An approach for the control of systems subject to harmonic disturbances with time-varying fundamental frequency is presented. The impetus for this approach is the active control of engine-induced vibrations in automotive vehicles, where the fundamental frequency, i.e., engine firing frequency, ranges from approximately 7 Hz at idle (800 rpm) to approximately 50 Hz (6000 rpm). The disturbance, which is assumed to enter the plant at the input, is modelled as the output of an autonomous state-space model, and a state observer is used to obtain estimates of the states of this disturbance model. From these state estimates, the disturbance is reconstructed and used as a control input (with a sign reversal). The state observer is time varying since it depends on the frequency measurement, which is commonly available in modern cars as an analogue or digital engine speed signal. Based on the current fundamental disturbance frequency, an observer gain is selected from a set of pre-computed gains. This provides a non-adaptive approach, where the frequency is used as a scheduling variable. Theoretical issues of the algorithm (observer design) are discussed, and real-time results (acceleration and sound measurements) obtained with an active control system for engine-induced vibrations in a car are presented. These results show a major reduction of sound and vibration levels in the passenger compartment of the vehicle. (C) 2003 Elsevier Ltd. All rights reserved.
