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)

Nonlinear Control of a Flexible Rotor Magnetic Bearing System: Robustness and the Indefinate Model

Previously published control strategies for magnetic bearings primarily focus on linear optimal control techniques. While these methods afford many advantages, conspicuously absent from the literature are detailed attempts at nonlinear control. Here, we obtain the equations of motion of an overhung flexible rotor supported in magnetic bearings with two different levels of model sophistication. We derive a generic nonlinear controller in the manner of feedback linearization, and compare the eigenanalysis and transient response of the two rotor models under the action of this >perfect model> controller. We then proceed to obtain a robust nonlinear controller through the sliding mode technique and demonstrate that robustness by implementing it on an uncertain model.Center for Electromechanic

Modelling and Control of an Annular Momentum Control Device

The results of a modelling and control study for an advanced momentum storage device supported on magnetic bearings are documented. The control challenge posed by this device lies in its dynamics being such a strong function of flywheel rotational speed. At high rotational speed, this can lead to open loop instabilities, resulting in requirements for minimum and maximum control bandwidths and gains for the stabilizing controllers. Using recently developed analysis tools for systems described by complex coefficient differential equations, the closed properties of the controllers were analyzed and stability properties established. Various feedback controllers are investigated and discussed. Both translational and angular dynamics compensators are developed, and measures of system stability and robustness to plant and operational speed variations are presented

Dynamics of a flexible rotor in magnetic bearings

Discussed is a magnetic bearing which was designed and tested in a flexible rotor both as support bearings and as a vibration controller. The design of the bearing is described and the effect of control circuit bandwidth determined. Both stiffness and damping coefficients were measured and calculated for the bearing with good agreement. The bearings were then placed in a single mass rotor as support bearings and the machine run through two critical speeds. Measurements were made of the vibration response in plain bushings and magnetic bearings. Comparisons were also made of the theoretical calculations with the measured peak unbalance response speeds. Finally, runs were made with the magnetic bearing used as a vibration controller

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

Robust and real-time control of magnetic bearings for space engines

Currently, NASA Lewis Research Center is developing magnetic bearings for Space Shuttle Main Engine (SSME) turbopumps. The control algorithms which have been used are based on either the proportional-intergral-derivative control (PID) approach or the linear quadratic (LQ) state space approach. These approaches lead to an acceptable performance only when the system model is accurately known, which is seldom true in practice. For example, the rotor eccentricity, which is a major source of vibration at high speeds, cannot be predicted accurately. Furthermore, the dynamics of a rotor shaft, which must be treated as a flexible system to model the elastic rotor shaft, is infinite dimensional in theory and the controller can only be developed on the basis of a finite number of modes. Therefore, the development of the control system is further complicated by the possibility of closed loop system instability because of residual or uncontrolled modes, the so called spillover problem. Consequently, novel control algorithms for magnetic bearings are being developed to be robust to inevitable parametric uncertainties, external disturbances, spillover phenomenon and noise. Also, as pointed out earlier, magnetic bearings must exhibit good performance at a speed over 30,000 rpm. This implies that the sampling period available for the design of a digital control system has to be of the order of 0.5 milli-seconds. Therefore, feedback coefficients and other required controller parameters have to be computed off-line so that the on-line computational burden is extremely small. The development of the robust and real-time control algorithms is based on the sliding mode control theory. In this method, a dynamic system is made to move along a manifold of sliding hyperplanes to the origin of the state space. The number of sliding hyperplanes equals that of actuators. The sliding mode controller has two parts; linear state feedback and nonlinear terms. The nonlinear terms guarantee that the systems would reach the intersection of all sliding hyperplanes and remain on it when bounds on the errors in the system parameters and external disturbances are known. The linear part of the control drives the system to the origin of state space. Another important feature is that the controller parameter can be computed off-line. Consequently, on-line computational burden is small

Synchronous response modelling and control of an annular momentum control device

Research on the synchronous response modelling and control of an advanced Annular Momentun Control Device (AMCD) used to control the attitude of a spacecraft is described. For the flexible rotor AMCD, two sources of synchronous vibrations were identified. One source, which corresponds to the mass unbalance problem of rigid rotors suspended in conventional bearings, is caused by measurement errors of the rotor center of mass position. The other sources of synchronous vibrations is misalignment between the hub and flywheel masses of the AMCD. Four different control algorithms were examined. These were lead-lag compensators that mimic conventional bearing dynamics, tracking notch filters used in the feedback loop, tracking differential-notch filters, and model-based compensators. The tracking differential-notch filters were shown to have a number of advantages over more conventional approaches for both rigid-body rotor applications and flexible rotor applications such as the AMCD. Hardware implementation schemes for the tracking differential-notch filter were investigated. A simple design was developed that can be implemented with analog multipliers and low bandwidth, digital hardware

Structural dynamics branch research and accomplishments for fiscal year 1987

This publication contains a collection of fiscal year 1987 research highlights from the Structural Dynamics Branch at NASA Lewis Research Center. Highlights from the branch's four major work areas, Aeroelasticity, Vibration Control, Dynamic Systems, and Computational Structural Methods, are included in the report as well as a complete listing of the FY87 branch publications