Sliding mode control for active magnetic bearing system with flexible rotor

Jang, Ming-Jyi; Chen, Chieh‐Li; Tsao, Yi-Ming

doi:10.1016/j.jfranklin.2005.01.006

Cited by 69 publications

(26 citation statements)

References 18 publications

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“…Chatter problem was avoided by assuming a smooth function instead of a discrete sign function. Jang et al [9] proposed another sliding mode control design scheme to compensate the nonlinear effects of the AMBflexible rotor system by treating the nonlinearities as disturbance action. This was achieved by separating the nonlinear magnetic bearing force into two parts as linear for low order terms and high order nonlinear terms.…”

Section: T X T B X T U T U T F T mentioning

confidence: 99%

Nonlinear optimal control of rotating flexible shaft in active magnetic bearings

Tombul

Banks

2011

Sci. China Technol. Sci.

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The optimal control of nonlinear systems has been studied for years by many researchers. However, the application of optimal control problem to nonlinear non-affine systems needs more attention. In this paper we propose an optimal control design technique for a class of nonlinear and control non-affine equations. The dynamic equations of a flexible shaft supported by a pair of active magnetic bearings (AMBs) are used as the nonlinear control non-affine equations. Mathematical model for the flexible beam is chosen to be the well known Timoshenko beam model, which takes rotary inertia and shear deformations into account, and it is assumed that the shaft is supported by two frictionless bearings at the ends. The effective control of such systems is extremely important for very high angular velocity shafts which are a feature of many modern machines. The control must be able to cope with unbalanced masses and hence be very robust. We shall approach the problem by discretising the Timoshenko beam model and using standard difference formulae to develop a finite-dimensional model of the system. Then we use a recently developed technique for controlling nonlinear systems by reducing the problem to a sequence of linear time-varying (LTV) systems. An optimal control designed for each approximating linear, time-varying system and recent results show that this method will converge uniformly on compact time intervals to the optimal solution. approximation technique, nonlinear optimal control, timoshenko beam, active magnetic bearings Citation:Tombul G S, Banks S P. Nonlinear optimal control of rotating flexible shaft in active magnetic bearings.

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Section: T X T B X T U T U T F T mentioning

confidence: 99%

Nonlinear optimal control of rotating flexible shaft in active magnetic bearings

Tombul

Banks

2011

Sci. China Technol. Sci.

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“…Moreover, an AMB system is inherently nonlinear system. The sliding mode controller with global invariance is proposed and the results show that the proposed scheme extends the operational range and the effects of rotor unbalance mass are minimized [22].…”

Section: Introductionmentioning

confidence: 99%

Active Vibration Control of the Flexible Rotor to Pass the First Bending Critical Speed in High Energy Density Magnetically Suspended Motor

Tang

Fang

Zheng

et al. 2015

Journal of Engineering for Gas Turbines and Power

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In order to minimizing the rotor displacement and the amplifier current mainly caused by the unbalance forces when the flexible rotor passes the first bending critical speed, the optimal controller is presented in this paper. The accurate modeling method for the flexible rotor based on the sine sweeping measurements is investigated. The design of the Kalman estimator and the choice of the variance matrix elements have been described. The optimal state feedback regulator with an integral controller has been used for stabilizing the system and the determination of the weight matrices has been investigated in detail. The influences of the specific elements of the weight matrices on the resonance peak of the flexible rotor when passing the first bending critical speed are analyzed. Finally, the running up test of the flexible rotor is implemented and the result shows the effectiveness of linear quadratic Gaussian (LQG) controller minimizing the rotor displacement and the amplifier current nearby the first bending critical speed. Furthermore, the comparison between the proportional-integral-differential (PID) controller with phase lead compensator and the LQG controller verifies the superiority of LQG controller in reducing the amplifier currents.

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“…Owing to material strength,windage loss and friction loss, rotors in motors, generators, pumps, turbo machinery and aero engines are always designed to flexible. Recently, the methods of passing through the bending critical speed include robust Hen control, f.1 integrated control, sliding mode control etc [2]- [5]. Those methods can compensate the control phase nearby the critical speed indirectly.…”

Section: Introductionmentioning

confidence: 99%

Optimal phase compensation control and experimental study of flexible rotor supported by magnetic bearing

Wang¹,

Fang²,

Zheng³

2012

2012 8th IEEE International Symposium on Instrumentation and Control Technology (ISICT) Proceedings

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In order to pass through the bending critical speed of flexible rotor system supported by magnetic bearing, the phase changes from the rotor's flexible deformation to magnetic force at bending critical frequency should be adjusted to increase its damping. In this paper, the optimal control phase of AMB controller is deduced from the theoretical model firstly. Then, the actual control phase is obtained using the method of dynamic analysis combined with model reference identification. Optimal phase to be compensated is determined finally. The experimental result shows that AMB controller added with a optimal phase compensator makes the rotor's flexible deformation minimum nearby the bending frequency.

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Sliding mode control for active magnetic bearing system with flexible rotor

Cited by 69 publications

References 18 publications

Nonlinear optimal control of rotating flexible shaft in active magnetic bearings

Nonlinear optimal control of rotating flexible shaft in active magnetic bearings

Active Vibration Control of the Flexible Rotor to Pass the First Bending Critical Speed in High Energy Density Magnetically Suspended Motor

Optimal phase compensation control and experimental study of flexible rotor supported by magnetic bearing

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