Gravity is usually neglected in the dynamic modeling and analysis of the transmission system, especially in some relatively lightweight equipment. The weight of wind turbine gearbox is up to tens of tons or even hundreds of tons, and the effects of gravity have not been explored and quantified. In order to obtain accurate vibration response predictions to understand the coupled dynamic characteristics of the wind turbine gear transmission system, a comprehensive, fully coupled, dynamic model is established by the node finite element method with gravity considered. Both time-domain and frequency-domain dynamic responses are calculated using the precise integration method with various excitations being taken into account. The results indicate that gravity has a significant impact on the vibration equilibrium position of central floating components, but the changing trends are different. Gravity does not change the composition of the excitation frequency, but will have a certain impact on the distribution ratio of the frequency components. And the high frequency vibrations are hardly affected by gravity. In addition, the load sharing coefficient is greater when gravity is taken into account, both of internal gearing and of external gearing system. When the planet gears have a certain position error in accordance with certain rules, the load sharing performance of the system will be better.

Compressible fluid flow modeling for inclined lines is a challenging phenomenon due to the nonlinearity of the governing equations and the spatial–temporal dependency of the fluid density. In this paper, the transmission line analytical model is applied to the determination of inclined compressible fluid flow's dynamics. To establish this model, an exact transcendent solution is developed by solving the Navier–Stokes equation in the Laplace domain. A transfer function approximation, allowing the fluid flow transients determination, is recovered from the exact solution using residual calculations. The error resulting from the polynomial fraction approximation of the transfer functions is circumvented through frequency response corrections for the approximation to meet the exact function steady-state behavior. The effect of gravity and fluid compressibility on the fluid flow dynamics as well as the interplay between those two factors are illustrated through the pressure and flow rate's frequency and time responses.

In this paper, the finite-time regulation problem of robot manipulators under saturated actuator inputs with position measurements only is addressed. A simple saturated finite-time proportional-derivative (PD) plus gravity compensation (PD+) controller is presented, in which the joint velocity is estimated by constructing a simple nonlinear filter. Global finite-time stability is shown by using Lyapunov stability theory and geometric homogeneity technique. The benefits of this design are that the proposed control can be easily implemented and ensures global finite-time stability with bounded control by selecting control gains a priori. Simulations and experimental results illustrate the expected performance of the proposed approach.

A new set of linearized differential equations governing relative motion of inner-formation satellite system (IFSS) is derived with the effects of J 2 as well as atmospheric drag. The IFSS consists of the “inner satellite” and the “outer satellite,” this special configuration formation endows its some advantages to map the gravity field of earth. For long-term IFSS in elliptical orbit, the high-fidelity set of linearized equations is more convenient than the nonlinear equations for designing formation control system or navigation algorithms. In addition, to avoid the collision between the inner satellite and the outer satellite, the minimum sliding mode error feedback control (MSMEFC) is adopted to perform a real-time control on the outer satellite in the presence of uncertain perturbations from the system and space. The robustness and steady-state error of MSMEFC are also discussed to show its theoretical advantages than traditional sliding mode control (SMC). Finally, numerical simulations are performed to check the fidelity of the proposed equations. Moreover, the efficacy of the MSMEFC is performed to control the IFSS with high precision.

In this paper, a very easy, numerically stable and computationally efficient method is presented, which allows the modeling and simulation of a flexible robot with high precision. The proposed method is developed under the hypotheses of flexible links having varying cross sections, of large link deformations and of time-varying geometrical and/or physical parameters of both the robot and the end-effector. This methodology uses the same approach of the modeling of rigid robots, after suitably and fictitiously subdividing each link of the robot into sublinks, rigid to the aim of the calculus of the inertia matrix and flexible to the aim of the calculus of the elastic matrix. The static and dynamic precision of the method is proved with interesting theorems, examples and some experimental tests. Finally, the method is used to model, control, and simulate a crane, composed of three flexible links and a cable with varying length, carrying a body with a variable mass.

We have developed an advanced magnetic suspension and balance system (MSBS), in which iron yokes are not used and a pair of strong magnets are installed to generate magnetic force compensating gravitational force applied to the aerodynamic models. By the introduction of these strong magnets, the electric power saving was realized. By not using iron yokes, not only the weight saving was realized but also the electrical response speed was increased due to the reduction of the inductance of the magnetic coils. The test section of the MSBS is 36 cm × 40 cm. We have developed the control method to support the model and give an arbitral movement of small amplitude at the center of the test section around five axes. In order to evaluate the characteristics of this MSBS, we performed the calibration tests of magnetic forces for our MSBS. We measured drag coefficients of a sphere aerodynamic model in order to confirm the performance of these MSBSs and had good agreements between the measured values and the values appeared in the common aerodynamic hand book. The MSBS has been studied and used in large scale laboratories. We think that these experimental results make the application of the MSBS into the wind tunnel experiment easier and can be the trigger to popularize it in small laboratories.

This paper presents a method of estimating road angles using state observers and three types of sensors (lateral acceleration sensors, longitudinal velocity sensors, and suspension displacement sensors). The proposed method differs from those in most existing literature in three aspects. First, a “full-state” vehicle model is used to describe nonlinear vehicle dynamics on a sloped road. Second, “switching observer” techniques are used to suggest suitable sensors and to construct state observers. Lastly, the road angles are described by three Euler angles, and two of them are estimated simultaneously. The analysis indicates that (1) road angles affect vehicle dynamics through components of the gravitational force acting on the vehicle body. These gravitational forces can be correctly estimated with an estimation accuracy less than 7.5%, even when road angles vary with time. (2) Those road angles can be correctly estimated only when the vehicle yaw angle is known.

This paper presents a practical method for automatic tip-over prevention and path following control of a redundant nonholonomic mobile modular manipulator. According to modular robot concept, the mobile platform is treated as a special module attached to the base of the modular manipulator, then an integrated structure is constructed and its dynamic modeling is performed. A new tip-over stability criterion based on the supporting forces is proposed in consideration of inertia, gravity, and acceleration. An online fuzzy logic (FL) self-motion planner and an adaptive neural-fuzzy controller (ANFC) are presented: The former is used to generate desired self-motions in a real-time manner, and the latter is used to prevent the robot from tipping over and to control the end-effector to follow a desired spacial trajectory at the same time. The proposed algorithm does not need any a priori knowledge of dynamic parameters and can suppress bounded external disturbances effectively. Simulation results for a real robot validate the dynamic modeling method and the controller design algorithm.

Studies on motion control of robot manipulators with elastic joints are basically aimed at improving robot performance in tracking or regulation tasks. In the interaction between robots and environment, instead, the main objective of a control strategy should be the reduction of the vibrational and chattering phenomena that elasticity in the robot joints can cause. This work takes into account working environments where unexpected interactions are experienced and proposes a compliance control scheme in the Cartesian space to reduce the counter effects of elasticity. Two theoretical formulations of the control law are presented, which differ for the term of gravity compensation. For both of them the closed-loop equilibrium conditions are evaluated and asymptotic stability is proven through the direct Lyapunov method. The two control laws are applied to a particular class of elastic robot manipulators, i.e., cable-actuated robots, since their intrinsic mechanical compliance can be successfully utilized in applications of biomedical robotics and assistive robotics. A compared experimental analysis of the two formulations of compliance control is finally carried out in order to verify stability of the two closed-loop systems as well as the capability to control the robot force in the interaction.

We present a new technique for multi-axis force/torque sensor calibration called shape from motion. The novel aspect of this technique is that it does not require explicit knowledge of the redundant applied load vectors, yet it retains the noise rejection of a highly redundant data set and the rigor of least squares. The result is a much faster, slightly more accurate calibration procedure. A constant-magnitude force (produced by a mass in a gravity field) is randomly moved through the sensing space while raw data is continuously gathered. Using only the raw sensor signals, the motion of the force vector (the “motion”) and the calibration matrix (the “shape”) are simultaneously extracted by singular value decomposition. We have applied this technique to several types of force/torque sensors and present experimental results for a 2-DOF fingertip and a 6-DOF wrist sensor with comparisons to the standard least squares approach.

In this paper, we study the boundedness of the Jacobian of the gravitational force vector of serial link robot manipulators with respect to the generalized coordinate vector. The uniform bound of this matrix plays an important role in the stability analysis and design of many control systems. In order to insure the existence of a uniform bound, it is typically assumed that manipulators under consideration have only revolute joints. We therefore propose a larger class of manipulators, referred to as class BD manipulators, for which a uniform bound exists. This bound can easily be computed using basic link parameters including the link masses, the Denavit-Hartenberg link parameters, and the link center of mass locations.

The unperturbed (fully nonlinear) stability of a magnetic bearing-rotor system having a single central backup bearing near the middle of the shaft is analyzed under conditions of magnetic bearing(s) failure for zero gravity using the Lyapunov second (direct) method; these results are shown to apply with gravity, based on observed similiaries of the nonlinear Lagrangian equations. These are completely general stability criteria for practical values of system parameters and conditions of system operation and failure. It turns out that the center-backup bearing configuration has some considerable advantages over conventional designs: in addition to known results for stability and instability, the system can be stable when one or both magnetic bearings fail (has negative stiffness). This “temporary stability” depends upon inherent gyroscopic forces and may be lost when dissipative forces are introduced. The results are applicable to other gyroscopic systems.

The dynamic manipulability ellipsoid is a common tool in robotics to measure the ability of a manipulator to produce arbitrary accelerations of the end-effector for a given set of torques at the joints. This article is intended to demonstrate that for a robot arm, when gravitational forces (due to arm and payload) are properly embedded into the derivation of the ellipsoid, these do not cause a compression in the volume of the ellipsoid, as stated in the original approach, but they just produce a translation of the ellipsoid which in general occurs along all task space directions. Further, we characterize the ellipsoid for redundant manipulators by investigating the properties of the manipulator Jacobian involved in the core of the ellipsoid. Numerical case studies are developed.

This paper proposes an actuator in the magnetic levitation system using a permanent magnet and an electromagnet. In this system, the gravity force of the masses is supported by a strong permanent magnet in which two identical poles face each other. The vibration due to external disturbances is controlled by use of the electromagnet by changing magnetic fluxes of one of the permanent magnets. The analytical expressions for obtaining the levitation force, spring constant, and the control force versus the electric current in the electromagnet were derived using the equation of the electromagnetic theory. Numerical simulations under the control using the optimal regulator for the magnetically levitated body were carried out. To verify the present theoretical results, experimental results were also obtained.

This work deals with two stochastic planar pursuit-evasion differential games where the pursuer is subject to constraints on its control magnitude and its control energy, whereas the evader is subject only to a magnitude constraint on its control. In the first game the motion of the players is confined to the horizonal plane, while in the second their motion is confined to the vertical plane. In both games, owing to thrust, drag, and gravitational forces, the pursuer has a variable speed. The treatment is concerned mainly with the question of how far a certain type of proportional navigation guidance law is a good approximation to an optimal feedback pursuit strategy.

Lyapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which “rocks” the pendulum out of its potential wells, in order to stabilize it at a unique vertical position. Simulation results indicate that a preliminary Lyapunov feedback controller can successfully overcome the nonlinearity and bring almost all trajectories to the target.

A spherical DC servo motor with three degrees of freedom is proposed. First, the process of generating three-dimensional torque is analyzed to obtain the torque constant matrix. The matrix elements are shown to vary with rotor inclination, and winding currents are shown to interfere with each other. Then, the dynamics of the spherical motor are investigated theoretically and experimentally, considering torque interference, gyro moment and gravity. Finally, the trajectory of the prototype motor is shown in order to clarify its abilities. This new spherical motor is expected to produce a smaller, a lighter mechanism, since no gears or linkages are needed.

This paper is concerned with the digital implementation and experimental evaluation of two adaptive controllers for robotic manipulators. The first is a continuous time model reference adaptive controller, and the second is a discrete time adaptive controller. The primary purpose of these adaptive controllers is to compensate for inertial variations due to changes in configuration and payload, as well as disturbances, such as Coulomb friction and/or gravitational forces. Experimental results are obtained from a laboratory test stand, which emulates an one-axis direct drive robot arm with variable inertia, as well as a Toshiba TSR-500V industrial robot. Experimental results from the test stand indicate that these adaptive control schemes are promising for the control of direct drive robot arms. Friction forces arising from the harmonic gear of the Toshiba robot were detrimental if not properly compensated. Because of a high gearing ratio, the advantage of adaptive control for the Toshiba arm could be shown only by detuning the controller.

A mathematical model and digital computer simulation of the human cardiovascular system and its controls are developed to simulate transient responses to bicycle ergometer exercise. The purpose of the model is to provide a method to analyze cardiovascular control hypotheses which cannot be tested easily in an animal or human. Complex cardiovascular control hypotheses are modeled for the control of heart period, peripheral flow resistances, venous tone, and other controlled variables. Control models are based on the use of proportional neurogenic controllers and linearized systems. Metabolic control models utilize simple mathematical models of oxygen uptake, oxygen deficit, and accumulating metabolites to simulate a transient metabolic state and indicate other chemical factors. Equations describing pulsatile blood flows, pressures, and volumes for 28 model sections of the uncontrolled cardiovascular circulatory system are solved. The circulatory system model is combined with the models of the controlling systems to simulate transient responses to exercise. Other characteristics of the combined model include gravity effects, muscle pumping, venous tone, venous valves, respiratory frequency, and intrathoracic pressure effects. Transient response characteristics and steady model values are presented and compared with experimental data. It is concluded that the neurogenic proportional controller hypothesis, combined with the metabolic control factors, can simulate sub-maximal exercise responses.

The time-optimal control of a system of rigid bodies connected in series by single-degree-of-freedom joints is studied. The dynamical equations of the system are highly nonlinear, and a closed-form representation of the minimum-time feedback control is not possible. However, a suboptimal feedback control, which provides a close approximation to the optimal control, is developed. The suboptimal control is expressed in terms of switching curves for each of the system controls. These curves are obtained from the linearized equations of motion for the system. Approximations are made for the effects of gravity loads and angular velocity terms in the nonlinear equations of motion. Digital simulation is used to obtain a comparison of response times of the optimal and suboptimal controls. The speed of response of the suboptimal control is found to compare quite favorably with the response speed of the optimal control.