This paper presents a new method of steady-state flow analysis in a water distribution network. First, a new model, which fully reflects the real state that quantities of water are withdrawn from the network at points along its links, is proposed. Second, outflows can be made possible to be given as functions of pressures. The formulated problem is solved by the Newton-Raphson method. Despite the existence of numerous demand points, only the heads at nodes where pipes meet are chosen as unknowns. In consequence, analysis using an acculate model of outflows is made possible without augmenting the practical scale of the problem.
The purpose of our research is to analyze stability of a geometrically controlled biped. The biped is planar and is composed of five links. Telescopic knee joints are employed to avoid the foot clearance problem. The ankle is not actuated then the robot is underactuated in single support phase. A geometric evolution of the biped configuration is controlled, instead of a temporal evolution. The input-output linearization with a PD control law and a feed forward compensation is used for geometric tracking. The temporal evolution is analyzed using Poincare map. The map is given by an analytic expression based on the angular momentum around the contact point. As a result, the radius of the circular arc foot affects to stability of walking, and speed of convergence decreases when the radius increases. Moreover a basin of attraction is broadened by choosing larger radius among the stable cyclic motion. Finally we discuss relationships of stability properties between the controlled system and passive dynamic walking.
A class of convolution operators on fixed interval with initial values is considered. The numerical computation of its spectra is attempted via a finite-dimensional approximation so-called fast sampling and hold. In contrast to the case of matrices, the spectrum of an operator is not continuous against small perturbations in general. This implies that a fine approximation does not necessarily lead to better estimates close to the true values. Therefore, one must provide a mathematical justification of the procedure depending on the operator of interest. In this paper, continuity of the spectrum of the convolution operator described above is proved and a numerical computation formula for the calculation of its eigenvalues is given.
This paper presents control system synthesis of providing a balance between safety and control performance according to the international standard on safety, IEC 61508. As a result, the existence of a trade-off between them is established quantitatively for the first time ever.