Consider a servomechanism that models an automatic pilot. Such a mechanism applies a torque to the steering control shaft so that the plane or boat will follow a prescribed course. Let y(t) be the true direction (angle) of the craft at time t and g(t) be the desired direction at time t, then e(t): = y(t)- g(t) denotes the error or deviation between the desired direction and the true direction. This servomechanism can be modeled by Iy"(t)= -ke(t), where I is the moment of inertia of the steering shaft and k is a positive proportionality constant. Determine the error e(t) for the automatic pilot if the shaft is initially at rest in the zero direction and the desired direction is g(t)= a, where a is a constant.
Consider a servomechanism that models an automatic pilot. Such a mechanism applies a torque to the steering control shaft so that the plane or boat will follow a prescribed course. Let y(t) be the true direction (angle) of the craft at time t and g(t) be the desired direction at time t, then e(t): = y(t)- g(t) denotes the error or deviation between the desired direction and the true direction. This servomechanism can be modeled by Iy"(t)= -ke(t), where I is the moment of inertia of the steering shaft and k is a positive proportionality constant. Determine the error e(t) for the automatic pilot if the shaft is initially at rest in the zero direction and the desired direction is g(t)= a, where a is a constant.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider a servomechanism that models an automatic pilot. Such a mechanism applies a torque to the steering control shaft so that the plane or boat will follow a
prescribed course. Let y(t) be the true direction (angle) of the craft at time t and g(t) be the desired direction at time t, then e(t): = y(t) - g(t) denotes the error or
deviation between the desired direction and the true direction. This servomechanism can be modeled by Iy"(t)= - ke(t), where I is the moment of inertia of the
steering shaft and k is a positive proportionality constant.
Determine the error e(t) for the automatic pilot if the shaft is initially at rest in the zero direction and the desired direction is g(t) = a, where a is a constant.
Click here to view the table of Laplace transforms.
Click here to view the table of properties of Laplace transforms.
e(t) =
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