Robust LPV control of a magnetic bearing suspension system with a convex optimization approach

High-speed rotor systems supported on active magnetic bearings have significant potential in various industrial applications. Because these systems are inherently unstable and the imbalance force and gyroscopic effects are dependent upon the rotor speed, control design for such systems is known to be a challenge. Based on the model of a flywheel energy storage device, we propose several control strategies for such systems.; When the rotor operates below the flexible modes, we formulate it as a rigid rotor model. An explicit H-infinity controller is constructed. The controller is in an explicit form of the rotor speed and can be tuned on line to achieve different closed loop performances. We next consider the case when the rotor is flexible. A controller with robust performance with regard to the uncertainty of natural frequencies, substructure modes and system parameters is of critical importance. The linear parameter varying (LPV) system model motivates the need for a controller that is scheduled on the varying parameter (rotor speed). To address the robust control problem in the LPV framework, a so-called robust LPV controller is proposed. We formulate it as a convex optimization problem. One approach is to formulate a single Lyapunov function for all the convex vertices. The performance is guaranteed and the controller is robustly stable for any trajectory and rate of the parameter variation. By introducing an extra variable in the LMI conditions, we propose a new synthesis method to reduce conservatism. A parameter dependent Lyapunov function is formulated so that different Lyapunov functions serve for different vertices of the convex set to attain better performance. We extend the synthesis method to multi-objective control and address the pole placement and damping constraint problem for our flexible structure control.; The LPV controller implementation is a challenge because the controller dynamics needs to be updated along with the varying parameter. To fully exploit the hardware and software capacity, several issues are addressed and off line discretization method is proposed. The simulation and implementation results demonstrate the robust performance of our design. Our robust LPV controller achieves better performance than the traditional Mu-synthesis design. The rotor vibrations in critical speed are significantly reduced.