Model reduction of porous-media problems using proper orthogonal decomposition

In the context of finite-element simulations of porous media, computing time and numerical effort is an important issue because the number of degrees of freedom of such coupled problems can become very large. Following this, model reduction plays an important role. A broad variety of materials exhibit a porous microstructure. In order to evaluate the overall response of these materials, a macroscopic continuum-mechanical modelling approach is used. Therefore, the complex inner structure of porous media is regarded in a multi-phasic and multi-component manner by means of the well-founded Theory of Porous Media (TPM). The mechanical behaviour of porous media is solved using the Finite-Element Method (FEM). The basic idea of model reduction is to transform a high dimensional system, in terms of the system's degrees of freedom, to a low dimensional subspace to minimise the computational effort while maintaining the accuracy of the solution. The method of proper orthogonal decomposition (POD) can be seen as a method to approximate a given data set with a low dimensional subspace. Furthermore, the POD method is independent of the type of the model and can be used for nonlinear systems as well as for systems of second order. In several applications, such as consolidation problems of partially saturated soils, commonly occurring motion sequences can be found, which can be used as typical “snapshots” of the system. Therefore, the application of the POD method to the simulation of porous media is discussed in the present contribution. Investigated computations of a biphasic standard problem show that the POD method reduces the numerical effort to solve the linearised system of equations in each iteration step. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic Modeling and Force Control of a Redundant Robot for Polishing Applications

For many robotic applications with tasks such as cutting, assembly or polishing, it is necessary to get in contact with the surrounding. In this paper a redundant robot with seven degrees of freedom in a metal polishing task is considered. For simulation as well as for the controller design a dynamic model of the robot and a contact model are required. The equations of motion of the robot are calculated with the Projection Equation in subsystem representation and the contact model contains linear tool elasticities and work piece elasticities. In the case of a polishing task, a constant contact force during the process is required even if the robot moves along a trajectory. Thus some degrees of freedom of the robot tool center point have to be position controlled while the other ones have to be force controlled. The redundant robot offers the possibility to avoid singular positions or to maximize the available end-effector forces within the inverse kinematics and is therefore best suited for polishing large objects. The actual process forces are measured with a six axis force-torque-sensor mounted at the tool center point. These forces are used in a parallel force/position control law to achieve the desired behavior. Results from measurements of a test arrangement are presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Dynamic Model for a Hybrid Articulated Robot

The dynamic modeling of hybrid systems, consisting of flexible and rigid parts results in large partial differential equation systems (PDE). With the assumption of small deflections and the Ritz expansion the PDE can be approximated by an ordinary differential equation system (ODE) but the number of degrees of freedom is generally high. In this paper a hybrid articulated robot with 2 flexible links and 6 joints is under consideration. The joints are equipped with Harmonic Drive gears with high gear ratio but relative low stiffness. Therefore additionally degrees of freedom are introduced for the elastic deflection of the gears. The links are modeled with flexibility in two bending directions and in torsional sense. To be able to achieve structured equations the projection equation in subsystem representation is used. The projection equation is based on the momentum and the angular momentum equations of each single finite or infinitesimal body which are projected into the space of minimal coordinates and subsequently are summed up. Groups of bodies are collected to the so called subsystems with separated describing velocities. These subsystems are linked together with the kinematical chain. Because the robot is tree structured it is possible to obtain an explicit expression for the second derivatives of the minimal coordinates with a recursive scheme (O(n) efficiency). The robot is controlled with a feed forward controller and a linear PD joint controller. Simulation results and measured data are presented and compared. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Decentralized Adaptive Robust State Feedback for Uncertain Large-Scale Interconnected Systems with Time Delays

The problem of the decentralized robust control is considered for a class of large-scale time-varying systems withdelayed state perturbations and external disturbances in the interconnections. Here, the upper bounds of the delayed stateperturbations and external disturbances in the interconnections are assumed to be unknown. Adaptation laws areproposed to estimate such unknown bounds; by making use of the updated values of the unknown bounds, decentralized linear and nonlinear memoryless robust state feedback controllers are constructed. Based on Lyapunov stability theoryand Lyapunov–Krasovskii functionals, as well as employing the proposed decentralized nonlinear robust state feedback controllers, it is shown that the solutions of the resulting adaptive closed-loop large-scale time-delay system can be guaranteed to be uniformly bounded and that the states converge uniformly and asymptotically to zero. It is also shown that the proposed decentralized linear robust state feedback controllers can guarantee the uniform ultimate boundedness of the resulting adaptive closed-loop large-scale time-delay system. Finally, a numerical example is given to demonstrate the validity of the results.     

Modelling of the robotic Powerball®: a nonholonomic,underactuated and variable structure-type system

The Powerball® is the commercial name for a gyroscopic device that is marketed as a wrist exerciser. The device has a rotor with two underactuated degrees of freedom, which can be actuated by the appropriate motion of human or robot wrist axes. After the initial spin, applying the appropriate motion and torques to the housing leads to a spin-up of the rotor. Finding these torques intuitively is an easy task for human operators, but a complex task for a technical consideration, for example, in robotics.

This article's main contribution is a novel dynamic model that considers friction effects. The presented model includes all three working principles of the device: free rotor mode and both modes of rotor rolling in the housing. The work introduces models with one and two degrees of freedom actuation, both of which are suitable for laboratory control experiments. An estimation of the friction is discussed, and both the simulation and the experimental results are presented to evaluate the models.     

Nonlinear Dynamics of Marine Systems in Random Waves

The dynamics of ships or offshore structures is influenced by several different effects, some of which have a distinctly nonlinear characteristic. Even though in many situations the motion can sufficiently be described by linear models, nonlinear phenomena play a crucial role in the investigation of some more critical operating conditions: Large amplitude motions, sudden jumps in the dynamical behavior and sensitivity to the initial conditions are likely to occur under some circumstances. The response of floating systems such as moored buoys and barges in regular waves can be approximated by analytical or numerical techniques. These analyses reveal the characteristics of different periodic motions. In order to determine how these responses change under a more general forcing, the motion of floating structures under the influence of random disturbances is described by probability distributions. Different mathematical tools can efficiently be applied to models with few degrees of freedom. The localized statistical linearization used here is also promising for larger systems. Modelling aspects of offshore structures and random waves are discussed as well as the determination of probability distributions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Remarks on a Strongly Nonlinear Model for Two‐Layer Flows with a Top Free Surface

We revisit in this paper the strongly nonlinear long wave model for large amplitude internal waves in two‐layer flows with a free surface proposed by Choi and Camassa [1] and Barros et al. [2]. Its solitary‐wave solutions were the object of the work by Barros and Gavrilyuk [3], who proved that such solutions are governed by a Hamiltonian system with two degrees of freedom. A detailed analysis of the critical points of the system is presented here, leading to some new results. It is shown that conjugate states for the long wave model are the same as those predicted by the fully nonlinear Euler equations. Some emphasis will be given to the baroclinic mode, where interfacial waves are known to change polarity according to different values of density and depth ratios. A critical depth ratio separates these two regimes and its analytical expression is derived directly from the model. In addition, we prove that such waves cannot exist throughout the whole range of speeds.     

Robust state estimation and fault diagnosis for uncertain hybrid nonlinear systems

Robust state estimation and fault diagnosis are challenging problems in the research of hybrid systems. In this paper, a novel robust hybrid observer is proposed for a class of uncertain hybrid nonlinear systems with unknown mode transition functions, model uncertainties and unknown disturbances. The observer consists of a mode observer for discrete mode estimation and a continuous observer for continuous state estimation. It is shown that the mode can be identified correctly and the continuous state estimation error is exponentially uniformly bounded. Robustness to unknown transition functions, model uncertainties and disturbances can be guaranteed by disturbance decoupling and selecting proper thresholds. The transition detectability and mode identifiability conditions are rigorously analyzed. Based on the robust hybrid observer, a robust fault diagnosis scheme is presented for faults modeled as discrete modes with unknown transition functions, and the analytical properties are investigated. Simulations of a hybrid three-tank system demonstrate that the proposed approach is effective.     

基于虚拟完整约束的欠驱动起重机控制方法

欠驱动系统的控制是非线性控制的一个重要领域,欠驱动系统指系统控制输入个数小于自由度个数的非线性系统.目前,欠驱动非线性系统动力学和控制研究的主要方法包括线性二次型最优控制方法和部分反馈线性化方法等,如何使系统持续的稳定在平衡位置一直是研究的难点.虚拟约束方法是指通过选择一个周期循环变化的变量作为自变量来设计系统的周期运动.该文以典型的欠驱动模型起重机为例,采用虚拟约束方法,使系统能够在平衡位置稳定或周期振荡运动.首先,通过建立虚拟约束,减少系统自由度变量;然后,通过部分反馈线性化理论推导出系统的状态方程;最后,通过线性二次调节器设计反馈控制器.仿真结果表明,重物在反馈控制下可以在竖直位置的附近达到稳定状态,反映了虚拟约束方法对欠驱动系统的有效性.     

Stabilization of sliding motion by partial stiction

Rotating friction disks are utilized in many drivetrain components such as dry clutches and their actuator systems. Even the simplest pin-on-disk or disk-on-disk mechanical systems with Coulomb friction reveal a rich dynamical behavior with different types of motions. Examining the radial dynamics of minimal friction disk models, it is a prevalent assumption to have pure sliding frictional contacts. Governed by the systems' design parameters and initial conditions, stable large amplitude motions at higher rotation speeds are possible. Using a Coulomb friction model with sticking and sliding instead, gives similar motions with alternating phases of sticking and sliding. However, the amplitude can be decreased significantly by these intermittent phases of stick and slip. It is suggested to exploit such motions with partial stiction in order to reduce amplitudes and thus stabilize the systems. Similar effects can be observed in 3D-multibody simulations and measurements of double clutch actuator systems. However, for these systems analytical treatment is not feasible any more due to the number of involved degrees of freedom. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Robust Tracking and Model Following Control with Zero Tracking Error for Uncertain Dynamical Systems

The problem of robust tracking and model following for a class of linear dynamical systems with time-varying uncertain parameters and disturbances is considered. A class of continuous (nonlinear) state feedback controllers is proposed for robust tracking of dynamical signals. The proposed robust tracking controllers can guarantee that the tracking error decreases asymptotically to zero in the presence of uncertain parameters and disturbances. A procedure for designing such a zero tracking state feedback controller is also introduced. Finally, a numerical example is given to demonstrate the validity of the results.     

Adaptive control of uncertain coupled mechanical systems with application to base-isolated structures

A problem of feedback stabilization is addressed for a class of uncertain nonlinear mechanical systems with n degrees of freedom and n_c < n control inputs. Each system of the class has the structure of two coupled subsystems with n_c and n_r degrees of freedom, respectively, a prototype being an uncertain base isolated building structure with n degrees of freedom actively controlled via actuators applying forces to specific degrees of freedom of the base movement, n_c < n in number. A nonlinear adaptive feedback strategy is described, which, under appropriate assumptions on the system uncertainties, guarantees a form of practical stability of the zero state. Numerical simulations are also presented to illustrate the application of the control strategy to a base isolated building.     

Decentralized Adaptive Robust Tracking and Model Following for Large-Scale Systems Including Delayed State Perturbations in the Interconnections

The problem of decentralized robust tracking and model following is considered for a class of uncertain large-scale systems including delayed state perturbations in the interconnections. In this paper, it is assumed that the upper bounds of the delayed state perturbations, uncertainties, and external disturbances are unknown. A modified adaptation law with σ-modification is introduced to estimate such unknown bounds, and on the basis of the updated values of these unknown bounds, a class of decentralized local memoryless state feedback controllers is constructed for robust tracking of dynamical signals. The proposed decentralized adaptive robust tracking controllers can guarantee that the tracking errors between each time-delay subsystem and the corresponding local reference model without time-delay decrease uniformly asymptotically to zero. Finally, a numerical example is given to demonstrate the validity of the results.     

Chaotic phenomena on a coupled nonlinear oscillator based on the rollins-hunt's model

Based on the Rollins-Hunt's model, chaotic phenomena in a driven coupled R-L-diode oscillator are examined numerically. It is found that a straightforward extension of this model to a system with two degrees of freedom is valid as far as the quasiperiodic route to chaos is concerned. However, this model is not sufficient to explain the intermittency and the quasiperiodic routes including the discontinuous (jump) bifurcations with hysteresis. Then it is shown that the additional nonlinearity due to variable capacitance of the diode is effective to explain the above phenomena. It is also shown that a two-dimensional discrete return map in which nonlinear terms are introduced in a characteristic form simulates systematically the numerical results. In particular, this map model can explain effectively the mechanisms which cause the intermittency and the cliscontinuous bifurcation.     

Model Based Trajectory Control of an Overhead Travelling Crane

Until now, most papers concerning control of overhead travelling cranes have only focussed on position control of the translational degrees of freedom, see for example [1], [3], [4], and [5]. With more advanced robotic applications envisaged, however, there is a demand for both trajectory control in six degrees of freedom and active damping of the weakly damped load oscillations due to the rope suspension [2]. Hence, a model based trajectory control is presented for an overhead travelling crane that has been upgraded with an orientation unit providing three additional axes. Starting from a central multibody model, decentralised design models are derived for each crane axis. By this, couplings between the axes are identified and appear as disturbance inputs in these decentralised design models. Each decentralised axis controller consists of linear state feedback, feedforward control, and observer based disturbance compensation and is derived in symbolic form. This allows for an adaptation of the complete control structure employing the gain scheduling technique with respect to varying system parameters like rope length and load mass. Couplings between the crane axes are compensated by feedforward control, whereas the e.ects of nonlinear friction forces are counteracted by combination of feedforward control and disturbance estimation. Experimental results, taken at a 5 t ‐ bridge crane, show the bene.ts of the proposed control scheme as regards control performance and steady‐state accuracy.     

A random forest application to contact‐state classification for robot programming by human demonstration

This paper addresses the non‐parametric estimation of the stochastic process related to the classification problem that arises in robot programming by demonstration of compliant motion tasks. Robot programming by demonstration is a robot programming paradigm in which a human operator demonstrates the task to be performed by the robot. In such demonstration, several observable variables, such as velocities and forces can be modeled, non‐parametrically, in order to classify the current state of a contact between an object manipulated by the robot and the environment in which it operates. Essential actions in compliant motion tasks are the contacts that take place, and therefore, it is important to understand the sequence of contact states made during a demonstration, called contact classification. We propose a contact classification algorithm based on the random forest algorithm. The main advantage of this approach is that it does not depend on the geometric model of the objects involved in the demonstration. Moreover, it does not rely on the kinestatic model of the contact interactions. The comparison with state‐of‐the‐art contact classifiers shows that random forest classifier is more accurate. Copyright © 2015 John Wiley & Sons, Ltd.     

The contributions regarding the conception,designing, modelling and the implementation in a flexible cell of fabrication of a modular serial robot

The authors of the presented paper are propose to relief the calculus, modelling and construction of the translation module of an industrial robot which possess in his cinematic chain five degrees of freedom, type TTRTR. It is propose a choosing variant of the direct current driving engine of the translation module, knowing the output momentum and calculating the input momentum. This is realized by equalize of an equation which results from dynamic modeling of the robot with a designing equation which keep in view the component elements of the structure of the module. The robot is composed by: module of translation on horizontal to the base of the robot (MTB-Sil), module of translation on vertical (MTV-Sil), module of rotation round the vertical axis from the robot's arm, module of translation from the structure of the robot's arm (MT-Sil) and module of orientation assembled with clamping device. In the paper, also is presented an economic study regarding the implementation of the analyzed robot in a manufactural cell concerning the manufacturing and assembling of some types of car radiators. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Simulation-free Nonlinear Model Order-reduction Approach and Comparison Study

In this paper, a new approach to the model order reduction of nonlinear systems is presented. This approach does not need a simulation of the original system, and therefore, it is suitable for large systems. By separating the linear and nonlinear parts of the original nonlinear model, the idea is to consider the nonlinearities of the resulting system as additional inputs. Based on the linear system from the last step, a known order-reduction method can be applied to find the coefficients of the nonlinear and the linear parts of a reduced-order model. Two different methods from linear-order reduction (balancing and truncation and Eitelberg's method with some modification) are used for this purpose, and their advantages and disadvantages are discussed. For comparison with some known methods in order reduction of nonlinear systems, three other methods are discussed briefly. Finally, a technical nonlinear system is reduced, and different methods are compared.     

Predictive Inference for the Elliptical Linear Model

This paper derives the prediction distribution of future responses from the linear model with errors having an elliptical distribution with known covariance parameters. For unknown covariance parameters, the marginal likelihood function of the parameters has been obtained and the prediction distribution has been modified by replacing the covariance parameters by their estimates obtained from the marginal likelihood function. It is observed that the prediction distribution with elliptical error has a multivariate Student'st-distribution with appropriate degrees of freedom. The results for some special cases such as the Intra-class correlation model, AR(1), MA(1), and ARMA(1,1) models have been obtained from the general results. As an application, theβ-expectation tolerance region has been constructed. An example has been added.