Stability Analysis Of Digital Pd Control Applied To Flexible Systems

Abstract

The work shows that the sampling in a digital PD controller of a flexible system may cause instability, while the continuous PD control system is stable. A procedure is introduced to define the stability regions analytically in the gain space. A closed form stability criterion is derived for a system consists of a single rigid mode and one flexible mode. The procedure is applied successfully also for the case of single rigid mode considering the computation time in addition to sampling period. A comparison with the literature shows that this procedure is straightforward, gives more accurate result and even corrects some stability regions published in the literature. A computer program is constructed using MATLAB to determine the stability region for a system that consists of a single rigid mode and arbitrary number of flexible modes. This simulates many practical systems such as flexible robot arms, disk-drive servos and antenna systems. The results show that the stability regions can be approximated by a right triangle in the gain space. Analytical expressions are derived to define such triangles.