0
Research Papers

# Design of Active Magnetic Bearing Controllers for Rotors Subjected to Gas Seal Forces

[+] Author and Article Information
Jonas S. Lauridsen

Department of Mechanical Engineering,
Technical University of Denmark,
Kongens Lyngby 2800, Denmark
e-mail: jonlau@mek.dtu.dk

Ilmar F. Santos

Professor
Mem. ASME
Department of Mechanical Engineering,
Technical University of Denmark,
Kongens Lyngby 2800, Denmark
e-mail: ifs@mek.dtu.dk

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received May 16, 2017; final manuscript received February 28, 2018; published online April 30, 2018. Assoc. Editor: Mazen Farhood.

J. Dyn. Sys., Meas., Control 140(9), 091015 (Apr 30, 2018) (14 pages) Paper No: DS-17-1254; doi: 10.1115/1.4039665 History: Received May 16, 2017; Revised February 28, 2018

## Abstract

Proper design of feedback controllers is crucial for ensuring high performance of active magnetic bearing (AMB) supported rotor dynamic systems. Annular seals in those systems can contribute significant forces, which, in many cases, are hard to model in advance due to complex geometries of the seal and multiphase fluids. Hence, it can be challenging to design AMB controllers that will guarantee robust performance for these kinds of systems. This paper demonstrates the design, simulation, and experimental results of model-based controllers for AMB systems, subjected to dynamic seal forces. The controllers are found using $H∞$ and μ synthesis and are based on a global rotor dynamic model in which the seal coefficients are identified in situ. The controllers are implemented in a rotor-dynamic test facility with two radial AMBs and one annular seal with an adjustable inlet pressure. The seal is a smooth annular type, with large clearance (worn seal) and with high preswirl, which generates significant cross-coupled forces. The $H∞$ controller is designed to compensate for the seal forces and the μ controller is furthermore designed to be robust against a range of pressures across the seal. In this study, the rotor is nonrotating. Experimental and simulation results show that significant performance can be achieved using the model-based controllers compared to a reference decentralized proportional-integral-derivative (PID) controller and robustness against large variations of pressure across the seal can be improved by the use of robust synthesized controllers.

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## Figures

Fig. 3

Overview of the forces acting on the rotor and sensor positions. The dots mark the input/output locations. The lines show the finite elements (FEs) of the shaft model.

Fig. 2

Cross section of the seal house at the inlet cavity section: ①—inlet injection nozzle, ②—inlet cavity, and ③—shaft. Adapted from Ref. [31].

Fig. 1

Test facility overview: ①—motor, ②—encoder, ③—belt drive, ④—intermediate shaft pedestal, ⑤—flexible coupling, ⑥—AMB A, ⑦—seal housing, and ⑧—AMB B

Fig. 8

Interconnection of actuator model Gact, rotordynamic model with uncertainty representation Gfi, performance weight functions WP and Wu, and controller K

Fig. 9

Interconnection rearranged to the augmented system P, externally connected to the controller and Δ̂ containing Δ for uncertain plant representation and ΔP as full complex perturbation for performance specification

Fig. 4

Updated/changed plant representation using upper LFT, Gupdated=Fu(Gfi,Δ)

Fig. 5

Comparison of experimental (solid lines) and global model (dashed) impulse response using 0.95 bar inlet pressure. The global model includes the seal coefficients identified for the given pressure. Current impulse disturbance from 0.05 s to 0.06 s is scaled in amplitude and shown as the dashed line.

Fig. 6

Comparison of experimental (solid lines) and global model (dashed) impulse response using 1.90 bar inlet pressure. The global model includes the seal coefficients identified for the given pressure. Current disturbance from 0.05 s to 0.06 s is scaled in amplitude and shown as the dashed line.

Fig. 7

Seal coefficients as a function of the pressure drop across the seal inlet marked with “x.” The solid lines show linear regression lines, estimated for each coefficient. The nominal pressure, used for the design of the model based controllers, is shown as the dashed line.

Fig. 11

The maximum amplitude of the compliance function using the three controllers. The solid lines indicate the performance of the controllers at nominal pressure. The lines marked with “- - ” indicate high pressure, i.e., +100% of pressure compared to the nominal pressure and the lines marked with “-.” indicate low pressure, i.e., −100% of pressure compared to the nominal pressure. The PID controller with high pressure is not shown since this makes the system unstable.

Fig. 10

Comparison of the direct and cross coupled gain ofthe controllers. Indices [14] represent node points [Aζ, Aη, Bζ, Bη]

Fig. 12

The maximum singular value of the unbalance function for the three controllers. The solid lines indicate the performance of the controllers at nominal pressure. The lines marked with “- -” indicate high pressure, i.e., +100% of pressure compared to the nominal pressure and the lines marked with “-.” indicate low pressure, i.e., −100% of pressure compared to the nominal pressure. The PID controller with high pressure is not shown since this makes the system unstable.

Fig. 13

Closed-loop output sensitivity of perturbed plant using PID, H∞, and μ controllers

Fig. 14

Impulse response of perturbed plant (a) using PID controller, (b) using H∞ controller, and (c) using μ controller. (d), (e), and (f) show the control action in response to the impulse disturbance.

Fig. 15

Impulse response of plant in the Aζ and Bη direction: (a) and (d) using PID controller; (b) and (e) using H∞ controller; and (c) and (d) using μ controller. ((a)–(c)) show the response when no pressure is applied. ((d)–(f)) show the response when 2.04 bar pressure is applied. Simulated responses are shown as solid lines and experimental responses are marked with “- -”. Current impulsive setpoint disturbance from 0.05 s to 0.06 s is scaled in amplitude and shown as the dashed line “Dis.”

Fig. 16

Impulse response of plant in Aζ and Bζ direction: (a) and (d) using PID controller; (b) and (e) using H∞ controller; and (c) and (d) using μ controller. ((a)–(c)) show the response when no pressure is applied. ((d)–(f)) show the response when 2.04 bar pressure is applied. Simulated responses are shown as solid lines and experimental responses are marked with “- -”. Current impulsive setpoint disturbance from 0.05 s to 0.06 s is scaled in amplitude and shown as the dashed line “Dis.”

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