Translations:Minimum delay/1/en

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We now shall discuss minimum delay and its relationship to feedback. At this point, let us expand our discussion about minimum delay and its relationship to feedback systems. For example, suppose that the desired direction of a ship is set on the gyrocompass. A feedback mechanism indicates the error between the desired direction and the actual direction of the ship. The error activates the guidance system, which consists of power amplifiers forcing the rudder in the direction that decreases the error. Because it takes time to supply the power to change the ship’s course, there is a time delay in the guidance system. Suppose that the ship is off course to starboard. The feedback mechanism indicates an error to starboard, and the power amplifiers force the rudders to port. Because of the time delay, the ship overshoots the gyro direction to port. Now the feedback mechanism indicates an error to port, and the power amplifiers force the rudders to starboard. Because of the time delay, the ship again overshoots the gyro direction, this time to starboard. The feedback mechanism now indicates an error to starboard, and because of the time delay, a third overshoot is produced, this time to port. These oscillations about the gyro direction can either increase in magnitude on each successive swing or can decrease. If they increase, the guidance system is unstable. If they decrease, it is stable. Clearly, the minimum-delay guidance system is the one that is stable. For example, in the layer-cake model of seismic stratigraphy, downgoing waves from an impulsive source have the minimumdelay property (Robinson and Treitel, 1976[1]; Loewenthal and Robinson, 2000[2]).

  1. Robinson, E. A., and S. Treitel, 1976, Net downgoing energy and the minimum-delay property of downgoing waves: Geophysics, 41, 1394–1396.
  2. Loewenthal, D., and E. A. Robinson, 2000, Relativistic combination of any number of collinear velocities and generalization of Einstein’s formula: Journal of Mathematical Analysis and Applications, 246, no. 1, 320–324.