multidimensional feedback control methods may be found in (2).
The present work involves an open loop deadbeat control method for m-D systems which may be viewed as an extension of the work of Rao and Janakiraman (3) for 1-D systems. Here, the deadbeat behaviour of a given system has the following meaning : specify an input sequence, that vanishes after a minimum number of steps in the space domain, such that the system output also vanishes after a minimumbut possibly different from the previous-number of steps in the space domain. The paper is organized as follows : in Section II the minimum space interval of the unknown input sequence is specified (beyond this space interval the input is zero), in Section III an appropriate input sequence is found within the above mentioned space interval, such that the output reaches zero within a possibly different but minimum space interval and in Section IV an example illustrates the validity of the proposed method.