Robust Attenuation of Frequency Varying Disturbances

Abstract

Systems described by differential equations with time-periodic coefficients have a long history in mathematical physics. Applications cover a wide area of systems ranging from helicopter blades, rotor-bearing systems, mechanics of structures, stability of structures influenced by periodic loads, applications in robotics and micro-electromechanical systems etc. (Rao, 2000; Sinha, 2005). Processes characterized by linear time-invariant or time-varying dynamics corrupted by sinusoidal output disturbance belong to this class of systems. Robust and adaptive analysis and synthesis techniques can be used to design suitable controllers, which fulfill the desired disturbance attenuation and other performance characteristics of the closed-loop system. Despite of the fact that LTP (Linear Time Periodic) system theory has been under research for years (Deskmuhk & Sinha, 2004; Montagnier et al., 2004) the analysis on LTPs with experimental data has been seriously considered only recently (Allen, 2007). The importance of new innovative ideas and products is of utmost importance in modern industrial society. In order to design more accurate and more economical products the importance of model-based control, involving increasingly accurate identification schemes and more effective control methods, have become fully recognized in industrial applications. An example of the processes related to the topic is vibration control in electrical machines, in which several research groups are currently working. Active vibration control has many applications in various industrial areas, and the need to generate effective but relatively cheap solutions is enormous. The example of electrical machines considered concerns the dampening of rotor vibrations in the so-called critical speed declared by the first flexural rotor bending resonance. In addition, the electromagnetic fields in the air-gap between rotor and stator may couple with the mechanic vibration modes, leading to rotordynamic instability. The vibration caused by this resonance is so considerable that large motors often have to be driven below the critical speed. Smaller motors can be driven also in super-critical speeds, but they have to be accelerated fast over the critical speed. Active vibration control would make it possible to use the motor in its whole operation range freely, according to specified needs given by the load process. Introducing characteristics of this kind for the electric drives of the future would be a major technological break-through, a good example of an innovative technological development. 13