Sliding mode control schemes of the static and dynamic types are proposed for the control of a magnetic levitation system. The proposed controllers guarantee the asymptotic regulation of the statesof the system to their desired values. Simulation results of the proposed controllers are given to illustrate the effectiveness of them. Robustness of the control schemes to changes in the parameters of the system is also investigated.

https://downloads.hindawi.com/journals/mpe/2004/657503.pdf

Sliding mode control of a magnetic levitation system

In this paper, nonlinear aspects of the control of magnetic bearings are studied. The authors design a nonlinear feedback law for the positioning of a shaft, and study the possibility of avoiding premagnetization currents, usually required when applying tangent linearization techniques. Using the flatness property, they propose simple solutions to the motion planning and stabilization problems according to the current complementarity condition or the current almost complementarity condition, that ensures that only one electromagnet in each actuator works at a time, or that one approaches arbitrarily close to this situation. The feedback synthesis is presented in both current and voltage control cases. In the latter case, a hierarchical control scheme, based on time-scale separation, is proposed, to avoid unbounded voltages at switchings that might result from the voltage linearizing feedback. Some implementation aspects are described and some experiments presented.

A nonlinear approach to the control of magnetic bearings

A nonlinear model of an inertial wheel supported by active magnetic bearings is presented. A nonlinear controller based on input-output linearization is then derived to stabilize this model. This is contrasted to the typical practice of obtaining a linear model via premagnetization of the bearings through a bias current. Experimental results demonstrate that the rotor vibration and energy consumption of the bearings are lower when the nonlinear control method is used. A sliding mode control method is also proposed so that control is achieved with only two values of voltage input, in much the same manner as pulse width modulation. Simulations are also presented to test the robustness of the sliding mode control.

Nonlinear control of a magnetic levitation system without premagnetization

In this paper we present the development of (1) a sliding mode controller for stabilization of the rotational dynamics of a vertical shaft magnetic bearing in addition to providing tracking capabilities, and (2) a sliding mode observer for state and disturbance estimation. Rotor imbalance causes sinusoidal disturbances which necessitates robustness inherent in sliding mode observers and controllers. The sliding mode control design includes (1) the definition of an equilibrium manifold upon which the magnetic bearing has the desired stability and tracking properties, and (2) the control selection from one of several potential control strategies for driving the system to this manifold and maintaining it there. A sliding mode observer strategy is proposed to estimate derivatives of measured signals in the presence of unmatched disturbances by filtering discontinuous approximations of the derivatives. Simulation results demonstrate the utility and robustness of a sliding mode controller and observer for stabilizing the rotational dynamics of a magnetic bearing.

A sliding mode observer and controller for stabilization of rotational motion of a vertical shaft magnetic bearing

The /spl mu/ synthesis design method was evaluated for a flexible rotor magnetic bearing system with a five-axis-control system using both simulations and experiments. After modeling the full-order system using the finite element method, the autors obtained a reduced-order model in the modal domain by truncating the flexible modes. After choosing appropriate weighting functions with respect to frequency, they designed the /spl mu/-synthesis control system using the /spl mu/-toolbox in MATLAB. They then carried out simulations of the control system for a flexible rotor magnetic bearing system with a five-axis-control system and obtained good performance. Next, they conducted experiments to verify the robustness of the controllers on a test rig during initial levitation. The /spl mu/ controllers provided robust stability and performance over a wide range of parameter variations in the test rig.

/spl mu/ synthesis of flexible rotor-magnetic bearing systems

In this paper, the sliding mode control, a typical method of nonlinear adaptive control and robust control, is applied to a magnetic bearing system. It has its roots in the relay and bang-bang control theory. Sliding mode control is a high-speed switching feedback control; for example, the gains in each feedback path switch between two values according td certain rules. This control law drive system's state trajectory to a user-chosen surface in the state space is called the sliding surface for all subsequent time. The sliding surface is called the switching surface by another name because if the state trajectory is above the surface, a control path has one gain and a different gain if the trajectory drops below the surface. From this control, the system is restricted to this surface and is stabilized. This method is very robust for parameter change, modelling error, disturbance, and so on. The sliding mode control method is compared with the PID control method for the flexible rotor supported by magnetic bearings by simulation and experiments on both the lift off and the rotation.

Hirotaka Yamaguchi

Papers

Robust Control of Magnetic Bearing Systems by Means of Sliding Mode Control.