Adaptive Control Of Active Balancing For Speed-Varying Rotor Systems

The harmful effects of unbalanced vibration in the modern high-speed rotating machineries have caused significant drop of productivity efficiency, precision reduction of products machined, even the whole machine damage. Realization of new technology, such as, high-speed and high-precision machining is restricted due to rotor imbalances. Standard off-line rotor balancing techniques can not solve time-varying rotor unbalance problems due to the transient nature of imbalances existed in rotating machinery operation. But, active balancing technology for rotor systems can solve these complicated problems and bring us significant economic benefits through combining other new and advanced technologies and increasing reliability for machinery operation.The rotor active balancing control methods obtained in the past, however, are limited to use for machines with constant rotating speed. Existed adaptive control methods can not be able to deal with speed-varying rotor balancing which often appears in modern industry. The adaptive control methods for speed-varying rotor active balancing systems studied in this dissertation are effectively applicable not only to general speed-varying rotors, but also to the speed-varying rotors with actuator time delay and the ones with actuator saturation. The adaptive controls for speed-varying rotor active balancing systems are systematically and thoroughly studied in this thesis. The contents of this dissertation are involved in studies on quasi steady-state condition of a slow speed-varying rotor system, gain-scheduling control of a quasi steady-state rotor active balancing system, adaptive control of active balancing for a fast speed-varying rotor with actuator time delay and adaptive control of active balancing for a fast speed-varying rotor with actuator saturation. The rotors to be studied include a Jeffcott rotor, a Jeffcott rotor with anisotropic bearings, a flexible rotor with single collocated balancing plane (actuator plane and measuring plane are almost the same one) and a flexible rotor with multiple collocated balancing planes.The differences and their transferring condition between a rotor dynamic model with constant speed and the one with speed-varying are investigated in the first part of this dissertation. With a speed-varying Jeffcott rotor as a fundamental model, on one hand, its transient unbalanced response is analytically solved; on the other hand, discretizing its varying rotating speed, a series of its general responses solved in each time step with a harmonic excitation whose constant frequency is one of those discretized finite rotating speeds are used to indicate approximately its transient responses. An appropriate qualitative condition so called quasi steady-state condition is found so that the latter can approximately replace the former.Gain-scheduling control for a quasi steady-state rotor active balancing system is studied in the second part of this dissertation. Under the premise of a rotor system satisfying the quasi steady-state condition, the influencing coefficient method based on the steady-state rotor balancing is extended to single-plane or multiple-plane gain-scheduling control of a rotor with slowly varying speed and all factors affecting the stability of a gain-scheduling control are analyzed. Numerical simulations verify that the gain scheduling control can effectively suppress imbalance-induced vibration of a rotor with slowly varying speed.Adaptive control techniques of active balancing for a rotor system with fast varying speed and actuator time delay are proposed and investigated in the third part of this dissertation. Firstly, without a prior knowledge of the rotor dynamics, a simple direct adaptive controller is designed for a strictly positive and real rotor system with actuator time delay, a Lyapunov-Krasovskii functional is constructed after an appropriate transformation of the original system model, the stability conditions for the adaptive control system with actuator time delay are derived. Secondly, adding a filter function, the active balancing system for a fast speed-varying Jeffcott rotor with actuator time delay can easily be converted to a strictly positive and real system, and thus it can use the derived adaptive controller satisfying the stability conditions. Numerical simulations show the proposed adaptive controller can effectively suppress the original imbalance-induced vibration of the fast speed-varying Jeffcott rotor with actuator time delay. Then, the adaptive control of active balancing for a speed-varying Jeffcott rotor with anisotropic bearings and actuator time delay is also investigated, and the efforts give emphasis to the effect of bearing anisotropy on actuator time delay. Finally, the adaptive control strategy of active balancing for a strictly positive and real rotor with actuator time delay is successfully extended to a flexible rotor with single collocated plane and a flexible rotor with multiple collocated planes. A series of numerical simulations demonstrate that the proposed controller is valid to suppress the imbalance-induced vibration of these rotor systems.In the fourth part of this dissertation, the adaptive control strategies which can notably reduce imbalance-induced vibration of rotor active balancing systems are proposed under a complicated situation including no prior knowledge of rotor dynamics, rotor with fast varying speed and actuator saturation. At first, a Lyapunov functional is constructed for a strictly positive and real rotor system with actuator saturation, its adaptive controller and the corresponding stability conditions are deduced. Then, a fast speed-varying Jeffcott rotor active balancing system with actuator saturation is considered as a research objective, its transfer function can become strictly positive and real by introducing a filter function so that the adaptive control law and the stability conditions derived above can be applicable to the Jeffcott rotor. Numerical simulations verify that the adaptive control strategy can perfectly suppress the original imbalance-induced vibration of the Jeffcott rotor with actuator saturation. Furthermore, the adaptive control of active balancing for a fast speed-varying Jeffcott rotor with anisotropic bearings and actuator saturation is studied, and the efforts emphasize how bearing anisotropy affects the adaptive control law. Finally, the adaptive control strategy of active balancing for a strictly positive and real rotor with actuator saturation is successfully extended to a flexible rotor with single collocated plane and actuator saturation and a flexible rotor with multiple collocated planes and actuator saturation. A series of numerical simulations show that the proposed adaptive control law can evidently reduce the original imbalance-induced vibration of these rotors and the actuator movement asymptotically approaches to its target value, the opposite of the original imbalance.A series of studying results of this dissertation possess important theoretical meanings and applicable value in engineering for the further front study on the transient dynamics of speed-varying rotors and their adaptive control techniques of active balancing.