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The paper reports on the implementation and the design of a controller for a fuel cell blower (FCB) with active magnetic bearings (AMBs). The cascaded position-flux-centralized controller is comprised of a centralized position control loop and an inner flux control loop. The last one is based on state estimation without explicit flux measurements. As the position control is not dependent on the magnetic field nonlinearities, such a control structure enables operation under a zero bias. The practical working implementation of a flux control for the industrial levitated rotor is shown for the first time. The flux control gives better results than current control for both normal and zero bias operation. The system is analyzed fully, combining rotor dynamics and power amplifier analyses simultaneously. The importance of using the coil voltage in addition to current and practical treatment of the flux control is revealed. The centralized position-flux controller is compared with a state-of-the-art cascaded position-current control, which has inner current control loops. The proposed control solution with a zero bias can achieve a dynamic performance comparable that of a controller with the classical bias current.

Fuel cell technology provides a clean energy source with high power density. To get a sufficient efficiency, losses in all components of the system should be minimized. Besides efficiency criteria, the technology poses challenges to blower machines that should operate with a high rotational speed to provide sufficient flow and, at the same time, endure high temperatures. In such conditions, traditional bearings cannot withstand high-speed operation without regular maintenance; further, lubrication is not acceptable for an oil-free system.

Active magnetic bearing (AMB) rotor systems are employed in high-speed applications in which other bearing alternatives are not feasible. AMBs, when used to support a high-speed rotor, constitute a coupled multiple-input multiple-output (MIMO), nonlinear, unstable plant with speed-dependent dynamics and disturbances [

A typical method to control AMB-rotor systems is to linearize a nonlinear plant around an operating point and applying a linear controller. However, when employing cost-efficient solutions, for example, no-bias operation and small-size actuators, the resulting unstable control plant becomes strongly nonlinear. The linear control design applied to a highly nonlinear system works only in a small neighborhood of the operating point. This limits the position control bandwidth and decreases the operating range with respect to control variables.

The classical AMB control system stabilizes the rotating shaft in five degrees of freedom (5 DOF) using a combination of radial and axial magnetic bearings. For the typical actuator configuration for each DOF, two opposite electromagnets generate attractive forces to the rotor.

Most AMB controllers use a cascaded structure with position and current feedback. In some cases, bearings are used themselves to get the position feedback [

For improved energy efficiencies, the current control with a reduced bias has been applied. To compensate for the resulting force nonlinearities, such methods, as, for example, inverse-nonlinearity-based compensation [

This paper presents a flux-controlled zero-biased AMB control system that does not require flux measurements. The proposed cascaded controller is comprised of an optimal centralized outer 4 DOF radial position controller and inner observer-based flux controllers with optimal flux observers. The experimental results, with operation under the zero-bias with flux observer gain scheduling, are shown. In that case, resistive losses of the bearing are significantly reduced compared with the traditional system with the bias current.

Most of the works that are related to AMB systems with flux control demonstrate the mathematical treatment of the problem. These results are supported by numerical examples and simulations, as in [

The practical working implementation of the radial suspension using the flux control (without flux measurement and with centralized outer control) for an industrial levitated rotor is shown for the first time. The flux control gives better results than the current control for both normal and zero bias operation. This approach helps to deal with nonlinearities enabling the use of zero bias or variable bias without the necessity of control adaptation (e.g., as required for stability in [

The most commonly used AMB rotor system comprises two eight-pole radial actuators, a motor, and a separate thrust AMB. For modeling and control synthesis, we consider the radial suspension that is decoupled from the axial AMB forces.

The case study AMB rotor system has a horizontal rotor (_{x}_{,PM} = 21 N/mm; rotor mass _{0} = 0.58 mm; clearance to the safety bearings from the geometric center 0.25 mm; average nominal inductance of the radial AMBs at the nominal air gap _{0} = 2.5 A; and the maximum current _{max} = 6 A. The AMB control system is implemented on a dSPACE DS1005-09 platform using a CMSS 65 Eddy Current Probe System compriseing three single-channel sensors installed on each of two measuring planes at the ends of the rotor. The AMB coils are driven by servo amplifiers in a half-bridge configuration. The amplifiers operate with a supply DC link voltage _{dc} = 60 V, which is the maximum voltage applied to the coils, and a switching frequency of 40 kHz. The sampling time is _{s} = 100 μs.

The rotor (

The matrices of the mechanical system description, ^{m}^{m}^{m}^{m}^{m}^{m}

In order to include the bearing stiffness matrices, _{i}_{x}_{f}_{s}_{b}

The analytical approximation of the magnetic force of a single electromagnet, _{1}, and of a pair of opposite electromagnets, _{1}, _{2}, and the rotor displacement, _{air}, _{0} and

The nominal values of the dynamic inductance, _{dyn}, and the velocity-induced voltage coefficient, _{u}

In a typical state-of-the-art inner current-voltage controller with a bias linearization and a differential driving mode, the reference voltage command provided to the driver is _{r}_{c}_{r}_{m}_{r}_{0} ± _{c} (_{cl},_{i}_{m} is the measured current. The loop bandwidth is approximately equal to the current feedback gain, _{c}, divided by the nominal inductance, _{bw} = ln(9)/_{rise}. Assuming the rise time from 10% to 90% of the steady-state maximum current value, _{max}, the _{c}

The system will be working without magnetic saturation if the maximum current value:

The case study system has been designed assuming a relatively safe value for the saturation flux density, _{sat} = 0.8

As an alternative to the current control in the inner loop, the flux control can be applied. However, instead of using the flux measurement [

The magnetic force of a single electromagnet and of a pair of oeppaosite electromagnets can be expressed by using the flux, Φ, instead of the current and air gap, as:

The magnetic force computation is now not dependent on the rotor position, as in _{r}, to the inner flux controllers (_{0}, and the control force signal, _{c}, such as _{r} = _{0} ± _{c}. The reference force can be changed to the reference flux:

The proportional current feedback is replaced with the flux feedback control _{r}_{Φ}(Φ_{r} − Φ_{m}), where the measured flux, Φ_{m}, can be replaced by the estimated value, Φ_{es}. The feedback gain, _{Φ}, replaces the current feedback gain, _{c}. Neglecting the coil resistance and assuming no saturation and no PWM or measurement delays, the closed inner-loop flux control dynamics, G_{cl,Φ}, can be approximated in the s-domain by:

Analogically to the current control, we obtain the maximum bandwidth of the inner flux control (approximated as a first-order system) with respect to the flux rise time from 10% to 90% of the maximum flux value when using the maximum voltage, _{dc}:

For this comparison, the inner-loop controller bandwidth is selected to have the same bandwidth as the current-controlled method ω_{bw} = 880 Hz.

When not measured, the fluxes can be calculated by integrating the applied voltages, _{1} and _{2}, are replaced by the corresponding reference values. The estimated flux, Φ_{es}, and current, _{es}, are computed by using the estimator:
_{Fe}(_{es}) is implemented as a look-up table-based magnetic saturation model for the iron of the electromagnets. The estimated flux density
_{Fe} are the flux paths in the air and in the iron of the AMBs; _{Fe} = 108 mm. In this work, the observer feedback gain, _{ob}, is computed when using the linearized model (15) and placing the closed-loop pole, so that its natural frequency and damping ratio are 1760 Hz and one, respectively. The current feedback in the flux estimator corrects the integration of the applied voltages. The described flux observer works well in the case of laminated radial AMBs. For the cases where high eddy currents and stray fluxes are expected, it is possible to include these effects in the observer when considering the axial bearing [

For the classical AMB controller, the force (2) is linearized about the operating point _{c}

The current stiffness, _{i}_{x}_{i}_{x}

For the selected operational point, the radial current stiffness _{i}_{x}

The open-loop transfer function of the complete plant in the Laplace domain using the state variable form can be written as

In general, controllers that apply the actuator model based on currents show degraded performance when moving away from the operating point (and improved performance in the operating point). For current-controlled bearings, the plant, as seen by the outer control loop, includes a destabilizing negative stiffness that couples the rotor position and the electromagnetic dynamics of the actuator.

The linearity of magnetic force increases for high bias currents. However, the high bias results in increased losses, a high bearing stiffness, and increased noise in position measurements, because of the high stiffness and current signal levels. To compensate for the influence of the rotor position and the bearing current on the inner-loop controllers and to keep their dynamics more linear, a variable feedback gain, _{c}

For the flux-controlled AMB, the outer position controller is synthesized based on the plant model without the actuator dynamics (1) and without the bearing stiffness matrices, but with the PM stiffness. As presented in

The air gap in the actuator location of the electromagnet,

Using

For zero magnetization or bias fluxes, the force slew rate is zero, and it grows with the growing bias. In practical machines, there are always some load forces, and even for the assumed zero-bias operation, the force slew rate is positive. In the studied machine, which is oriented horizontally, there is a gravity force load to overcome by four out of eight radial electromagnets. Therefore, in the zero-bias operation:
_{0} = 2.5 A) and the zero-biased pair of opposite AMBs when applying maximum voltage commands. The force vector changes direction to overcome gravity at the maximum design current. It is seen that for the zero-bias case, the force changes very slowly when the force vector is close to zero. When the force values approach the maximum force value, the force slew rate is the same for both cases. According to the nonlinear simulation illustrated in

For testing the flux-based zero-bias control, a Linear-quadratic-Gaussian (LQG) outer position controller is synthesized [

The discussed current- and flux-controlled AMB operation is demonstrated experimentally. The experiment set-up and devices used for the measurements are explained in [_{0} = 2.5 A, while the flux control operates with zero bias. The initial lift-up is presented in

The measured output sensitivity function accesses the AMB system stability [

The experimental results show that the use of the linear centralized position control in the outer control loop of the flux-controlled AMB rotor system is feasible by using flux observers in the inner control loops instead of flux measurements without explicit identification of the plant's parameters. The tested cascaded control with the flux-controlled AMB not only shows better robustness to modeling errors and higher bandwidth compared with the current-controlled system, but also without changing the outer controller, it enables operation at a zero bias and within magnetic saturation. Because of the zero bias, the static losses are reduced.

The linear outer-loop controller has a reduced number of states as a result of omitting the states corresponding to the inner control dynamics when compared with the classical current-controlled AMB controller. However, the implementation of the inner loop flux observers is considerably more complex than the basic feedback in the current-controlled AMBs.

The flux-controlled AMBs show less oscillations and a smaller overshoot during step response and the initial lift-up, as well as lower sensitivity peaks. The experimental step responses and the measured sensitivity peaks differ from the simulations and analytical results. The experimental responses could be improved when using a plant model with the identified parameters and not the design parameters for the synthesis of controllers. Future studies will focus on the development of the adaptive inner and outer controllers for variable bias operation, as well as system identification.

Rotor model with locations of radial sensor planes (dashed line with arrows), radial actuator planes (solid line with arrows) and motor (solid line with two arrows) in the active magnetic bearing (AMB) rotor system.

Cascaded control diagrams. For current (flux)-controlled AMB, the centralized controller provides a vector of four control currents, _{c} (forces _{c}), and after biasing the vector of eight reference currents, _{r} (forces _{r}), to the inner control loops. Additionally, the inner flux loops require the vector of estimated rotor displacements in bearing planes _{mb}. _{r}, _{m}, _{r}, _{m} are vectors of reference positions, measured currents, reference voltages, and bearing force rotor displacements in sensor planes, respectively.

Comparison of the force growth for the biased AMB with _{0} = 2.5 A and for the zero-bias case when the rotor remains in the central position.

Simulated step position reference and disturbance force responses of the selected position and current signals of the centralized radial AMB rotor system. _{x}_{pA} and _{x}_{mA} are the coil currents resulting in the magnetic force generation that acts in the positive and negative direction of the

Measured initial levitation of the rotor from the safety bearings at both rotor ends.

Measured step response at the A-end in the

Measured maximum singular values for output sensitivity functions at a standstill.

Measured maximum singular values for output sensitivity functions at 11, 000 rpm.

Eigenvalues of the open-loop systems.

^{−1}) |
^{−1}) | |
---|---|---|

Current-controlled AMB | ±242.5 | 0 |

±312.3 | 0 | |

±5493 | 0 | |

| ||

Current-controlled AMB with PM | ±256.4 | 0 |

±318.9 | 0 | |

±5493 | 0 | |

| ||

Flux-controlled AMB | 0 | 0 |

| ||

Flux-controlled AMB with PM | ±22.28 | 0 |

±102.9 | 0 |

The authors would like to thank the Finnish Funding Agency for Technology and Innovation (TEKES) for their financial support to the project “SaLUT-FCB to Business”, Janne Nerg and Jussi Sopanen and other research team members of Lappeenranta University of Technology (LUT) and Saimaa University of Applied Sciences (SAIMIA) for invaluable contributions toward the development of the case study prototype. The work has also been supported by Academy of Finland No. 270012 and No. 273489, and partially supported with Statutory Work of Department of Automatic Control and Robotics, Faculty of Mechanical Engineering, Bialystok University of Technology, No. S/WM/1/2012.

The authors declare no conflicts of interest.