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Active magnetic bearing (AMB) system has been recently employed widely as an ideal equipment for high-speed rotating machines. The inherent challenges to control the system include instability, nonlinearity and constricted range of operation. Therefore, advanced control technology is essential to optimize AMB system performance. This paper presents an application of model predictive control (MPC) based on linear parameter-varying (LPV) models to control an AMB system subject to input and state constraints. For this purpose, an LPV model representation is derived from the nonlinear dynamic model of the AMB system. In order to provide stability guarantees and since the obtained LPV model has a large number of scheduling parameters, the parameter set mapping (PSM) technique is used to reduce their number. Based on the reduced model, a terminal cost and an ellipsoidal terminal set are determined offline and included into the MPC optimization problem which are the essential ingredients for guaranteeing the closed-loop asymptotic stability. Moreover, for recursive feasibility of the MPC optimization problem, a slack variable is included into its cost function. The goal of the proposed feedback control system is twofold. First is to demonstrate high performance by achieving stable levitation of the rotor shaft as well as high capability of reference tracking without violating input and state constraints, which increases the overall safety of the system under disturbances effects. Second is to provide a computationally tractable LPVMPC algorithm, which is a substantial requirement in practice for operating the AMB system with high performance over its full range. Therefore, we propose an LPVMPC scheme with frozen scheduling parameter over the prediction horizon of the MPC. Furthermore, we demonstrate in simulation that such frozen LPVMPC can achieve comparable performance to a more sophisticated LPVMPC scheme developed recently and a standard NL MPC (NMPC) approach. Moreover, to verify the performance of the proposed frozen LPVMPC, a comparison with a classical controller, which is commonly applied to the system in practice, is provided.

We analyse the novel dynamics arising in a nonlinear rotor dynamic system by investigating the discontinuity-induced bifurcations corresponding to collisions with the rotor housing (touchdown bearing surface interactions). The simplified Föppl/ Jeffcott rotor with clearance and mass unbalance is modelled by a two degree of freedom impact-friction oscillator, as appropriate for a rigid rotor levitated by magnetic bearings. Two types of motion observed in experiments are of interest in this paper: no contact and repeated instantaneous contact. We study how these are affected by damping and stiffness present in the system using analytical and numerical piecewisesmooth dynamical systems methods. By studying the impact map, we show that these types of motion arise at a novel non-smooth Hopf-type bifurcation from a boundary equilibrium bifurcation point for certain parameter values. A local analysis of this bifurcation point allows us a complete understanding of this behaviour in a general setting. The analysis identifies criteria for the existence of such smooth and non-smooth bifurcations, which is an essential step towards achieving reliable and robust controllers that can take compensating action. [ABSTRACT FROM AUTHOR]

Magnetic bearings use magnetic forces to support various machine components. Because of the non-contact nature of this type of suspension, magnetic bearing technology offers a number of significant advantages over conventional bearings, such as rolling element and fluid film bearings. An active magnetic bearing basically consists of an electromagnetic actuator, position sensors, power amplifiers, and a feedback controller. All of these components are characterized by nonlinear behavior and therefore the entire system is inherently nonlinear. However, in simulations of the dynamic behavior of magnetic bearing systems, the nonlinearities are usually neglected to simplify the analysis and only linear models are used. Moreover, many control techniques currently used in magnetic bearing systems are generally designed by ignoring nonlinear effects. The main reason for simplification is the intractability of the complexity of the actual model. In fact, the inherent nonlinear properties of magnetic bearing systems can lead to dynamic behavior of a magnetically suspended rotor that is distinctly different from that predicted using a simple linearized model. Therefore, the nonlinearities should be taken into account. This literature review is focused on the nonlinear dynamics of magnetic bearing systems and it provides background information on analytical methods, nonlinear vibrations resulting from a rotor contacting auxiliary bearings, and other active topics of research involving the nonlinear properties of magnetic bearing systems, such as nonlinear self-sensing magnetic bearings and nonlinear control of magnetic bearings. The review concludes with a brief discussion on current and possible future directions for research on the nonlinear dynamics of magnetic bearing systems. [ABSTRACT FROM AUTHOR]

This paper proposes a new nonlinear-disturbance observer for multivariable minimum-phase systems with arbitrary relative degrees. The model uncertainties and the system nonlinearities are treated as disturbances. The estimation of individual disturbances is independent of each other and the derivatives of the disturbances can be independently estimated. The proposed formulation is inspired by the variable structure-control method and adaptive algorithms where the aproii information concerning the upper bounds of the disturbances and their derivatives is not required. The nonlinear-disturbance observer is robust to the types of disturbances. Stability analysis shows that the estimation error decreases exponentially to a steady value, which is determined by the design parameters. To illustrate the method, the proposed design is applied to a vertical-shaft magnetic-bearing system where the rotational disturbances and their derivatives are estimated based on a linearized model of the rotational motion. Simulation results show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]