Active Magnetic Bearing Spindle Research Articles

Integrated MIMO fault detection and disturbance observer-based control

This paper presents a new method of disturbance observer-based control (DOBC) for multi-input-multi-output (MIMO) highly-coupled unstable systems. In contrast to the current input–output approach for stable single-input-single-output (SISO) systems, the Youla parameterization of stabilizing controllers by full order state observer (FOSO) feedback control is shown more appropriate for general MIMO systems, while retaining the intuitive aspects of DOBC design. We propose a general MIMO DOBC expanded from this single FOSO stabilizing control, where a parallel number of FOSOs for fault detection, state estimation, and disturbance observer are integrated to achieve the relevant operational requirements and performance. Within this integrated control system, we propose a MIMO disturbance observer design method by a game-theoretic detection filter (GTDF) design. The DOBC design features GTDF disturbance decoupling followed by H-infinity model matching to establish the desired bandwidth for each channel of the decoupled disturbance observer. The proposed DOBC is applied to an open-loop unstable MIMO Active Magnetic Bearing Spindle (AMBS). Experimental results are presented to demonstrate the design method and control performance.

Inversion Based Adaptive Feedforward Control for Multivariable Systems

Abstract This paper presents a novel adaptive feedforward control (AFC) method for rejecting sinusoidal disturbances with known frequencies acting on multi-input-multi-output (MIMO) discrete time linear systems based on the H-infinity synthesis. First, the gradient AFC (GAFC) for MIMO systems is reviewed, and the linear time invariant (LTI) equivalent form of the GAFC is approximated for stability analysis. For single-input-single-output (SISO) systems, this paper shows small adaptation gains guarantee the stability of GAFC for any disturbance frequency. Then inspired by the stability of SISO GAFC, the inversion based AFC (IAFC) is proposed for MIMO systems. In this method, the GAFC is compensated by an H-infinity model matching filter, which renders nearly decoupled systems with fixed time delays. The LTI analysis, simulation study and experimental results from an open-loop unstable MIMO Active Magnetic Bearing Spindle (AMBS) are presented to demonstrate the stability and effectiveness of the proposed IAFC in rejecting narrow-band disturbances.

Multivariable Disturbance Observer Based Control with the Experiment on an Active Magnetic Bearing Spindle

This paper presents a new method of disturbance observer based control (DOBC) for multi-input-multi-output (MIMO) highly-coupled unstable systems based on the game theory and the H-infinity synthesis. First motivated by the Youla parameterization of full order state observer feedback control, a full order state observer (FOSO) based DOBC is proposed for single-input-single-output (SISO) systems. Then inspired by the FOSO based DOBC design, a disturbance decoupling method is proposed for MIMO systems using game theoretic observer design. By using error dynamics from the proposed observers, single-input-multi-output (SIMO) virtual plants are constructed. Inverses of those virtual plants for a certain bandwidth are found by solving the model matching problem using H-infinity solver. The proposed DOBC is applied to an open loop unstable MIMO Active Magnetic Bearing Spindle (AMBS). Simulation and experimental results show that the disturbances are effectively estimated and compensated.

MIMO Repetitive Control of an Active Magnetic Bearing Spindle

Abstract: We present the identification and control of an open loop unstable MIMO Active Magnetic Bearing Spindle (AMBS) for machining applications. A 20th order model is obtained from reducing a higher order model identified by the ARX method. For verification purposes, the model is compared to the system’s frequency responses obtained by the frequency sweep method. The model is used to design a linear quadratic optimal controller, where the weighting gains are tuned by simulation and experiment. A plug-in repetitive controller for asymptotic regulation and tracking of signals synchronous to the spindle rotation is designed by formulating the control design as a model matching filter design problem. The model matching’s optimal solutions for the non-minimum phase MIMO stabilized system are obtained respectively for H ∞ and H 2 norm minimizations. Simulation and experimental results are presented to compare the proposed MIMO repetitive control design methods and demonstrate the control performance.

Magnetic Bearing Spindle Tool Tracking Through <inline-formula><tex-math>${\mu}$</tex-math> </inline-formula>-Synthesis Robust Control

A method is presented for tooltip tracking in active magnetic bearing (AMB) spindle applications. The proposed tool tracking approach uses control of the AMB air gap to achieve the desired tool position. A μ-synthesis-based controller is designed for the AMBs with the goal of robustly minimizing the difference between the tool reference and estimated tool position. In such a way, the model-based control approach concurrently addresses the tracking problem and the inability to directly measure real-time tool position in the presence of machining disturbances. To ensure the tractability of the control problem, a model of the desired tracking dynamics is included in the plant. The method is demonstrated on a high-speed AMB boring spindle. To confirm the tool tracking capability, characteristic part geometries are traced including stepped, tapered, and convex profiles. Tool tracking is demonstrated for the rotating AMB spindle in the range of 90 μm. Also, static and dynamic external loading is applied to the spindle tool location to confirm the disturbance rejection ability of the closed-loop system.

Performance Enhancement for AMB Systems Using Unstable $H_{\infty}$ Controllers

Controllers synthesized using H∞ methods provide good disturbance attenuation for active magnetic bearing spindles. The synthesized controllers are often unstable when the spindle exhibits flexible dynamics. In this paper, we design and implement controllers using different models for an experimental active magnetic bearing (AMB) system. For an AMB model that contains flexible dynamics, the synthesized H∞ controllers promise higher performance but are found to be unstable. To implement an unstable controller, we use a Youla parametrization-based method and seamlessly switch from a stable to an unstable controller. The improved benefits of the unstable controllers for disturbance attenuation are demonstrated using experimental measurements.

Chatter milling modeling of active magnetic bearing spindle in high-speed domain

A new dynamical modeling of Active Magnetic Bearing Spindle (AMBS) to identify machining stability of High Speed Milling (HSM) is presented. This original modeling includes all the minimum required parameters for stability analysis of AMBS machining. The stability diagram generated with this new model is compared to classical stability lobes theory. Thus, behavior's specificities are highlighted, especially the major importance of forced vibrations for AMBS. Then a sensitivity study shows impacts of several parameters of the controller. For example, gain adjustment shows improvements on stability. Side milling ramp test is used to quickly evaluate the stability. Finally, the simulation results are then validated by HSM cutting tests on a 5 axis machining center with AMBS.

System modeling and robust control of an AMB spindle : part II a robust controller design and its implementation

This paper discusses an entire procedure for a robust controller design and its implementation of an AMB (active magnetic bearing) spindle, which is part II of the papers presenting details of system modeling and robust control of an AMB spindle. Since there are various uncertainties in an AMB system and reliability is the most important factor for applications, robust control naturally gains attentions in this field. However, tight evaluations of various uncertainties based on experimental data and appropriate performance weightings for an AMB spindle are still ongoing research topics. In addition, there are few publications on experimental justification of a designed robust controller. In this paper, uncertainties for the AMB spindle are classified and described based on the measurement and identification results of part I, and an appropriate performance weighting scheme for the AMB spindle is developed. Then, a robust control is designed through the mixedμ synthesis based on the validated accurate nominal model of part I, and the robust controller is reduced considering its closed loop performance. The reduced robust controller is implemented and confirmed with measurements of closed-loop responses. The AMB spindle is operated up to 57,600 rpm and performance of the designed controller is compared with a benchmark PID controller through experiments. Experiments show that the robust controller offers higher stiffness and more efficient control of rigid modes than the benchmark PID controller.

System modeling and robust control of an AMB spindle: part I modeling and validation for robust control

This paper discusses details of modeling and robust control of an AMB (active magnetic bearing) spindle, and part I presents a modeling and validation process of the AMB spindle. There are many components in AMB spindle : electromagnetic actuator, sensor, rotor, power amplifier and digital controller. If each component is carefully modeled and evaluated, the components have tight structured uncertainty bounds and achievable performance of the system increases. However, since some unknown dynamics may exist and the augmented plant could show some discrepancy with the real plant, the validation of the augmented plant is needed through measuring overall frequency responses of the actual plant. In addition, it is necessary to combine several components and identify them with a reduced order model. First, all components of the AMB spindle are carefully modeled and identified based on experimental data, which also render valuable information in quantifying structured uncertainties. Since sensors, power amplifiers and discretization dynamics can be considered as time delay components, such dynamics are combined and identified with a reduced order. Then, frequency responses of the open-loop plant are measured through closed-loop experiments to validate the augmented plant. The whole modeling process gives an accurate nominal model of a low order for the robust control design.

New design of cylindrical capacitive sensor for on-line precision control of AMB spindle

A new cylindrical capacitive sensor (CCS) design for the displacement measurement of precision active magnetic bearing (AMB) spindle is presented in this paper. This research is motivated by the problem that the existing 4-segment CCS is still sensitive to the third harmonic component of the geometric errors of a rotor. The procedure of designing a new CCS starts from the modeling and error analysis of CCS. The angular size of CCS is set up as a design parameter, and a new configuration, i.e., 8-segment CCS, is introduced to possess an arbitrary angular size. The optimum sensor geometry to minimize the effects of geometric errors is determined through the minimum norm approach. Experimental results with test rotors have confirmed the improvement in geometric error suppression.