Nonlinear Sampled-Data Systems with a Generalized Hold Polynomial-Function for Fast Sampling Rates

Abstract

It is well-known that such non-conventional digital control schemes, such as generalized sampled-data hold functions, have clear advantages over the conventional single-rate digital control systems. However, they have theoretical negative aspects that deviation of the input can lead to intersample oscillations or intersample ripples. This paper investigates the zero dynamics of sampled-data models, as the sampling period tends to zero, composed of a new generalized hold polynomial function, a nonlinear continuous-time plant and a sampler in cascade. For a new design of generalized hold circuit, the authors give the approximate expression of the resulting sampled-data systems as power series with respect to a sampling period up to the some order term on the basis of the normal form representation for the nonlinear continuous-time systems, and remarkable improvements in the stability properties of discrete system zero dynamics may be achieved by using proper adjustment. Of particular interest are the stability conditions of sampling zero dynamics in the case of a new hold proposed. Also, an insightful interpretation of the obtained sampled-data models can be made in terms of minimal intersample ripple by design, where the ordinary multirate sampled systems have a poor intersample behavior. It has shown that the intersample behavior arising from the multirate input polynomial function can be localised by appropriately selecting the design parameters based on the stability condition of the sampling zero dynamics. The results presented here generalize the well-known notion of sampling zero dynamics from the linear case to nonlinear systems.