Adaptive control of active balancing system for a fast speed-varying Jeffcott rotor with actuator time delay

Due to actuator time delay existing in an adaptive control of the active balancing system for a fastspeed-varying Jeffcott rotor, if an unsynchronized control force (correction imbalance) is applied to the system,it may lead to degradation in control efficiency and instability of the control system. In order to avoid theseshortcomings, a simple adaptive controller was designed for a strictly positive real rotor system with actuatortime delay, then a Lyapunov-Krasovskii functional was constructed after an appropriate transform of this sys-tem model, the stability conditions of this adaptive control system with actuator time delay were derived. Afteradding a filter function, the active balancing system for the fast speed-varying Jeffcott rotor with actuator timedelay can easily be converted to a strictly positive real system, and thus it can use the above adaptive controllersatisfying the stability conditions. Finally, numerical simulations show that the adaptive controller proposedworks very well to perform the active balancing for the fast speed-varying Jeffcott rotor with actuator timedelay.