On improving time-delay control under certain hard nonlinearities

Time-delay control (TDC), owing to its simplicity and unusual performance against parameter variations and disturbances, has been noted and recognized as a promising technique. We have observed, however, that in the presence of so-called hard nonlinearity such as saturation or static friction, TDC reveals some problems commonly found in other methods like PID control or disturbance observer. Specifically, when the system has a saturation limit, TDC shows the windup phenomenon; when static friction and Stribeck effect are dominant, TDC reveals the stick-slip phenomenon. In this paper, we have reported these phenomena associated with TDC, presented their causes, and proposed their remedies. Specifically, through analysis, simulation, and experiment, we have shown that both the phenomena cause serious degradations in control performance; that they result from a common cause, the inherent integral effect in TDC; and that the proposed compensators are effective enough to handle the phenomena. In addition to their effectiveness, the proposed compensators have unusual simplicity and efficiency that matches the positive attributes of the original TDC.