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Optimal trajectory planning problems are often formulated as constrained variational problems. In general, solutions to variational problems are determined by appropriately discretizing the underlying objective functional and solving the resulting nonlinear differential equation(s) and/or nonlinear programming problem(s) numerically. These general solution techniques often require a significant amount of time to be computed, and therefore are of limited value when optimal trajectories need to be frequently computed and/or recomputed. In this paper, a realistic class of optimal trajectory planning problems is defined for which the existence of fast numerical solution techniques are demonstrated. To illustrate the practicality of this class of trajectory planning problems and the proposed solution techniques, three optimal trajectory planning problems for spray coating applications are formulated and solved. Based on the proposed discretization technique, it is shown that these problems can be reduced to either a linear program or a quadratic program, which are readily solved. In contrast, using the standard discretization of these problems generally leads to nonconvex nonlinear programming problems that require a significant amount of computation to arrive at a (possibly) locally optimal solution. Index Terms - Optimization, spray coating, trajectory planning.

The classic cascaded boost–buck converter has inductors at the input and output ports of the converters, which makes it an ideal interface for bidirectional battery charging applications, where accurate current control and low ripple currents are required. This article proposes a split duty cycle coupled multiphase variant applied to the cascaded boost–buck converter and utilizes coupled inductor features to achieve very lower current ripples at the output, lower power losses, and reduction in magnetic component volume. Moreover, current sharing between each phase is inherently implemented, making it suitable for a high-conversion-ratio bidirectional operation in systematic energy storage applications, where the low-voltage port has very high current. This article covers a split duty cycle converter operation principle using coupled inductors between the input and the multiphase output. Magnetic component design and selection guidelines are presented. The proposed control method and the coupled inductor structure are validated by simulation and experimental results. [ABSTRACT FROM AUTHOR]