• Energy Research

Saving energy is one of the main topics of discussion in the modern world due to the limitation of energy resources and the deterioration of the environment on earth. It is, therefore, timely to consider saving the dissipative energy in a manipulator system in PTP motion control.This paper deals with the determination of the optimal trajectory which can minimize the dissipative energy in actuators of a horizontally articulated manipulator. The dissipative energy is dependent on the operating time and the angular functions of the joints. First it is proved that each optimal angular function is anologous, even for different operating times, and that the dissipative energy is inversely proportinal to the cube of the operating time. When obtaining the optimal angular functions by solving the two-point-boundary-value problem with non-linearity, it is essential to select a good starting function for the angles so that the solution does not fall into a local minimum. Therefore this paper proposes a starting function so that the driving currents of the joints can be reduced. The simulations show that the optimal trajectory based on the proposed starting function is effective in saving energy.

Abstract : A 14-month program is described which culminated in fabrication and limited flight tests of a cockpit meter instrumentation system displaying aircraft specific energy and energy rate (specific excess power). Detailed account is given of the analysis and design processes, including man-in-the-loop hybrid simulation and display, through which the meter and its uses were developed. Preliminary flight test results are also cited.

Abstract The problem of cooperative optimization of trajectory and main design parameters of spacecraft, equipped with propulsion systems with energy accumulation, during low Earth orbit formation and correction in non-central gravitational field is considered. The working principle of these propulsion systems is a periodic cycle of energy accumulation from the energy source at the passive stages of orbital transfer, and its discharge to supply power to the engine during the active stages of orbital transfer. The special characteristics of propulsion systems with energy accumulation is limited operation time per one switching, which determines by the energy, stored in an accumulator. For design-ballistic analysis, the mass model of the spacecraft with an uncontrollable power-limited engine with energy accumulator is used. The general problem is separated into dynamic and parametric parts. Using averaging mathematical models of motion and Pontriagin's maximum principle, the calculation method of the ballistic characteristics of approximately-optimal orbital transfer is obtained. The method of design-ballistic optimization is obtained as an iterative procedure. It was found, that inclusion of an energy accumulator in a propulsion system provides an increasing of orbital transfer efficiency.

Abstract : The object of this study is to find the trajectories which a high performance aircraft would employ to maximize the change in specific energy during a prescribed turn. These values of the change in specific energy are compared to the changes in specific energy which result from a minimum time turn. A suboptimal control approach, which uses both gradient and second-order techniques, is employed to find the maximum specific energy trajectories. The results of the study show that turning times slightly greater than the minimum turning time allow large increases in aircraft specific energy, and that the trajectories can be flown with simple control inputs. (Author)

The efficiency with which any system uses available energy is often an important measure of the performance of that system. Rockets operate by transforming carried energy of various forms into useful kinetic energy of the payload portion of the vehicle. The efficiency of this transformation is usually not examined in favor of maximizing the change in velocity, V, of the rocket vehicle. However, missions such as launch vehicles, interplanetary missions or other complex trajectories where the initial mass of the vehicle is a large economic driver may benefit from more efficiently expending the energy that is required to be carried. A review of rocket propulsion efficiency is presented. Various definitions of efficiency are discussed such as optimizing the end kinetic energy of the vehicle as a function of mass ratio or optimizing the end kinetic energy as a function of total energy carried. It is shown through derivations of the V equation with changing exhaust velocity during the rocket operation that increases in V may be achieved over the constant exhaust velocity case. For a given amount of propellant energy the optimum manner in which propellant should be expelled is discussed. The potential magnitude of the increase in V is shown through example calculations. The discussion is expanded to a volume limited chemical rocket system where the exhaust velocity depends on the mixture ratio of the oxidizer and fuel. Increases in V are shown by example calculations with various restrictions on propellant loading.

In this article, a description of the kinetic energy partition values (or energy ratios) of serial chain mechanisms, as well as their rates of change, are presented. These energy ratios are indicators of the kinetic energy distribution within the system and they exploit the structure of the effective inertia matrix. The rates of change of the kinetic energy partition values with respect to the input parameters of the system indicate the sensitivity of change of the kinetic energy, meaning that a high value for the partition value rate of change together with a high operational state implies that the amount of kinetic energy flowing in the system is large further implying a loss of precision in the system due to large inertial torques applied about the joint axes. Two design criteria, one based on the kinetic energy partition values and another based on their rates of change, are presented. A two degree-of-freedom (DOF) mechanism is used to illustrate the solution of a multi-criteria design optimization problem where three design criteria are considered: a kinetic energy partition value criterion, a force capability criterion and an effective mass criterion. The design variables for the optimization problem are the transmission reduction ratios of the actuators. It is shown that the reduction ratios significantly influence the kinetic energy distribution within the system due to the high levels of kinetic energy in the rotary mass of the prime movers.

The mass and energy expended during the transfer of a space vehicle from one orbit to another depend both on the magnitude of the orbital change and on the spacecraft propulsion variables. In the present paper the optimum time behaviour of these variables is investigated: that is, those functions which maximize the residual mass of the spacecraft, or which minimize the total energy required for a given total equivalent velocity change. It is found that an optimum relation exists between the flow of mass and of energy, and that, provided this condition is satisfied, the results depend only on the total energy supplied, and not on the way it is released. The optimum functions and maximum mass ratios derived in the paper apply in the general case where the efficiency of the propulsion system varies with exhaust velocity, and when the ejected mass possesses intrinsic energy in addition to that supplied from a separate source. Formulae are also developed for the maximization of the useful or disposable mass, and various examples are given.

In the hyperspherical coordinates, by using splines as basis functions we can accurately calculate the energy levels of helium. Unlike the standard configuration-interaction (CI) method and the modified configuration-interaction (MCI) method [S. P. Goldman, Phys. Rev. Lett. 73, 2541 (1994)], which involve two-dimensional integrations, our method involves only one-dimensional integrations. Also, given the excellent numerical properties of B splines, we are able to obtain the ground-state energy of helium, using only double precision calculations, with relative errors of 3.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$, which is almost 3 orders of magnitude better than the usual CI method.