Stability of a force control system with sampled-data feedback

Sampled-data control, or digital control, is a major control technology in modern engineering. Based on digital computers, it provides actuators with control inputs in terms of discrete signals. A sampled-data control system is a controlled time-continuous system under sampled-data control. The paper investigates the effects of sampled-data controls on the system stability via an SDOF force control system under sampled PD (proportional-derivative) feedbacks, by means of stability analysis for discrete systems. In order to highlight the role of the sampled-data controls, the uncontrolled system is assumed to be fully free. Unlike in the previous studies where the sampled displacement signal and the sampled velocity signal are synchronic, the study focuses on the system stability for the case when the sampled displacement signal and the sampled velocity signal are not synchronic. A key observation is that when the controller uses the sampled velocity signal as well as the sampled displacement signal delayed an additional sampling period, the controlled system admits a largest stable region of the feedback gains and it decays fastest to the unique equilibrium, among the three sampled-data controllers. The paper gives a discussion of this phenomenon from the viewpoint of mechanics.