Rotors on Active Magnetic Bearings: Modeling and Control Techniques

In the last decades the deeper and more detailed understanding of rotating machinery dynamic behavior facilitated the study and the design of several devices aiming at friction reduction, vibration damping and control, rotational speed increase and mechanical design optimization. Among these devices a promising technology is represented by active magnetic actuators which found a great spread in rotordynamics and in high precision applications due to (a) the absence of all fatigue and tribology issues motivated by the absence of contact, (b) the small sensitivity to the operating conditions, (c) the wide possibility of tuning even during operation, (d) the predictability of the behavior. This technology can be classified as a typical mechatronic product due to its nature which involves mechanical, electrical and control aspects, merging them in a single system. The attractive potential of active magnetic suspensions motivated a considerable research effort for the past decade focused mostly on electrical actuation subsystem and control strategies. Examples of application areas are: (a) Turbomachinery, (b) Vibration isolation, (c) Machine tools and electric drives, (d) Energy storing flywheels, (e) Instruments in space and physics, (f) Non-contacting suspensions for micro-techniques, (g) Identification and test equipment in rotordynamics. This chapter illustrates the design, the modeling, the experimental tests and validation of all the subsystems of a rotors on a five-axes active magnetic suspension. The mechanical, electrical, electronic and control strategies aspects are explained with a mechatronic approach evaluating all the interactions between them. The main goals of the manuscript are: • Illustrate the design and the modeling phases of a five-axes active magnetic suspension; • Discuss the design steps and the practical implementation of a standard suspension control strategy; • Introduce an off-line technique of electrical centering of the actuators; • Illustrate the design steps and the practical implementation of an online rotor selfcentering control technique. The experimental test rig is a shaft (Weight: 5.3 kg. Length: 0.5 m) supported by two radial and one axial cylindrical active magnetic bearings and powered by an asynchronous high frequency electric motor. The chapter starts on an overview of the most common technologies used to support rotors with a deep analysis of their advantages and drawbacks with respect to active magnetic bearings. Furthermore a discussion on magnetic suspensions state of the art is carried out highlighting the research efforts directions and the goals reached in the last years. In the central sections, a detailed description of each subsystem is performed along with the modeling steps. In particular the rotor is modeled with a FE code while the actuators are considered in a linearized model. The last sections of the chapter are focused on the control strategies design and the experimental tests. An off-line technique of actuators electrical centering is explained and its advantages are described in the control design context. This strategy can be summarized as follows. Knowing that: a) each actuation axis is composed by two electromagnets; b) each electromagnet needs a current closed-loop control; c) the bandwidth of this control is depending on the mechanical airgap, then the technique allows to obtain the same value of the closed-loop bandwidth of the current control of both the electromagnets of the same actuation axis. This approach improves performance and gives more steadiness to the control behavior. The decentralized approach of the control strategy allowing the full suspensions on five axes is illustrated from the design steps to the practical implementation on the control unit. Furthermore a selfcentering technique is described and implemented on the experimental test rig: this technique uses a mobile notch filter synchronous with the rotational speed and allows the rotor to spin around its mass center. The actuators are not forced to counteract the unbalance excitation avoiding saturations. Finally, the experimental tests are carried out on the rotor to validate the suspension control, the off-line electrical centering and the selfcentering technique. The numerical and experimental results are superimposed and compared to prove the effectiveness of the modeling approach

Non-dimensional design approach for electrodynamic bearings

Electrodynamic bearings (EDBs) are passive magnetic bearings that exploit the interaction between eddy currents developed in a rotating conductor and a static magnetic field to generate forces. Similar to other types of magnetic suspensions, EDBs provide contactless support, thus avoiding problems with lubrication, friction and wear. The most interesting aspect of EDBs is that levitation can be obtained by passive means, hence, no electronic equipment, such as power electronics or sensors, are necessary. Despite their promising characteristics, rotors running on EDBs are still lacking a design procedure; furthermore, at present the static behavior of a bearing can only be defined by means of finite element analyses. The aim of the present paper is to present a methodology that allows performing a first approximation design without resorting to detailed FE analyses. The methodology is based on the use of non-dimensional parameters, similar to the analysis of fluid bearings (Sommerfeld number). The non-dimensional quantities are derived using dimensional analysis, and contain the main geometrical and physical parameters determining the EDBs' performance. The relation between the non-dimensional quantities characterizing the static performance of the EDB is derived using FE simulations and is presented in the form of graph

Model and Design of a Power Driver for Piezoelectric Stack Actuators

A power driver has been developed to control piezoelectric stack actuators used in automotive application. A FEM model of the actuator has been implemented starting from experimental characterization of the stack and mechanical and piezoelectric parameters. Experimental results are reported to show a correct piezoelectric actuator driving method and the possibility to obtain a sensor-less positioning contro

Model and design of a double frequency piezoelectric resonator

A novel design of a multifrequency mechanical resonator with piezoelectric materials for energy harvesting is presented. The electromechanical response is described by a finite element model, which predicts the output voltage and the generated powe

Trade-off analysis and design of a Hydraulic Energy Scavenger

In the last years there has been a growing interest in intelligent, autonomous devices for household applications. In the near future this technology will be part of our society; sensing and actuating will be integrated in the environment of our houses by means of energy scavengers and wireless microsystems. These systems will be capable of monitoring the environment, communicating with people and among each other, actuating and supplying themselves independently. This concept is now possible thanks to the low power consumption of electronic devices and accurate design of energy scavengers to harvest energy from the surrounding environment. In principle, an autonomous device comprises three main subsystems: an energy scavenger, an energy storage unit and an operational stage. The energy scavenger is capable of harvesting very small amounts of energy from the surroundings and converting it into electrical energy. This energy can be stored in a small storage unit like a small battery or capacitor, thus being available as a power supply. The operational stage can perform a variety of tasks depending on the application. Inside its application range, this kind of system presents several advantages with respect to regular devices using external energy supplies. They can be simpler to apply as no external connections are needed; they are environmentally friendly and might be economically advantageous in the long term. Furthermore, their autonomous nature permits the application in locations where the local energy grid is not present and allows them to be ‘hidden' in the environment, being independent from interaction with humans. In the present paper an energy-harvesting system used to supply a hydraulic control valve of a heating system for a typical residential application is studied. The system converts the kinetic energy from the water flow inside the pipes of the heating system to power the energy scavenger. The harvesting unit is composed of a hydraulic turbine that converts the kinetic energy of the water flow into rotational motion to drive a small electric generator. The design phases comprise a trade-off analysis to define the most suitable hydraulic turbine and electric generator for the energy scavenger, and an optimization of the components to satisfy the systems specification

Predictive Control Framework for Thermal Management of Automotive Fuel Cell Systems at High Ambient Temperatures

Environmental conditions have a significant effect on the performance of fuel cell systems. This paper studies the vehicle hydrogen consumption, the thermal management system, and the thermal loads of an automotive fuel cell system. A predictive control framework for thermal management is investigated to minimize the overall hydrogen consumption. Initially, a numerical modeling approach for the automotive fuel cell system is presented from electrochemical and thermal perspectives. Then, the problem formulation related to the thermal management strategy is presented and solved with an optimization method based on dynamic programming (DP). The implemented DP exploits the a priori knowledge of the driving mission to appropriately control the fuel cell system gross power and the operation of the radiator fan, the coolant pump, and the compressor. Optimization constraints involve maintaining the fuel cell stack temperature below the operational limit and avoiding the thermal system from being activated when the vehicle is at rest. The fuel cell system is tested while the vehicle performs different numbers of repetitions of the Worldwide Harmonized Light Vehicle Test Procedure (WLTP) at high ambient temperature. Using the proposed predictive control framework for thermal management, results demonstrate that an average 62.5% to 63.0% efficiency can be attained by the fuel cell stack in extreme ambient conditions both in short distance and long distance driving missions

Hardware-in-the-Loop Assessment of a Data-Driven State of Charge Estimation Method for Lithium-Ion Batteries in Hybrid Vehicles

This paper presents the design and hardware-in-the-loop (HIL) experimental validation of a data-driven estimation method for the state of charge (SOC) in the lithium-ion batteries used in hybrid electric vehicles (HEVs). The considered system features a 1.25 kWh 48 V lithium-ion battery that is numerically modeled via an RC equivalent circuit model that can also consider the environmental temperature influence. The proposed estimation technique relies on nonlinear autoregressive with exogenous input (NARX) artificial neural networks (ANNs) that are properly trained with multiple datasets. Those datasets include modeled current and voltage data, both for charge-sustaining and charge-depleting working conditions. The investigated method is then experimentally validated using a Raspberry Pi 4B card-sized board, on which the estimation algorithm is actually deployed, and real-time hardware, on which the battery model is developed, namely a Speedgoat baseline platform. These hardware platforms are used in a hardware-in-the-loop architecture via the UPD communication protocol, allowing the system to be validated in a proper testing environment. The resulting estimation algorithm can estimate the battery SOC in real-time, with 2% accuracy during real-time hardware testing

Model predictive control for comfort optimization in assisted and driverless vehicles

This paper presents a method to design a Model Predictive Control to maximize the passengers’ comfort in assisted and self-driving vehicles by achieving lateral and longitudinal dynamic. The weighting parameters of the MPC are tuned offline using a Genetic Algorithm to simultaneously maximize the control performance in the tracking of speed profile, lateral deviation and relative yaw angle and to optimize the comfort perceived by the passengers. To this end, two comfort evaluation indexes extracted by ISO 2631 are used to evaluate the amount of vibration transmitted to the passengers and the probability to experience motion sickness. The effectiveness of the method is demonstrated using simulated experiments conducted on a subcompact crossover vehicle. The control tracking performance produces errors lower than 0.1 m for lateral deviation, 0.5 for relative yaw angle and 1.5 km/h for the vehicle speed. The comfort maximization results in a low percentage of people who may experience nausea (below 5%) and in a low value of equivalent acceleration perceived by the passenger (below 0.315 m=s 2 ‘‘not uncomfortable’’ by ISO 2631). The robustness at variations of vehicle parameters, namely vehicle mass, front and rear cornering stiffness and mass distribution, is evaluated through a sensitivity analysis