Optimal control for flexible rotor with active magnetic bearing based on virtual co-location and state feedback decoupling

Abstract

To effectively suppress vibrations in an active magnetic bearing flexible rotor system, we propose an optimal control strategy based on virtual co-location and state feedback decoupling. First, we develop the mathematical model of the system using the finite element method and employ modal truncation to simplify the system order. This reduces the number of state variables and facilitates controller design. Next, a Luenberger full-dimensional state observer is employed to correlate the displacement at the sensor position with that required at the active magnetic bearing position, achieving virtual co-location of the system. Subsequently, employing the state feedback decoupling method, the active magnetic bearing flexible rotor system with complex multivariable coupling is resolved into four independent single-input, single-output subsystems. Based on this framework, the system’s stability and bearing air gap are imposed as constraints, while the overshoot, settling time, and vibration amplitude of control system are taken as the optimization objectives. An evaluation function is then constructed based on the specific importance assigned to each optimization criterion. The multidimensional visualization method is applied to optimize the controller parameters of the decoupled subsystem, identifying the optimal feasible region for the control parameters P and D. Subsequently, a system simulation model validates the control performance of the proposed strategy. The findings demonstrate that the control algorithm effectively mitigates vibrations in the active magnetic bearing flexible rotor system, exhibiting traits of robust stability, minimal overshoot, rapid adjustment, and high resilience to interference. Compared with the traditional decentralized PID control, the maximum amplitude of the active magnetic bearing flexible rotor system with the control strategy proposed in this paper can be reduced from 20 µm to 5.4 µm in the full speed range.