# Magnetic Levitation Control Based on Flux Density and Current Measurement
## 1 Introduction  
Active magnetic levitation is found nowadays in industrial systems where contact-free operation is advantageous. Typical applications include the support of compressors, turbines and flywheels in vacuum, manufacturing, and oil-and-gas industrial fields [1; 2; 3; 4]. High efficiency, low maintenance cost and control of the hovering dynamics are some of the key benefits of this technology [1; 5]. In a nutshell, active magnetic levitation systems aim to control the position of the levitating object by varying the force imposed with an electromagnet. Their inherent nonlinear and unstable open loop nature motivate a substantial research effort mainly focused on the investigation of more effective actuator architectures [6; 7] and the development of advanced control strategies to improve their dynamic performance, stability and robustness [8; 9; 10]. Additionally, since the performance of such systems is heavily influenced by the quality of the position feedback, the displacement sensing technique represents a crucial element. Typically, the displacement measurement is performed exploiting a variety of technologies such as optical, capacitive, magnetic, and electromagnetic sensing [1; 11]. Optical sensors are easy to use and suitable for large air gaps [12], but prone to resolution loss due to diffraction effects [1]. Capacitive sensing features high resolution but is expensive and sensitive to dirt and dust [11; 13]. Magnetic sensors have a good resolution but are sensitive to external magnetic fields [1]. Eddy-current and inductive sensors have good sensitivity, robustness, and immunity to dust [14; 15; 16]. Alternative solutions are the so-called self-sensing techniques, where the displacement sensor is not present, and the position of the levitating object is determined fromthe direct measurement of other variables, typically voltage and current in the electromagnet coil [1; 17; 18; 19]. This reduces significantly cost, weight, and hardware complexity. A significant amount of research focuses on observer-based estimation relying on a mathematical model of the system [20; 21; 22]. Other techniques exploit the functional relationship between the magnetic circuit inductance and the position of the levitated object [23; 24; 25]. A further position sensing solution determines the displacement through the measurement of the flux density at the air gap along with the current flowing in the electromagnet coil. The addition of the flux density at the air gap with respect to the afore-mentioned self-sensing solutions improves the robustness and performance, while reducing the effects of plant-model mismatch and unmodeled dynamics [20; 26]. However, in the authors' knowledge, the literature related to this approach is limited. In [27], a Hall effect magnetic field sensor is installed between the electromagnet and the levitating object. A permanent magnet (PM) is also added to the levitating object. In this configuration, the sensed magnetic flux density is dominated by the behaviour of the PM and the displacement can be correlated with this measurement. However, as stated by the authors, the measurement of the magnetic flux density from the suspended object is corrupted by the magnetic behaviour of the coil, which is neglected in the sensing technique. This deficiency is addressed in [28] with a more precise sensing solution. The disturbance introduced by the solenoid field is evaluated numerically through a finite element (FE) model. A sensor fusion algorithm based on the unscented Kalman filter is adopted for the displacement estimation in real time. This paper proposes a position control approach exploiting the measurements of the coil current and the magnetic flux density at the air gap to obtain the displacement of the mover. Unlike the aforementioned works, the mover is ferromagnetic and does not include any PM elements. In this case, the magnetic flux density strongly depends on both, the coil current and the mover position.