Reactive control of a two-body point absorber using reinforcement learning

In this article, reinforcement learning is used to obtain optimal reactive control of a two-body point absorber. In particular, the Q-learning algorithm is adopted for the maximization of the energy extraction in each sea state. The controller damping and stiffness coefficients are varied in steps, observing the associated reward, which corresponds to an increase in the absorbed power, or penalty, owing to large displacements. The generated power is averaged over a time horizon spanning several wave cycles due to the periodicity of ocean waves, discarding the transient effects at the start of each new episode. The model of a two-body point absorber is developed in order to validate the control strategy in both regular and irregular waves. In all analysed sea states, the controller learns the optimal damping and stiffness coefficients. Furthermore, the scheme is independent of internal models of the device response, which means that it can adapt to variations in the unit dynamics with time and does not suffer from modelling errors

Derivation of the stiffness terms for a multi-cable spreader suspension system with stiff elastic cables

At its simplest a multi-cable spreader suspension system consists of a rectangular spreader suspended below a rectangular trolley by four cables of equal length. These four cables are attached to the corners of the spreader and when the system is in its undisturbed configuration they are all vertical, and consequently parallel. If we insist that all the cables are inextensible and remain taut then in the case of combined translation and rotation of the spreader this is not a well defined problem because it represents an over-determined system. In fact, if the cables are inextensible then one of them will go slack in the case of combined translational and rotational motions. As an alternative approach we can assume that the cables stretch slightly and this is the modelling strategy adopted here. That is, in this paper we present the initial development of an analytical model of a multi-cable spreader suspension system where the four cables are approximated by linear elastic cables of high stiffness k. To be more specific, we derive the fundamentally all-important stiffness terms in the equations of motion for the above problem

The implementation of an automated method for solution term-tracking as a basis for symbolic computational dynamics

This article proposes that additional mathematical information, inherent and implicit within mathematical models of physical dynamic systems, can be extracted and visualized in a physically meaningful and useful manner as an adjunct to standard analytical modelling and solution. A conceptual methodology is given for a process of term-tracking within ordinary differential equation (ODE) models and solutions for engineering dynamics problems, and for a visualization based on a powerful new Mathematica implementation of the standard Tooltip graphical user interface facility. It is shown that the method is logical, generic, and unambiguous in its application, and that a useful visualization tool can be devised, and structured in such a way that the user can be given as much or as little information as is required to assimilate the problem to hand. The article shows by means of examples of code written expressly for the purpose that a term-tracking and visualization methodology can be constructed in a computationally effective manner within Mathematica and applied to a semi-automated variant of the method of multiple scales. It is implicitly obvious that this approach can therefore be applied to almost any algorithmic symbolic solution method, and therefore there could be physical applications which are potentially well beyond the chosen domain of non-linear engineering dynamics

The theory and application of a classical Eulerian multibody code

The topic of multibody analysis deals with the automatic generation and subsequent solution of the equations of motion for a system of interconnected bodies. Many academic and industrial computer programs have been developed to carry out this task. However, although some of these programs can obtain the equations of motion in fully symbolic form, it is believed that all the existing programs for multibody analysis solve these equations numerically. The idea behind the research which underpins this paper is to select and implement a symbolic version of an existing multibody algorithm and then to integrate it with a recently developed solver which can obtain approximate analytical solutions to the equations of motion. The present paper deals with the selection of this multibody method. The theory behind the chosen method (the Roberson and Schwertassek algorithm) is described in some detail but also in a much more concise form than can be found in the literature. In addition, a fully worked example of the application of the multibody algorithm to a practical physical problem is given. Such examples are rare in the literature, and so it is intended that this paper can serve as a basis for enhanced didactic practice in this traditionally difficult subject are

A Lagrangian multibody code for deriving the symbolic state-space equations of motion for open-loop systems containing flexible beams

In this study, the development of a symbolic multibody code is described. This code uses Lagrange’s equations to derive automatically the state-space equations of motion, in relative coordinates, for open-loop systems made up of rigid bodies and flexible Timoshenko beams. The algorithm is then encoded in Mathematica as the package MultiFlex.m and the straightforward application of MultiFlex to two examples with 1 degree of freedom and 14 degrees of freedom, respectively, is presented. The MultiFlex package represents one part of a suite of programs which are being developed by the authors in order to provide entirely symbolic analysis of multi-degree of freedom problems in engineering dynamic

On the derivation of the equations of motion for a parametrically excited cantilever beam

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