Stabilization of Active Magnetic Bearing Systems in the Case of Defective Sensors

Abstract

Many control methods for stabilizing magnetically levitated rotors are proposed in literature. However, most of these systems have in common that the degrees of freedom of the rigid rotor can directly be calculated from the sensor values. This assumption is fulfilled for most active magnetic bearing (AMB) systems if all sensors are working. This article deals with the question if it is possible to stabilize an AMB system if one or more sensors are defective. In this case, a direct calculation of the degrees of freedom from the sensor values is not possible. This article proofs that the defective system is observable for a wide operating range. However, for some parameter constellations the system becomes not observable for specific rotor speeds. The possibility of an observability loss is only present for isotropic magnetic bearings. If anisotropic bearings are modeled the loss of observability is not present anymore. It can be shown that the magnetic bearing system, which is used for the experimental verification, is observable in the predefined operating range without the requirement of an anisotropy. In this article, the cases with one and with two defective radial sensors are investigated. At standstill the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> plane and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i> – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> plane are decoupled. Hence, both cases have equal behavior in the plane with the defective sensor. However, for the rotating system both planes are coupled and the properties of both systems are different. To stabilize the levitating system, a controller is developed using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> method. To limit the computational effort of the digital signal processor the control structure is predefined as eighth-order state space system. Finally, the stabilization of the system with two defective sensors is experimentally validated on a turbomolecular pump with a magnetically levitated rotor.