Riccati difference equation in optimal control for magnetic bearings

A model predictive optimal control method for magnetically suspended flywheel is presented. In order to suppress the conical whirl of the rotor caused by gyroscopic effect, the synchronization error is added to the traditional quadratic performance index. The target performance index is composed of the translatory error, the synchronization error, and the control output predicted by the discrete-time state model. The optimal controller is obtained by means of iterating a Riccati difference equation (RDE). Stability of the control scheme is investigated through fake algebraic Riccati technique (FART). The robust performance of the controller with respect to control parameters is studied by simulation. Results of the simulation and experiment on a compact magnetically suspended flywheel demonstrate that the proposed controller with consideration of the synchronization error is very effective to suppress the conical whirl caused by gyroscopic effect.

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