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- W173637820 abstract "Suppose we have a rocket on a movable platform which may be slightly misaligned from the vertical position and we want to correct this misalignment just before the rocket is launched by applying a control force to the platform. In this chapter, we construct a simple model which can be used to determine such a control force in the case where the misalignment occurs in the direction parallel to the wheels of the platform. For our initial model, following Ogata [1], we will model the rocket as an inverted pendulum with its mass concentrated at the tip. We will assume that the platform rolls without resistance along the ground and that the mass and length of the rocket and the mass of the platform are known with a relative error less than .0001. Certain constraints will be imposed on the control force and the motion of the rocket which we will refer to as design criteria. We assume the following launch sequence. The rocket is initially at rest and constrained by a mechanical arm to be within 1 degree of vertical. Ten seconds before lift-off the mechanical arm is removed and a control force is applied to the platform to bring the rocket into a vertical position within 4 seconds. During the time remaining before lift-off, subsystem go/no-go signals are analyzed and a launch go/no-go decision is made. Beginning with our idealized physical model, we derive a mathematical, state-space model consisting of a system of 4 nonlinear ordinary differential equations. The state variables are the angle of the rocket from vertical, the position of the platform, and their time derivatives. We linearize these equations for small angular deviations of the rocket from vertical arriving at a linear system of ordinary differential equations. We use state feedback to control the system in which case the control force is represented as a linear combination of the state variables. Now standard linear control theory can be applied. The response of the linear system is governed by the eigenvalues of the system matrix, and the eigenvalues of the system matrix determine the control force. We use the following design procedure to find a suitable control force. Choose a set of eigenvalues for the linear system. Compute the corresponding control force. Simulate the nonlinear system using the computed control and evaluate the response. Repeat until all design criteria are satisfied." @default.
- W173637820 created "2016-06-24" @default.
- W173637820 creator A5078203945 @default.
- W173637820 date "1997-01-01" @default.
- W173637820 modified "2023-09-27" @default.
- W173637820 title "Vertical Stabilization of a Rocket on a Movable Platform" @default.
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