An Analysis of Non-Linear Sampled-Data Feedback Control Systems

Abstract

Higher order sampled-data feedback systems which contain a saturating element or a backlash element are investigated in this paper. This study introduces a new approach to the analysis of non-linear sampled-data control systems. At first the authors describe a new analytical method for such systems using the theorem of Periodically Interrupted Electric Circuits and how to apply the Digital Computer (KDC-1) to this theorem. The method presented here can be applied to any higher order systems with any non-linear elements by making use of the digtal computer simulation of the above theorem and the non-linear element. Some illustrative examples are given to clarify the method involved. One example of the third order sampled-data feedback system with a saturating element is investigated in case of initial conditions being given without external forces, a unit step function and sine wave inputs being given. The examples show that in the case of a step input as well as initial conditions existing, slight variations of initial values result in difierent modes of periodic oscillations, while in the case of a sinusoidal input, a slight modification of non-linear characteristics results in forced oscillations in one case and in sub-harmynic oscillations in another. Two illustrative examples of the second order system with a backlash element are considered in the case where the linear system is followed by the backlash or follows the backlash. Some results obtained by numerical computations are presented to show the performance of the system dynamics on the basis of the new analytical method presented here.