Effects of delay on effective band drift in nonlinear saturation control system

For active control systems, all operations in thecontrol process are not instantaneous. It implies that various delays existinevitably in the real-time control systems. In fact, time delay in controlsystem is derived from measurement of system states, caused by physicalprosperities of the equipment used for control and transport delay, byperforming on-line computation, filtering and processing data and bycalculating and executing the control forces as required. Thus, effects ofthe delays in the designed controller should be considered since they cannotbe eliminated even with the present technology. It should be noted that dueto the complexity of the nonlinear dynamical system, most scholars studiedthe effect of delay on the control performance in the linear dynamicalsystem. However, the effect of both nonlinearity and delay on dynamicalbehaviors of the system is very complex. The authors investigate theeffective band drift due to internal resonance frequency deviation existedin the nonlinear saturation control system. The effects of delays incontrol, feedback and self-feedback signals on effective band drift andbandwidth are studied. Then, the effective band drift may be controlled bychoosing appropriate delays. From the examples illustrated, in the originalsystem without considering delays, the effective band may drift to theprimary resonance point upward or downward when the internal resonancefrequency deviation exists. Moreover, the greater the absolute values ofinternal resonance frequency deviation is, the greater the effective bandwill drift. The effective band drift can lead to the performance degradationof vibration suppression about the primary resonance point. However, theeffective band drift can be eliminated by choosing appropriate delays ofcontrol, feedback and self-feedback signals according to the changes ofinternal resonance frequency deviation. Meantime, the effective bandwidth isbroadened. Both analytical and numerical results show that the greater theabsolute values of internal resonance frequency deviation is, the moreeffects of the delays on the effective band drift and bandwidth will be.