Practice articleStable control of magnetically suspended motor with heavy self-weight and great moment of inertia
Introduction
The rotor in flywheel energy storage system (FESS) [1], [2], [3] has form of a big disk with great equatorial moment of inertia to generate large driving moment or to store a large amount of mechanical energy. Moreover, in order to improve the working efficiency and guarantee the stability of rotational machine when the rotor works at a high speed, some novel suspension and supporting ways such as gas bearing [4], [5], [6], oil film bearing [7], [8] and magnetic bearing [9], [10], [11] were applied in the rotational machinery. Especially, the active magnetic bearing (AMB) is promising to be used in the rotational machine because of its advantages on active controllability, non-contact friction, lubrication-free and long lifespan. There are many products of high speed rotational machinery using the AMB system, for example, the magnetically suspended flywheel for attitude control of satellite [12], [13], the magnetically suspended centrifugal compressor [14], [15] and the magnetically suspended vacuum pump [16], [17], [18]. Therefore, the stable control of magnetically suspended rotor is the research focus of the magnetically suspended rotational machinery. In general, the proportional–integral–derivative (PID) control [19], [20], [21] was applied in the closed-loop control of MSM based on the displacement feedback. Other control methods such as the Kalman filter [22], the fuzzy control [23], [24], [25], the adaptive control [26], [27] and the sliding-mode control (SMC) [28], [29], [30] were reported in the control engineering of MSM as well. Aiming at further improving the ability on disturbance attenuation of the MSM, the robust control method was also proposed and tested in the practical control engineering. A high performance hybrid control scheme with a feedback control and an inner-loop disturbance observer (DOB) was used to suppress constant and harmonic disturbances acting on the MSM at different rotational speeds [31], [32]. In a high-speed AMB spindle system, a -synthesis controller [33] was designed to minimize the error between the reference position and the estimated position, this method corrected the inability to measure real-time position in the presence of machining disturbance. In a three-pole AMB rotor system, the robust stabilization control using two stages of SMC was proposed to reduce the mismatch uncertainties due to the magnetic coupling and the actuator dynamics [34]. A robust controller [35] was designed for the active vibration control of radial homo-polar AMB rotor system, and experimental results showed that the control system had good performances on the transient response and the robustness. A robust fuzzy controller based on the Takagi–Sugeno fuzzy model was proposed for a nonlinear AMB system with time-varying parametric uncertainty [36], and it was more tractable and accessible. The control was proposed to attenuate the disturbance in a flexible MSM system [37]. A controller with -synthesis based on the model incorporating uncertainty was designed in a horizontal MSM system [38], the limits of allowable parameter changes for robust stability were tested and established.
However, the model uncertainties caused by the variation of current stiffness and displacement stiffness in the MSM were not yet analyzed. In above-mentioned literatures, the displacement stiffness and the current stiffness are viewed as the constant values without influence of variable airgap and external disturbance. Especially, compared to the MSM with light self-weight, the controllable airgap in the heavy self-weight MSM easily deflect from the nominal equilibrium position when different loads are mounted on the MSM, and then the current stiffness and the displacement stiffness would deviate from the nominal values. Moreover, different initial positions of the MSM also lead to uncertainties of the current stiffness and the displacement stiffness in the practical situation. A transient displacement deflection possibly makes the current stiffness and the displacement stiffness deviate from the nominal values when the MSM is suffered from disturbances such as the wind drag at high speed and the self-excited vibration. More importantly, the unstable MSM rotor with heavy self-weight possibly generates great shock on the stator part, and then the whole MSM system would be broken. So, the risk of unstable MSM rotor with heavy self-weight is raised with the rotational speed. Almost publications were focused on the static suspension control of the MSM, and the gyroscopic coupling of the MSM at dynamic rotation was not mitigated, but it could generate disturbance on the dynamic rotation control of the MSM.
Above all, compared to the MSM rotor in the above-mentioned references, the stable control of the MSM with heavy self-weight and great moment of inertia is still challenging, especially the MSM with heavy self-weight and great moment of inertia has variable rotational speed and indefinite initial suspension position. The stable control considering the variable rotational speed and indefinite initial suspension position is critical to improve the robust stability and the disturbance attenuation of the MSM with heavy self-weight and great moment of inertia. In this article, robust control functions are designed to the static suspension and dynamic rotation of the MSM rotor, so the robust stability of the MSM rotor is improved. Therefore, this robust control method is potential to be applied into the control engineering of the MSM rotor with a heavy self-weight and great moment of inertia, and the stable operational range of the MSM rotor with a heavy self-weight and great moment of inertia is expanded.
This article is organized as follows. The dynamic characteristics of the MSM rotor are studied in Section 2. Furthermore, the robust control functions of translation and radial rotation are designed in Section 3. Simulations about translation and radial rotation of the MSM rotor are conducted in Section 4. Moreover, experiments are conducted to verify the effectiveness of designed control functions in Section 5. Finally, the conclusion is given.
Section snippets
Structure of MSM
The structure of MSM system is illustrated in Fig. 1(a), and it consists of a suspension system, a permanent magnet synchronous motor (PMSM) and a sensor system. The suspension system includes radial AMB, axial AMB and back-up ball bearing. The radial AMB controls the radial motion of the MSM rotor, and the difference between magnetic forces of the radial AMBs at top-end and bottom-end generates torque to control the radial rotation of the MSM rotor. The axial AMB located at above-side and
Control loop of translation
The translational control loop of the MSM rotor is shown in Fig. 6. The control system includes the stiffness regulator and the damping regulator . The control voltage is converted into the control current through the amplifier . the dynamic displacements of the MSM rotor are measured by the displacement sensors with sensitivity coefficient . The magnetic force is expressed in terms of the current stiffness and the displacement stiffness as
Based on the displacement
Uncertainty response of translation
This part is to analyze the influence of uncertainties about the current stiffness and the displacement stiffness, simulation is focused on axial translation and radial rotations of the MSM rotor. Considering uncertainties of the current stiffness and the displacement stiffness in Section 2.3, the varying range of the axial current stiffness is [400 N/A, 500 N/A], and the uncertain range of the axial displacement stiffness is [ N/mm, −1600 N/mm]. The response curve of translation is
Experimental setup
The experimental setup in Fig. 17 consists of three parts including the mechanical system, the measurement system and the control system. The mechanical system has the radial AMB, the axial AMB and the PMSM. The vacuum pump is used to reduce the wind drag when the PMSM works at a high speed, and the vacuum gauge could measure the vacuum degree of the MSM system. The eddy current displacement sensors mounted on the stator part measure dynamic displacements of the MSM rotor. The displacement
Conclusion
The initial suspension position of the MSM rotor affects the current stiffness and the displacement stiffness, and then its suspension process is affected. Moreover, external disturbances acting on the MSM rotor also affect the nominal values of the current stiffness and the displacement stiffness. Therefore, robust control functions are designed to attenuate the disturbance for translation and radial rotation respectively. When the pulse-type, the sinusoidal-type and the random-type
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This work is supported by The Hong Kong Polytechnic University [grant number CRG RUMT16900506r].
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