Abstract
For the purpose of implementation by digital devices, a continuous-time system, which models a system in the real world. should be replaced by a discrete-time one. To have a correspondence between those two kinds of systems, a continuous-time signal must be limited within a signal space that has a freedom in a discrete sense. In digital control theory, it is commonly assumed that the input signal is a staircase one. The degree of freedom with the signal space of staircase functions is one degree per sampling interval. In this paper, we aim at the design of a family of models which includes and generalizes the conventional sampled-data, systems by employing the piecewise polynomial functions of degree (m-1) with a parameter of (m-2) times continuous differentiability. The conventional model is the special case of the proposed family of models. While the conventional model solely depended on the parameter of sampling interval to vary the accuracy of approximation, the proposed model has, in addition, the adaptability by choosing the parameter m appropriate to the input signal. This feature enables more efficient calculation in simulation as shown in a numerical example.
