In this paper, the problem of optimal path following for a high speed planing boat is addressed. First, a nonlinear mathematical model of the boat’s dynamics is derived and then the Serret-Frenet frame is presented to facilitate the path following control design. To sat More
In this paper, the problem of optimal path following for a high speed planing boat is addressed. First, a nonlinear mathematical model of the boat’s dynamics is derived and then the Serret-Frenet frame is presented to facilitate the path following control design. To satisfy the constraints on the states and the input controls of the boat's nonlinear dynamics and minimize both the cross tracking and heading error, a nonlinear optimal controller is formed. To solve the resulted nonlinear constrained optimal control problem, the Gauss pseudospectral method (GPM) is used to transcribe the optimal control problem into a nonlinear programming problem (NLP) by discretization of states and controls. The resulted NLP is then solved by a well-developed algorithm known as SNOPT. The results illustrate the effectiveness of the proposed approach to tackle the boat path following problem.
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Abstract: A time domain semi-analytical solution to study thermoelastic creep behavior of functionally graded rotating axisymmetric disks with variable thickness is presented. The rate type governing differential equations for the considered structure are derived and an More
Abstract: A time domain semi-analytical solution to study thermoelastic creep behavior of functionally graded rotating axisymmetric disks with variable thickness is presented. The rate type governing differential equations for the considered structure are derived and analytically solved. To solve these equations, the disk is divided into some virtual sub-domains. General solution of equilibrium equations in each sub-domain can be obtained by imposing the continuity conditions at the interface of the adjacent sub-domains together with global conditions. Finally, solution in terms of rate of stress and strain is obtained. The advantage of present work, is to avoid simplifications and restrictions, which are normally associated with other creep solution techniques in the literature. Results for the stress and strain rates presented due to centrifugal force and thermal loadings for different boundary conditions. Results obtained are verified with those available in the literature for easier cases.
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