Một phương pháp điều khiển tối ưu phản hồi trạng thái cho hệ thống ổ đỡ từ chủ động 4 bậc tự do rotor cứng = an optimal state feedback control method for 4 degrees of freedom- rigid rotor active magnetic bearing system

Trần Xuân Minh Tạp chí KHOA HỌC & CÔNG NGHỆ 122(08): 155 - 160

155

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 which should not be neglected.

Many different control methods have been

applied successfully for AMB, with or

without the mention of the gyroscopic effect

[4-9]. These include conventional

decentralized approaches such as PD, PID…

and nonlinear control methods such as

* Tel: 0913 354975

feedback linearization, backstepping… [4, 5],

[7], [9]. A new trend for modern control

methods is also attracted many interests.

These centralized methods consisting of Pole￾placement, LQR, LQG, H∞, μ-synthesis… [6,

7], [9] increase quickly due to the rapid

development of the sensor technology and

digital signal processing recently. As a result,

measurement and computation tasks of

various physical signals can be implemented

easily for the purpose of feedback control.

In this research work, a fully mathematical

model of 4-DOF AMB is described, in which

the gyroscopic effect is also included in the

system dynamics. A modern centralized

control method is designed for a MIMO radial

suspension system. By using this approach,

the optimal controller is then proposed in

order to yield high performance for the

system in terms of control energy and control

error. Obtained results show that an

improvement in dynamic performance of the

system can be achieved.

This paper is structured in four parts. Part 2

dedicates to modeling of the system in terms

of dynamics and electromagnetic issues. The

control design is described in part 3. Part 4 is

the computation and simulation results.