Publications

This paper presents the work on the real time implementation of digital controllers applied to magnetic bearings to levitate high speed rotor systems. Microprocessor is employed for digital signal processing. The control loop consists of PID controller, tracking and fixed notch filters, lead compensators, and feedforward stage, etc. The controller is implemented with TI TMS320C67 processor incorporated with LabVIEW data acquisition and graphical user interface. Digital signal processing techniques including bilinear transformation, frequency pre-warping, digital filter design and I/O communications are applied to implement the control rule. The real time controller has been successfully applied to the levitations of a Revolver Test Rig in Vibration Control Lab at Texas A&M and the Energy Storage Flywheel System used by industries for vehicles.

 

Real time digital control of magnetic bearings with microprocessors

Flux coupling in heteropolar magnetic bearings permits remaining active coils to assume actions of failed coils to produce force resultants identical to the un-failed actuator. This fault-tolerant control usually reduces load capacity because the redistribution of the magnetic flux which compensates for the failed coils leads to premature saturation in the stator or journal. A distribution matrix of voltages which consists of a redefined biasing voltage vector and two control voltage vectors can be optimized in a manner that reduces the peak flux density. An elegant optimization method using the Lagrange multiplier is presented in this paper. The linearized control forces can be realized up to certain combination of 5 poles failed for the 8 pole magnetic bearing. Position stiffness and voltage stiffness are calculated for the fault-tolerant magnetic bearings. Simulations show that fault-tolerant control of the multiple poles failed magnetic bearings with a horizontal flexible rotor can be achieved with reduced load capacity.

 

Optimized Realization of Fault-Tolerant Heteropolar Magnetic Bearings

A unique control approach is developed for prescribed large motion control using magnetic bearings in a proposed active stall control test rig. A finite element based, flexible shaft is modeled in a closed loop system with PD controllers that generate the control signals to support and to shake the rotor shaft. A linearized force model of the stall rig with 16 magnetic poles (4 opposing C-cores) yields stability and frequency responses. The non-linear model retains the non-linearities in Ampere’s law, Faraday’s law and the Maxwell stress tensor. A fuzzy logic control system is then designed to show the advantages over the conventional controllers with the fully non-linear model.

 

NON-LINEAR FUZZY LOGIC CONTROL FOR FORCED LARGE MOTIONS OF SPINNING SHAFTS

This paper presents theoretical models and simulation results for the synchronous, thermal transient, instability phenomenon known as the Morton effect. A transient analysis of the rotor supported by tilting pad journal bearing is performed to obtain the transient asymmetric temperature distribution of the journal by solving the variable viscosity Reynolds equation, a 2D energy equation, the heat conduction equation, and the equations of motion for the rotor. The asymmetric temperature causes the rotor to bow at the journal, inducing a mass imbalance of overhung components such as impellers, which changes the synchronous vibrations and the journal’s asymmetric temperature. Modeling and simulation of the cyclic amplitude, synchronous vibration due to the Morton effect for tilting pad bearing supported machinery is the subject of this paper. The tilting pad bearing model is general and nonlinear, and thermal modes and staggered integration approaches are utilized in order to reduce computation time. The simulation results indicate that the temperature of the journal varies sinusoidally along the circumferential direction and linearly across the diameter. The vibration amplitude is demonstrated to vary slowly with time due to the transient asymmetric heating of the shaft. The approach’s novelty is the determination of the large motion, cyclic synchronous amplitude behavior shown by experimental results in the literature, unlike other approaches that treat the phenomenon as a linear instability. The approach is benchmarked against the experiment of de Jongh.

 

Morton Effect Cyclic Vibration Amplitude Determination for Tilt Pad Bearing Supported Machinery

Previously published work on applied impact damping typically relates to SDOF models or simple MDOF models such as the classical cantilever beam. Structural models often require an extremely large number of DOF with mode shapes that are generally very complex. Dynamics simulation of these typically becomes both complicated and time consuming. The nonlinear behavior of impact dampers further complicates such simulation in that standard linear solutions are not possible. The primary objective in this research extends previous work by applying impact dampers to MDOF structures that are modeled with general three-dimensional ‘ ‘beam” finite elements. Modal-based models of the MDOF systems and efficient impact damper tracking algorithms were also developed that significantly reduced CPU time for simulation. Significant among the objectives was obtaining an impact damper design for the MDOF casing structure of the Space Shuttle Main Engine (SSME), High-Pressure Oxygen Turbo-Pump (HPOTP), subject to pump rotor shaft unbalance. Impact damper performance is based on suppression of vibration at casing critical frequencies for rotor speed ranges, at rotor full speed, and very high unbalance to simulate a defect such as losing an impeller blade fragment or a cracked bearing [6]. Simulations show significant reductions in vibration at the casing critical frequencies and very high unbalance levels while little or no improvement was observed off resonance. Additionally, the previous work with an experimental rotor bearing system (RBS) and impact damper was modeled using the developed modal-based methods. Simulation of the resulting model response shows remarkable agreement with the experimental. Finally, both the RBS and the HPOTP were modeled and simulated as unstable systems with attached impact dampers. The simulations predict that the impact damper is an excellent stabilizing mechanism for a range of instability river values. Simulation of the models in this research with the developed modal based algorithms were accomplished with excellent efficiency, and accurate results.

 

Modeling and Simulation Methods for MDOF Structures and Rotating Machinery With Impact Dampers

Theory and simulation results have demonstrated that four, variable speed flywheels could potentially provide the energy storage and attitude control functions of existing batteries and control moment gyros on a satellite. Past modeling and control algorithms were based on the assumption of rigidity in the flywheel’s bearings and the satellite structure. This paper provides simulation results and theory, which eliminates this assumption utilizing control algorithms for active vibration control (AVC), flywheel shaft levitation, and integrated power transfer and attitude control (IPAC), that are effective even with low stiffness active magnetic bearings (AMBs) and flexible satellite appendages. The flywheel AVC and levitation tasks are provided by a multiple input–multiple output control law that enhances stability by reducing the dependence of the forward and backward gyroscopic poles with changes in flywheel speed. The control law is shown to be effective even for (1) large polar to transverse inertia ratios, which increases the stored energy density while causing the poles to become more speed dependent, and for (2) low bandwidth controllers shaped to suppress high frequency noise. Passive vibration dampers are designed to reduce the vibrations of flexible appendages of the satellite. Notch, low-pass, and bandpass filters are implemented in the AMB system to reduce and cancel high frequency, dynamic bearing forces and motor torques due to flywheel mass imbalance. Successful IPAC simulation results are presented with a 12% initial attitude error, large polar to transverse inertia ratio (IP/IT), structural flexibility, and unbalance mass disturbance.

 

MIMO Active Vibration Control of Magnetically Suspended Flywheels for Satellite IPAC Service

This paper presents the theory and numerical results of utilizing four gimbaled, magnetically suspended, variable speed flywheels for simultaneous satellite attitude control and power transfer (charge, storage, and delivery). Previous variable speed control moment gyro models and control algorithms assumed that the flywheel bearings were rigid. However, high speed flywheels on spacecraft will be supported by active magnetic bearings, which have flexibility and in general frequency dependent characteristics. The present work provides the theory for modeling the satellite and flywheel systems including controllers for stable magnetic bearing suspension for power transfer to and from the flywheels and for attitude control of the satellite. A major reason for utilizing flexible bearings is to isolate the imbalance disturbance forces from the flywheel to the satellite. This g-jitter vibration could interfere with the operation of sensitive onboard instrumentation. A special control approach is employed for the magnetic bearings to reject the imbalance disturbances. The stability, robustness, tracking, and disturbance rejection performances of the feedback control laws are demonstrated with a satellite simulation that includes initial attitude error, system modeling error, and flywheel imbalance disturbance.

 

Magnetically Suspended VSCMGs for Simultaneous Attitude Control and Power Transfer IPAC Service

The rotor/stator configurations considered are washer-shaped laminate stack (WL), tape-wound laminate stack (TL), U-shaped laminate stacks (UL), solid metal (S), and solid wedge pieces. Since preloading reduces rotor vibration, the effects of preloading a WL rotor and TL stator system on the flux density/input current transfer function magnitude and phase are determined from tests. Since eddy currents result in power loss and phase lag, tests are performed on four rotor/stator pairs, i.e., WL/TL, TL/TL, TL/UL, and S/S, to find the one with minimal eddy currents. For S/S, the test results are compared with those obtained from a two-dimensional finite element analysis, for Silicon-Iron and Hiperco-27. Since overhanging the rotor beyond the stator is a common practice, the effect of this on the fringing of magnetic flux is studies using finite element analysis.

 

Magnetic thrust bearing concepts- Tests and analyses

Multiple objective genetic algorithms (MOGAs) simultaneously optimize a control law and geometrical features of a set of homopolar magnetic bearings (HOMB) supporting a generic flexible, spinning shaft. The minimization objectives include shaft dynamic response (vibration), actuator mass and total actuator power losses. Levitation of the spinning rotor and dynamic stability are constraint conditions for the control law search. Nonlinearities include magnetic flux saturation, and current and voltage limits. Pareto frontiers were applied to identify the best-compromised solution. Mass and vibration reductions improve with a two control law approach.

 

Magnetic Bearing Rotordynamic System Optimization Using Multi-Objective Genetic Algorithms

The use of magnetic bearings (MB) for support of space based flywheels can provide significant improvement in efficiency due to reduction in drag torque. A NASA supported program directed through the Texas A&M Center for Space Power has been formed to advance the technology of MB’s for satellite flywheel applications. The five areas of the program are: (a) Magnetic Field Simulation, (b) MB controller Development, (c) Electromechanicai Rotordynamics Modeling, (d) Testing and (e) Technology Exchange. Planned innovations in these tasks include eddy current drag torque and power loss determination including moving conductor effects, digital (DSP) based control for high speed operation, MATLAB-based coupled flexible rotor/controller/actuator electromechanical model with fuzzy logic nonlinear control, and ultra high speed>100krpm measurement of drag torque. The paper examines these areas and provides an overview of the project.

 

magnetic bearing development for support of satellite flywheels