Multi - objective sliding mode control of active magnetic bearing system

Active Magnetic Bearing (AMB) system is known to inherit many nonlinearity effects due to its rotor dynamic motion and the electromagnetic actuators which make the system highly nonlinear, coupled and open-loop unstable. The major nonlinearities that are associated with AMB system are gyroscopic effect, rotor mass imbalance and nonlinear electromagnetics in which the gyroscopics and imbalance are dependent to the rotational speed of the rotor. In order to provide satisfactory system performance for a wide range of system condition, active control is thus essential. The main concern of the thesis is the modeling of the nonlinear AMB system and synthesizing a robust control method based on Sliding Mode Control (SMC) technique such that the system can achieve robust performance under various system nonlinearities. The model of the AMB system is developed based on the integration of the rotor and electromagnetic dynamics which forms nonlinear time varying state equations that represent a reasonably close description of the actual system. Based on the known bound of the system parameters and state variables, the model is restructured to become a class of uncertain system by using a deterministic approach. In formulating the control algorithm to control the system, SMC theory is adapted which involves the formulation of the sliding surface and the control law such that the state trajectories are driven to the stable sliding manifold. The surface design involves the transformation of the system into a special canonical representation such that the sliding motion can be characterized by a convex representation of the desired system performances. Optimal Linear Quadratic (LQ) characteristics and regional pole-clustering of the closed-loop poles are designed to be the objectives to be fulfilled in the surface design where the formulation is represented as a set of Linear Matrix Inequality optimization problem. For the control law design, a new continuous SMC controller is proposed in which asymptotic convergence of the system’s state trajectories in finite time is guaranteed. This is achieved by adapting the equivalent control approach with the exponential decaying boundary layer technique. The newly designed sliding surface and control law form the complete Multi-objective SMC (MO-SMC) and the proposed algorithm is applied into the nonlinear AMB in which the results show that robust system performance is achieved for various system conditions. The findings also demonstrate that the MO-SMC gives better system response than the reported ideal SMC (I-SMC) and continuous SMC (C-SMC)

Active magnetic bearings applied to industrial compressors

The design and shop test results are given for a high-speed eight-stage centrifugal compressor supported by active magnetic bearings. A brief summary of the basic operation of active magnetic bearings and the required rotor dynamics analysis are presented with specific attention given to design considerations for optimum rotor stability. The concerns for retrofits of magnetic bearings in existing machinery are discussed with supporting analysis of a four-stage centrifugal compressor. The current status of industrial machinery in North America using this new support system is presented and recommendations are given on design and analysis requirements for successful machinery operation of either retrofit or new design turbomachinery

Chatter milling modeling of active magnetic bearing spindle in high-speed domain

A new dynamical modeling of Active Magnetic Bearing Spindle (AMBS) to identify machining stability of High Speed Milling (HSM) is presented. This original modeling includes all the minimum required parameters for stability analysis of AMBS machining. The stability diagram generated with this new model is compared to classical stability lobes theory. Thus, behavior’s specificities are highlighted, especially the major importance of forced vibrations for AMBS. Then a sensitivity study shows impacts of several parameters of the controller. For example, gain adjustment shows improvements on stability. Side milling ramp test is used to quickly evaluate the stability. Finally, the simulation results are then validated by HSM cutting tests on a 5 axis machining center with AMBS

VIBRATION BASED DAMAGE IDENTIFICATION OF TIME-VARYING DYNAMICAL SYSTEMS

This thesis develops and explores two new kinds of vibration-based damage identification methodologies suitable for dynamical systems with periodically time-varying coefficients; 1) a Floquet based method (Methodology I) and, 2) a Sideband Frequency Response Function (FRF) method (Methodology II). One important class of dynamical systems where periodic time-varying parametric terms naturally arise is rotordynamic systems. For the case of a flexible shaft-rotor system with multiple open cracks, this thesis explores a new Least Squares damage identification approach based on Floquet theory with iterative eigenvector estimate updating. It is found that this method is able to detect the location and severity of multiple cracks with the assistance of control inputs from an Active Magnetic Bearing (AMB). However, it is also found that this method could not effectively identify the crack angle. To overcome this shortcoming, the new Sideband FRF based methodology is developed which utilizes the measured changes in transfer function magnitude and phase due to structural damage at the primary and side-band frequencies of the damaged periodically time-varying dynamical system. This method provides the advantages of arbitrary interrogation frequency and multiple inputs/outputs which greatly enriches the dataset for damage identification. This damage identification algorithm utilizes an iterative least square approach combined with a Newton-Raphson technique to estimate the damage parameters. The effectiveness of this method is thoroughly explored for a flexible rotor system and a planar truss both with breathing cracks. In each case, damage estimation is performed using time-domain vibration data taken from full nonlinear simulations of the cracked structures. The results show that this new method successfully estimated the crack depths, locations and angles for the case of multiple simultaneous damages

Design of Robust AMB Controllers for Rotors Subjected to Varying and Uncertain Seal Forces

This paper demonstrates the design and simulation results of model based controllers for AMB systems, subjected to uncertain and changing dynamic seal forces. Specifically, a turbocharger with a hole-pattern seal mounted across the balance piston is considered. The dynamic forces of the seal, which are dependent on the operational conditions, have a significant effect on the overall system dynamics. Furthermore, these forces are considered uncertain. The nominal and the uncertainty representation of the seal model are established using results from conventional modelling approaches, i.e. Computational Fluid Dynamics (CFD) and Bulkflow, and experimental results. Three controllers are synthesized: I) An H∞ controller based on nominal plant representation, II) A μ controller, designed to be robust against uncertainties in the dynamic seal model and III) a Linear Parameter Varying (LPV) controller, designed to provide a unified performance over a large operational speed range using the operational speed as the scheduling parameter. Significant performance improvement is shown for robust control, incorporating model uncertainty, compared to nominal model based control

Detecting Cracked Rotors Using Auxiliary Harmonic Excitation

Cracked rotors are not only important from a practical and economic viewpoint, they also exhibit interesting dynamics. This paper investigates the modelling and analysis of machines with breathing cracks, which open and close due to the self-weight of the rotor, producing a parametric excitation. After reviewing the modelling of cracked rotors, the paper analyses the use of auxiliary excitation of the shaft, often implemented using active magnetic bearings to detect cracks. Applying a sinusoidal excitation generates response frequencies that are combinations of the rotor spin speed and excitation frequency. Previously this system was analysed using multiple scales analysis; this paper suggests an alternative approach based on the harmonic balance method, and validates this approach using simulated and experimental results. Consideration is also given to some issues to enable this approach to become a robust condition monitoring technique for cracked shafts

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