This study determines the threshold for the computational rate of actuator motor controllers for unmanned underwater vehicles necessary to accurately follow discontinuous square wave commands. Motors must track challenging square-wave inputs, and identification of key computational rates permit application of deterministic artificial intelligence (D.A.I.) to achieve tracking to a machine-precision degree of accuracy in direct comparison to other state-of-art approaches. All modeling approaches are validated in MATLAB simulations where the motor process is discretized at varying step-sizes (inversely proportional to computational rate). At a large step-size (fast computational rate), discrete D.A.I. shows a mean error more than three times larger than that of a ubiquitous model-following approach. Yet, at a smaller step size (slower computational rate), the mean error decreases by a factor of 10, only three percent larger than that of continuous D.A.I. Hence, the performance of discrete D.A.I. is critically affected by the sampling period for discretization of the system equations and computational rate. Discrete D.A.I. should be avoided when small step-size discretization is unavailable. In fact, continuous D.A.I. has surpassed all modeling approaches, which makes it the safest and most viable solution to future commercial applications in unmanned underwater vehicles.
This chapter will introduce the space environment satellites must operate in, the motion they make in orbit, and their orientation while in orbit. The forces acting on the spacecraft will be considered, along with the implications of conservation of energy. The fundamentals of orbital mechanics will be presented, so common orbits can be visualized and discussed in terms of the six classical orbital elements. Perturbations impacting the orbit are covered for a better understanding of how orbits change over time. The inertial frame of reference will be defined and then transformed into body coordinates of the satellite using the direction cosine matrix and quaternions to describe the attitude of the spacecraft. A variety of modern attitude control techniques will be developed in the following chapters.
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