An optimal state feedback controller is then designed in order to directly formulate the performance objectives of the control system and provides the best possible control system for a given set of performance objectives. Zero steady-state error of system outputs is also given by the means of integrators which are added into the system. As a result, MIMO system’s responses achieve quick stabilization and good performances. | Trần Xuân Minh Tạp chí KHOA HỌC & CÔNG NGHỆ 122(08): 155 - 160 AN OPTIMAL STATE FEEDBACK CONTROL METHOD FOR 4 DEGREES OF FREEDOM - RIGID ROTOR ACTIVE MAGNETIC BEARING SYSTEM Tran Xuan Minh* Thai Nguyen University of Technology SUMMARY Based on mechanical – electrical – magnetic principles, the paper presents detailed analyses to build a completed mathematical model for 4 degree of freedom - rigid rotor active magnetic bearing (AMB) system. Gyroscopic effect, one of significant reasons affecting to performances of system is mentioned in this research. By using the centralized approach, a state-space model for multi-input multi-output (MIMO) active magnetic bearing system is built. An optimal state feedback controller is then designed in order to directly formulate the performance objectives of the control system and provides the best possible control system for a given set of performance objectives. Zero steady-state error of system outputs is also given by the means of integrators which are added into the system. As a result, MIMO system’s responses achieve quick stabilization and good performances. Keywords: Active Magnetic Bearing (AMB); gyroscopic; MIMO; state-space; Linear Quadratic Regulator (LQR) INTRODUCTION* Active Magnetic Bearing (AMB) comprises a set of electromagnetic mechanisms to provide bearing forces which suspend rotor shaft freely in space. These systems utilize feedback control methods to stabilize the rotating motion of them. This advanced bearing technology offers many significant advantages, compared to conventional bearings, since mechanical non-contact between rotor shaft and static parts is generated by electromagnets. With a suitable active control approach, damping and bearing stiffness characteristics of AMB can be adjusted [1, 2]. Control methods contribute an important role in designing an AMB system. In many applications, however, the performance of a controller is highly influenced by the coupled impact in motion of the system .
