No abstract

A practical magnetic-bearing control system has been designed based upon modeling and simulation of the dynamics of a jet engine turbine shaft and bearing system. Simulations include models for flexible rotor dynamics, magnetic actuators, auxiliary touchdown bearings, ordinary and extraordinary external loads, and disturbances from rotor imbalance, stator vibration, and noise. The shaft model includes a motor-generator which acts as an uncontrolled negative stiffness. The control system is decentralized, running independently for each of the five physical axes of control (1 axial, 4 radial). The fundamental algorithm is classical PID: proportional for broadband stiffness, integrator (with anti-windup) for high load-carrying capacity, and derivative to dampen disturbances. Additional phase lead is provided via a first-order pole-zero pair. The vibration due to rotor imbalance is eliminated by an autobalancing algorithm. Compensation for magnetic actuator non-linearity and varying rotor-stator gap is provided by feedback of sensed magnetic flux, using sensor coils built into the actuator. The control design can be readily implemented using a commercial Digital Signal Processing system. The magnetic bearing actuators will be driven with commercial power amplifiers via customized front-end electronics. Based upon simulations, the design goal has been achieved of keeping the shaft within two mils of its desired location at the magnetic bearings, under all normal loads. Under extreme external loads, the capacity of the magnetic bearings will be exceeded and touchdown will occur upon backup mechanical bearings. Simulation shows that the control design handles this critical event, which determines the force slew rate required from the actuators.

No abstract

Analysis of the wave-induced motion of underwater vehicles near the ocean surface is a difficult task. First, the action of the fluid must be decomposed into ideal (inviscid) and real (viscous) effects. Next, each effect must be modeled as to its interaction with the submerged body. The effect of the body on the waves must be considered. In shallow water, the ocean bottom has many effects: energy-dissipation tends to reduce wave height; land-proximity restricts the wave direction; and the bottom boundary changes the shape of the waves, attenuating the vertical (but not the horizontal) component of motion. This paper presents mathematical models for predicting realistic wave-generated forces and moments on submersible vehicles. Included are models which generate typical wave spectra for deep and shallow waters, models for wave kinematics as affected by flat or sloping bottoms, and models for forces and moments on submersibles due to these surface waves. Forces and moments are computed using two alternative methods. One is a fast method based on analytical integration of dynamic pressure forces over the surface of an elongated ellipsoidal body. It gives first-order forces and moments limited to horizontal and restrained bodies. The second method, based on the Froude-Krylov approach, uses numerical integration of dynamic pressures to give forces and moments on any shape hull in any attitude. Unlike the first method, it can be extended to include broaching of the sea surface by the body. Hydrodynamic forces due to an unrestrained body’s motion are accounted for with “added mass” terms. These mathematical models have been implemented in the C language in a real-time computer simulation. They are actively used to study the dynamic performance and control of submersibles at periscope depths.

Simple closed‐form solutions for the statistics of coverage gaps (holidays) associated with parallel lane surveys are derived. In particular, theoretical results for mean holiday area, mean holiday dimensions, and frequency of encounter of random holidays are presented. For verification, the latter are compared with the results of computer simulations of first‐order Markov processes.