Force Control Compensation Method with Variable Load Stiffness and Damping of the Hydraulic Drive Unit Force Control System

Each joint of hydraulic drive quadruped robot is driven by the hydraulic drive unit（HDU）, and the contacting between the robot foot end and the ground is complex and variable, which increases the difficulty of force control inevitably. In the recent years, although many scholars researched some control methods such as disturbance rejection control, parameter self-adaptive control, impedance control and so on, to improve the force control performance of HDU, the robustness of the force control still needs improving. Therefore, how to simulate the complex and variable load characteristics of the environment structure and how to ensure HDU having excellent force control performance with the complex and variable load characteristics are key issues to be solved in this paper. The force control system mathematic model of HDU is established by the mechanism modeling method, and the theoretical models of a novel force control compensation method and a load characteristics simulation method under different environment structures are derived, considering the dynamic characteristics of the load stiffness and the load damping under different environment structures. Then, simulation effects of the variable load stiffness and load damping under the step and sinusoidal load force are analyzed experimentally on the HDU force control performance test platform, which provides the foundation for the force control compensation experiment research. In addition, the optimized PID control parameters are designed to make the HDU have better force control performance with suitable load stiffness and load damping, under which the force control compensation method is introduced, and the robustness of the force control system with several constant load characteristics and the variable load characteristics respectively are comparatively analyzed by experiment. The research results indicate that if the load characteristics are known, the force control compensation method presented in this paper has positive compensation effects on the load characteristics variation, i.e., this method decreases the effects of the load characteristics variation on the force control performance and enhances the force control system robustness with the constant PID parameters, thereby, the online PID parameters tuning control method which is complex needs not be adopted. All the above research provides theoretical and experimental foundation for the force control method of the quadruped robot joints with high robustness.

Multi-Channel Force Control System for Static Loading

An eight-channel force loading system is presented, which adopts position control system and force control system switching model, small flow servo valve controlled capacious cylinder system scheme, intelligent PID algorithm and distributed load approach. Through the analyses of the equivalent model of valve controlled cylinder force subsystem, a controller based on intelligent PID algorithm is designed, which is not sensitive to the variation of parameters such as environmental stiffness. According to the coupling of multiple load channels, a distributed load approach is employed in the superior monitor computer. Experimental results show that the system designed has high precision and robustness.

Theoretical study of the nonlinear force-loading control in single-molecule stretching experiments

Force spectrum measurements with constant loading rates are widely used in single-molecule manipulation experiments to study the mechanical stability and force response of biomolecules.Force-dependent transition rates can be obtained from the transition force distribution,but it is limited to the force range with non-zero force distribution.Although constant loading rate control can be realized with magnetic tweezers,the loading rate range is limited due to the slow movement of permanent magnets.Non-linear exponential and exponential squared force loading functions are more feasible in magnetic tweezers,while there is no theoretical result available for these two kinds of non-linear force loading functions.In this study,we solved the unfolding process of a protein following Bell's model under nonlinear exponential and exponential squared force loading functions,which offer a broader range of unfolding force distribution compared to the traditional constant loading rate experiments.Furthermore,we derived two force loading functions,which can produce uniform unfolding force distribution.This research contributes fundamental equations for the analysis of experimental data obtained through single-molecule manipulation under nonlinear force loading controls,paving the way for the use of nonlinear force control in magnetic tweezer experiments.

Cumulative Deformation of Soft Clay Under Cyclic Loading

Reconstituted specimens are prepared by means of vacuum preloading. Both static and cyclic triaxial tests are carried out, with the specimens consolidated under different principal stress ratios. A finite element method is put forward for calculating the cumulative deformation of soft clay under cyclic loading.

Test Study on Current Force on Mooring Ships

In respect of an offshore berthing pillar, the test study result of current force acting on mooring ships is described in this paper. Empirical and semi-empirical relationships of current force coefficient are given according to the angle between the flow direction and the ship's longitudinal axis, which are coincident with the result of theoretical analysis.

NON-LINEAR DYNAMIC BEHAVIOR OF THERMOELASTIC CIRCULAR PLATE WITH VARYING THICKNESS SUBJECTED TO NONCONSERVATIVE LOADING

The non-linear dynamic behaviors of thermoelastic circular plate with varying thickness subjected to radially uniformly distributed follower forces are considered. Two coupled non-linear differential equations of motion for this problem are derived in terms of the transverse deflection and radial displacement component of the mid-plane of the plate. Using the Kantorovich averaging method, the differential equation of mode shape of the plate is derived, and the eigenvalue problem is solved by using shooting method. The eigencurves for frequencies and critical loads of the circular plate with unmovable simply supported edge and clamped edge are obtained. The effects of the variation of thickness and temperature on the frequencies and critical loads of the thermoelastic circular plate subjected to radially uniformly distributed follower forces are then discussed.

Dynamic Response Analysis of Risers Subjected to Combined Wave and Current Loading

A dynamic response analysis in the frequency domain is presented for risers subjected to combined wave and current loading. Considering the effects of current, a modified wave spectrum is adopted to compute the linearized drag force. An additional drag force convolution term is added to the linearized drag force spectrum, therefore the error is reduced which arises from the truncation of higher order terms in the drag force auto-correlation function. An expression of linearized drag force spectrum is given taking the relative velocity into account. It is found that the additional term is a fold convolution integral. In this paper dynamic responses of risers are investigated, while the influence of floater motion on risers is considered. The results demonstrate that the accuracy of the present method reaches the degree required in time domain analysis.

Implementation of Particle Swarm Optimization Algorithm in Matlab Code for Hyperelastic Characterization

The purpose of this paper is to demonstrate the applicability of Particle Swarm Optimization algorithm to determine material parameters in incompressible isotropic elastic strain-energy functions using combined tension and torsion loading. Simulation of rubber behavior was conducted from the governing equations of the deformation of a cylinder composed of isotropic hyperelastic incompressible materials. Four different forms of strain-energy function were considered based respectively on polynomial, exponential and logarithmic terms to reproduce load force (N) and torque (M) trends using natural rubber experimental data. After highlighting the minimization of the objective function generated in the fitting process, the study revealed that a particle swarm optimization algorithm could be successfully used to identify the best material parameters and characterize the behavior of rubber-like hyperelastic materials.

Investigation of Micro-mechanical Response of Asphalt Mixtures by a Three-dimensional Discrete Element Model

The micro-mechanical response of asphalt mixtures was studied using the discrete element method. The discrete element sample of stone mastic asphalt was generated first and the vehicle load was applied to the sample. A user-written program was coded with the FISH language in PFC3 D to extract the contact forces within the sample and the displacements of the particles. Then, the contact forces within the whole sample, in asphalt mastic, in coarse aggregates and between asphalt mastic and coarse aggregates were investigated. Finally, the movement of the particles in the sample was analyzed. The sample was divided into 15 areas and a figure was drawn to show how the balls move in each area according to the displacements of the balls in each area. The displacements of asphalt mastic balls and coarse aggregates were also analyzed. The experimental results explain how the asphalt mixture bears vehicle load and the potential reasons why the rutting forms from a micro-mechanical view.

Local Joint Flexibility Multibrace Tubular Joints

The local joint flexibility matrix of multibrace tubular joints (uniplanar and multiplanar joints) is defined. The formulation for computing the elements of local flexibility factor matrix of multibrace tubular joints by semi-analytic method is presented in this paper. The stiffening effect of unloaded braces and cross-flexibility between braces are discussed. Using the local flexibility of unibrace joints instead of that of multibrace joints in conventional structural analysis will lead the result to an unsafe side.

Structural Analysis of Platforms with the Effect of Joint Flexibility

A modified space beam element is presented in this paper to consider the local joint flexibility of T, Y tubular joints subjected to axial forces and in-plane bending moments for analysis of platforms. Two numerical examples are shown to verify the efficiency and validity of the method presented here.

EXPERIMENTAL STUDIES ON DYNAMIC PROPAGATION OF CRACKS UNDER BIAXIAL COMPRESSION

This paper deals with the initiation and non-coplaner propagation of cracks under biaxial compression. The running process of the propagating cracks is successfully recorded with the method of dynamic photoelasticity. A series of important fracture parameters such as cracks propagating velocity, critical opening loading and initial angle of cracks growth under biaxial compression is calculated. Results show that the stress field in front of the non-closed crack tip under biaxial compression is a mixed-mode singular field, the dynamic propagation of the new tensile cracks is just stable and shows distinct stages, but the unstable crack appears under high loads and results in the rupture of the matrix.

DAMAGE ANALYSIS BY BOUNDARY ELEMENT METHOD

The response of cracked bodies subjected to loading was investigated by the boundary element method in this paper. The two-law elastic-cohesive-softening model was used for crack propagation analysis. The interface conditions for uncracked, craze, open crack, adhesive crack and slid crack parts were discussed and the corresponding incremental iteration algorithm was given. A simplified damage propagation model was presented. The technique has been applied to some specific examples which give the evidence that the method is satisfactory and efficient.

TIME-DOMAIN SOLUTIONS FOR HYDRODYNAMIC FORCES AND MOMENTS ACTING ON A 3-D BODY MOVING IN WAVES

In this paper, based on transient free-surface Green function and panel method, accurate wave exciting forces and moments acting on an arbitrary 3-D body moving at constant forward speed are given by using a time domain algorithm under the condition of a linearized free surface.

VERIFICATION AND COMPARISON OF FORMULAS FOR BED LOAD TRANSPORT

Several typical formulas for bed load transport are examined based on field data. It is concluded that the Einstein formula provides good estimates for the bed load transport rate while other ones predict much lower transport rates. The main reason for the under-prediction is that Dp, the effective diameter of particles, is too large as a representative diameter of the bed material for gravel streams with partially movable bed. Performance of these formulas can be significantly improved if D35 is adopted instead of Dp.

EXPERIMENTAL STUDY ON THE SECOND-ORDER DIFFRACTION WAVE PRESSURE AND FORCE ON A CIRCULAR CYLINDER UNDER STOKES WAVE ACTION

This paper presents the model test to measure the second-order wave pressure and forces on a circular cylinder fixed in Stokes wave with a given draught. The distributions of second-order oscillating and steady wave pressure on the wet surface of the cylinder and second order oscillating wave forces were obtained in this test, but the second-order steady wave force was not able to be measured due to its very small magnitude. The test results also show that third-order wave force may be greater than the second-order force when wave frequencies are high. The experimental results were compared with the corresponding calculation results of Reference [3].

Aerostatic Stability of Long-Span Cable-Stayed Bridges: Parametric Study

This paper presents a method to analyze the nonlinear aerostatic stability of cable-stayed bridges including all three components of the wind load and the geometric nonlinearity. The analysis was used to investigate the effects of the wind angle of incidence, the wind load of individual bridge elements, the sagging of cable elements, the changes of tower height and the changes of side span length on the aerostatic stability of cable-stayed bridges. The results show that the wind angle of incidence and the wind loads on the cables have an important effect on the aerostatic stability of cable-stayed bridges.