A Study of Active Rotor-Blade Vibration Control using Electro-Magnetic Actuation - Part I: Theory

This is the first paper in a two-part study on active rotor-blade vibration control. Blade faults are a major problem in bladed machines, such as turbines and compressors. Moreover, increasing demands for higher efficiency, lower weight and higher speed imply that blades become even more susceptible to vibrational problems. Passive damping methods, such as frictional damping, are typically used for this kind of machines, working very well at the specific design conditions. However, when the running conditions exceed the design specification, then passive damping devices become inefficient. Active control then might become a feasible technique to suppress vibrations, to improve performance and to prolong machinery lifetime. Over the years, extensive research has been undertaken on the subject active control of rotor-blade vibrations. Most of the work concerns blade vibration control using actuators fixed directly in the blades. However, due to the impracticability and problems by fixing actuators in the rotating blades, it is for practical application of great interest to study whether the vibrations can be controlled using shaft-based actuators, i.e. electro-magnetic bearings. In this framework, the present paper gives a theoretical contribution into the controllability and observability analysis of rotor-blade systems with the aim of investigating this field. The analysis is based on time-variant modal analysis, due to the time-periodic dynamical characteristics of this kind of system. Moreover, it gives a contribution into the design of active time-periodic modal controllers, capable to cope with the system time-periodicity. Special emphasis is given to the study of rotor and blade vibration control using only shaft-based actuation. A periodic time-variant mathematical model for the rotor-blade system is derived. The model is transformed into a modal form by calculation of time-varying modal matrices using Hill¿s method of infinite determinants. The modal model is used to analyse the controllability and observability by two methods; (I) a visual observation of the time-varying mode shapes; (II) calculation of quantitative measures of modal controllability and observability. The results obtained show that the all vibration modes can only be controlled using shaft-based actuation if the system is deliberately mistuned, while actuators have to be placed acting onto both the blades and onto the shaft if the system has identical tuned blades. Time-periodic modal state feedback controllers are designed based on the modal model and numerical simulations are provided to show the efficiency of the designed active controllers for a tuned as well as a mistuned rotor-blade system.