AVC Using a Backstepping Design Technique

This chapter deals with the vibration attenuation or vibration suppression by means of feedback control techniques applied to decrease the dynamic response of a rotor assumed as active magnetic dynamic damping which is common in rotating machinery supported by active magnetic bearings. Position control systems applied on active magnetic bearings are using sometimes nonlinear robust control techniques. Backstepping control algorithms have been successfully applied to control active magnetic bearings in recent industrial applications. Consequently, when such an algorithm is being applied to control the radial shaft position, active vibration control should be performed taking advantage of the use of the same control algorithm. In the proposed methodology it is applied the Backstepping algorithm in cascade with a master conventional PID controller. The main functions of the cascade strategy are summarized as, desired radial shaft trajectory and radial position generation, rotor stabilization and vibration attenuation. Backstepping methodology provides a rather straightforward way to design the slave or cascade controller suitable for an unstable nonlinear system such as a magnetic bearing. Stabilization of the closed-loop system is achieved by incorporating appropriate Lyapunov functions which are inherent to the Backstepping algorithm. The global asymptotic stability is ensured when the derivative of the Lyapunov function is rendered negative definite by the control law. The closed loop damping or vibration attenuation is achieved according requirements by on-line determining and selecting the appropriate gains and parameters for the implemented control strategy as function of the fundamental vibration characteristics. The aim to continue with research activities on this technologic field after more then three decades of intensive work, obeys to the fact that some modern machines require the characteristics and advantages of applying such technology (Gerhard Schweitzer, Eric H. Maslen Editors, 2009). The main characteristics of AMB based machines where the rotor is supported by radial active magnetic bearings are summarized as follows: The unbalance compensation.The most relevant characteristic of an AMB deals with the active compensation of shaft disturbances, such vibration due to residual unbalance which can be effectively measured and identified by the AMB control system. The signal is used to either generate counteracting and compensating bearing forces or to shift the rotor axis in such away that the rotor is rotating force-free. The positioning precision.The radial precision with which the position of the rotor can be controlled, is mainly determined by the precision or quality of the measurement signal within the control loop. Conventional inductive sensors, (eddy current based sensors) for example, have a measurement resolution of about 1/100 to 1/1000 of a millimetre.