Positive position and acceleration feedback control for the unbalance response in a rotor-bearing system

This work describes the problem of the unbalance response compensation in a rotor-bearing system using two control techniques based on measurements of the radial displacements or accelerations directly in a magnetorheological (MR) bearing suspension. The rotor-bearing system is modeled using finite element methods (FEM) for a Jeffcott-like rotor with one planar disk, two nonorthotropic supports, one traditional journal bearing and other similar but supported on an arrangement with two MR dampers. The mathematical model consists of two finite elements, with a total of 6 degrees of freedom for each horizontal and vertical direction. For the rotating speed regulation a PID control, is applied in order to track a proper speed profile to pass over the first critical speeds (runup or coast down). Control schemes to compensate the unbalance in the rotor are: a positive position feedback (PPF) control, which requires only the measurement of one radial displacement in the MR suspension, and another scheme based on the measurement of the radial acceleration, known as positive acceleration feedback (PAF). Both control schemes require only one sensor (proximitor or accelerometer) for each control input and they demand small control efforts. For the control design and physical implementations, we use the so-called Choi-Lee-Park polynomial model for both MR dampers, which can adequately describe the highly nonlinear and hysteresis behaviors for this type of actuators. Finally, by means of some numerical simulations are illustrated the dynamic and robust performance of the overall control system.