Global motion analysis of energy-based control for 3-link planar robot with a single actuator at the first joint

This paper studies nonlinear control of a 3-link planar robot moving in the vertical plane with only the first joint being actuated while the two other revolute joints are passive (called the APP robot below). A nonlinear energy-based controller is proposed, whose objective is to drive the APP robot into an invariant set where the first link is in the upright position and the total mechanical energy converges to its value at the upright equilibrium point (all three links are in the upright position). By presenting and using a new property of the motion of the APP robot, without any condition on its mechanical parameters, this paper proves that if the control gains are larger than specific lower bounds, then only a measure-zero set of initial conditions converges to three strictly unstable equilibrium points instead of converging to the invariant set. This paper presents numerical results for a physical 3-link planar robot to validate the obtained theoretical results and to demonstrate a switch–and–stabilize maneuver in which the energy-based controller is switched to a linear state feedback controller that stabilizes the APP robot at its upright equilibrium point.     

基于虚拟力概念的柔性臂空间机器人模糊退步自适应控制算法设计

讨论了漂浮基柔性臂空间机器人系统的动力学模拟、运动轨迹跟踪控制算法设计及柔性振动主动抑制。采用多体动力学建模方法并结合假设模态法,建立了漂浮基柔性臂空间机器人的系统动力学模型。基于该模型,针对系统惯性参数未知情况,提出了刚性运动基于模糊基函数网络自适应调节的退步控制算法,以完成柔性臂空间机器人载体姿态及机械臂各关节铰的协调运动。然后,为了主动抑制系统柔性振动,运用虚拟力的概念,构造了同时反映柔性模态和刚性运动轨迹的混合期望轨迹,通过改造原有的控制算法,提出了基于虚拟力概念的模糊退步自适应控制算法;这样不但保证了之前刚性运动控制方案对模型不确定的鲁棒性,而且能主动抑制柔性振动,从而提高了轨迹跟踪性能。理论分析及数值仿真算例均表明了控制方法的可行性。     

空间机器人捕获卫星操作基于柔顺装置的无源模糊避撞柔顺控制

讨论了漂浮基空间机器人在轨捕获非合作卫星过程避免关节受冲击及过载破坏的避撞柔顺控制问题。在关节电机与机械臂之间配置了一种柔顺装置——旋转型串联弹性执行器(RSEA),其作用一是在捕获阶段,通过其内置弹簧的变形来缓冲捕获过程中被捕获卫星对空间机器人关节产生的冲击能量;二是在捕获完成后的镇定运动阶段,结合所设计的避撞柔顺策略来适时开关关节电机以保证关节冲击力矩受限在安全范围。首先,根据拉格朗日法及牛顿-欧拉法分别建立了含柔顺装置空间机器人与目标卫星系统的动力学方程;之后,结合整个系统动量守恒关系、系统运动几何及位置约束关系,建立了捕获操作后两者形成混合体系统的动力学方程。在此基础上,针对捕获操作后不稳定的混合体系统,提出了一种基于无源性理论的避撞柔顺模糊控制方案以实现其镇定控制。最后,通过仿真实验验证了所提避撞柔顺策略的有效性。     

A fast stable control strategy based on system energy for a planar single-link flexible manipulator

Nonlinear Dynamics - This paper presents a stable control strategy based on system energy for a Planar Single-Link Flexible Manipulator (PSLFM) to quickly realize its control objective, which is to...     

Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances

In this paper, the composite nonlinear feedback control method is considered for robust tracking and model following of uncertain linear systems. The control law guarantees that the tracking error decreases asymptotically to zero in the presence of time varying uncertain parameters and disturbances. For performance improvement of the dynamical system, the proposed robust tracking controller consists of linear and nonlinear feedback parts without any switching element. The linear feedback law is designed to allow the closed loop system have a small damping ratio and a quick response while the nonlinear feedback law increases the damping ratio of the system as the system output approaches the output of the reference model. A new collection of different nonlinear functions used in the control law are offered to improve the reference tracking performance of the system. The proposed robust tracking controller improves the transient performance and steady state accuracy simultaneously. Finally, the simulations are provided to verify the theoretical results.     

A preview driver model based on sliding-mode and fuzzy control for articulated heavy vehicle

Meccanica - To investigate the driver/articulated vehicle directional dynamics, combined with the structural characteristics of articulated heavy vehicles (AHVs) and preview driver model theory, a...     

A linear solver based on algebraic multigrid and defect correction for the solution of adjoint RANS equations

A new solution approach for discrete adjoint Reynolds‐averaged Navier–Stokes equations is suggested. The approach is based on a combination of algebraic multigrid and defect correction. The efficient interplay of these two methods results in a fast and robust solution technique. Algebraic multigrid deals very well with unstructured grids, and defect correction completes it in such a way that a required second‐order accuracy of the solution is achieved. The performance of the suggested solution approach is demonstrated on a number of representative benchmarks.Copyright © 2014 John Wiley & Sons, Ltd.     

A model for high temperature creep of single crystal superalloys based on nonlocal damage and viscoplastic material behavior

A model for high temperature creep of single crystal superalloys is developed, which includes constitutive laws for nonlocal damage and viscoplasticity. It is based on a variational formulation, employing potentials for free energy, and dissipation originating from plasticity and damage. Evolution equations for plastic strain and damage variables are derived from the well-established minimum principle for the dissipation potential. The model is capable of describing the different stages of creep in a unified way. Plastic deformation in superalloys incorporates the evolution of dislocation densities of the different phases present. It results in a time dependence of the creep rate in primary and secondary creep. Tertiary creep is taken into account by introducing local and nonlocal damage. Herein, the nonlocal one is included in order to model strain localization as well as to remove mesh dependence of finite element calculations. Numerical results and comparisons with experimental data of the single crystal superalloy LEK94 are shown.     

An effective computational algorithm for rate-independent crystal plasticity based on a single crystal yield surface with an application to tube hydroforming

Up to now, several computational methods have been proposed for crystal plasticity models. The main objective of these computational methods has been to overcome the problem with the non-uniqueness of active slip systems during the plastic deformation of a single crystal. Crystal plasticity models based on a single crystal yield function have been proposed as alternative algorithms to overcome this problem. But the problem with these models is that they use a highly non-linear yield function for the crystal, which makes them computationally expensive. In this paper, a computational method is proposed that would modify a single crystal yield function in order to make it computationally efficient. Also to better capture experimental data, a new parameter is introduced into the single crystal yield function to make it more flexible. For verification, this crystal plasticity model was directly applied for the simulation of hydroforming of an extruded aluminum tube under complex strain paths. It was found that the current model is considerably faster than the previous crystal plasticity model based on a power-law type single crystal yield surface. Due to its computational efficiency, the current crystal plasticity model can also be used to calculate the anisotropy coefficients of phenomenological yield functions.     

A novel multidimensional solution reconstruction and edge‐based limiting procedure for unstructured cell‐centered finite volumes with application to shallow water dynamics

On unstructured meshes, the cell‐centered finite volume (CCFV) formulation, where the finite control volumes are the mesh elements themselves, is probably the most used formulation for numerically solving the two‐dimensional nonlinear shallow water equations and hyperbolic conservation laws in general. Within this CCFV framework, second‐order spatial accuracy is achieved with a Monotone Upstream‐centered Schemes for Conservation Laws‐type (MUSCL) linear reconstruction technique, where a novel edge‐based multidimensional limiting procedure is derived for the control of the total variation of the reconstructed field. To this end, a relatively simple, but very effective modification to a reconstruction procedure for CCFV schemes, is introduced, which takes into account geometrical characteristics of computational triangular meshes. The proposed strategy is shown not to suffer from loss of accuracy on grids with poor connectivity. We apply this reconstruction in the development of a second‐order well‐balanced Godunov‐type scheme for the simulation of unsteady two‐dimensional flows over arbitrary topography with wetting and drying on triangular meshes. Although the proposed limited reconstruction is independent from the Riemann solver used, the well‐known approximate Riemann solver of Roe is utilized to compute the numerical fluxes, whereas the Green–Gauss divergence formulation for gradient computations is implemented. Two different stencils for the Green–Gauss gradient computations are implemented and critically tested, in conjunction with the proposed limiting strategy, on various grid types, for smooth and nonsmooth flow conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

A finite strain kinematic hardening constitutive model based on Hencky strain: General framework, solution algorithm and application to shape memory alloys

The logarithmic or Hencky strain measure is a favored measure of strain due to its remarkable properties in large deformation problems. Compared with other strain measures, e.g., the commonly used Green-Lagrange measure, logarithmic strain is a more physical measure of strain. In this paper, we present a Hencky-based phenomenological finite strain kinematic hardening, non-associated constitutive model, developed within the framework of irreversible thermodynamics with internal variables. The derivation is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts, and on the use of the isotropic property of the Helmholtz strain energy function. We also use the fact that the corotational rate of the Eulerian Hencky strain associated with the so-called logarithmic spin is equal to the strain rate tensor (symmetric part of the velocity gradient tensor). Satisfying the second law of thermodynamics in the Clausius-Duhem inequality form, we derive a thermodynamically-consistent constitutive model in a Lagrangian form. In comparison with the available finite strain models in which the unsymmetric Mandel stress appears in the equations, the proposed constitutive model includes only symmetric variables. Introducing a logarithmic mapping, we also present an appropriate form of the proposed constitutive equations in the time-discrete frame. We then apply the developed constitutive model to shape memory alloys and propose a well-defined, non-singular definition for model variables. In addition, we present a nucleation-completion condition in constructing the solution algorithm. We finally solve several boundary value problems to demonstrate the proposed model features as well as the numerical counterpart capabilities.     

Adaptive synchronization control based on QPSO algorithm with interval estimation for fractional-order chaotic systems and its application in secret communication

In this paper, the synchronization problem and its application in secret communication are investigated for two fractional-order chaotic systems with unequal orders, different structures, parameter uncertainty and bounded external disturbance. On the basis of matrix theory, properties of fractional calculus and adaptive control theory, we design a feedback controller for realizing the synchronization. In addition, in order to make it better apply to secret communication, we design an optimal controller based on optimal control theory. In the meantime, we propose an improved quantum particle swarm optimization (QPSO) algorithm by introducing an interval estimation mechanism into QPSO algorithm. Further, we make use of QPSO algorithm with interval estimation to optimize the proposed controller according to some performance indicator. Finally, by comparison, numerical simulations show that the controller not only can achieve the synchronization and secret communization well, but also can estimate the unknown parameters of the systems and bounds of external disturbance, which verify the effectiveness and applicability of the proposed control scheme.     

A model for lipid membranes with tilt and distension based on three-dimensional liquid crystal theory

The relationship between the two-dimensional theory of tilted lipid membranes and three-dimensional liquid crystal theory is discussed in detail. The latter framework furnishes an appropriate foundation for membrane theory and facilitates a straightforward reduction to a well-posed two-dimensional model. This emerges as a special case of the Cosserat theory of elastic shells and incorporates a model of generalized capillarity in which the membrane energy responds to surface curvature and also to surface dilation and its gradient.     

A discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of short wave exterior Helmholtz problems on unstructured meshes

Recently, a discontinuous Galerkin method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution of the Helmholtz equation in the mid-frequency regime. This method was fully developed however only for regular meshes, and demonstrated only for interior Helmholtz problems. In this paper, we extend it to irregular meshes and exterior Helmholtz problems in order to expand its scope to practical acoustic scattering problems. We report preliminary results for two-dimensional short wave problems that highlight the superior performance of this discontinuous Galerkin method over the standard finite element method.     

An efficient numerical solution for linear stability of circular jet: A combination of Petrov–Galerkin spectral method and exponential coordinate transformation based on Fornberg's treatment

This paper presents the linear stability analysis of a round jet in a radially unbounded domain using a spectral Petrov–Galerkin scheme coped with exponential coordinate transformation based on Fornberg's treatment. A Fourier–Chebyshev Petrov–Galerkin spectral method is described for the computation of the linear stability equations based on half a Gauss–Lobatto mesh. Complex basis functions presented here are exponentially mapped as Chebyshev functions, which satisfy the pole condition exactly at the origin, and can be used to expand vector functions efficiently by using the solenoidal condition. The mathematical formulation is presented in detail focusing on the solenoidal vector field used for the approximation of the flow. The scheme provides spectral accuracy in the present cases and the numerical results are in agreement with former works. Copyright © 2008 John Wiley & Sons, Ltd.     

A divide and conquer algorithm for constrained multibody system dynamics based on augmented Lagrangian method with projections-based error correction

This paper presents a?new parallel algorithm for dynamics simulation of general multibody systems. The developed formulations are iterative and possess divide and conquer structure. The constraints equations are imposed at the acceleration level. Augmented Lagrangian methods with mass-orthogonal projections are used to prevent from constraint violation errors. The proposed approaches treat tree topology mechanisms or multibody systems which contain kinematic closed loops in a?uniform manner and can handle problems with rank deficient Jacobian matrices. Test case results indicate good accuracy performance dependent on the expense put in the iterative correction of constraint equations. Good numerical properties and robustness of the algorithms are observed when handling systems with single and coupled kinematic loops, redundant constraints, which may repeatedly enter singular configurations.     

A frontal method based solution of the quasi-three-dimensional finite element model for interconnected aquifer systems. Steady and unsteady equations,with the E.N.S. method for fluid mass balance evaluation

The quasi-three-dimensional equations controlling the groundwater flow in heterogeneous and interconnected aquifer systems are discretized by finite elements, considering also the aquifer branching. A new method for fluid mass balance evaluation based on the equivalent nodal source (E.N.S.) concept allows one to express the balance in conservative terms, and interpret finite element equations as nodal balance equations. The solution of the system is based on the frontal method. Use of substructures limits the frontal increase in correspondence to the aquifer branching. In the steady state, the frontal method is integrated with an iterative solution technique to eliminate the frontal increase caused by the presence of aquitards. It converges very rapidly, using a forcing technique with an automatic parameter definition. In the unsteady case the same scope is achieved using a predictor-corrector procedure which employs the Crank-Nicolson method in the corrector phase. This very stable procedure permits use of fairly long time-steps and concerns the case of source terms depending on piezometry (problem of interaction between water table and river). This method has been tested with several fairly complex cases.     

A numerical method based on boundary integral equations and radial basis functions for plane anisotropic thermoelastostatic equations with general variable coefficients

A boundary integral method with radial basis function approximation is proposed for numerically solving an important class of boundary value problems governed by a system of thermoelastostatic equations with variable coefficients. The equations describe the thermoelastic behaviors of nonhomogeneous anisotropic materials with properties that vary smoothly from point to point in space. No restriction is imposed on the spatial variations of the thermoelastic coefficients as long as all the requirements of the laws of physics are satisfied. To check the validity and accuracy of the proposed numerical method, some specific test problems with known solutions are solved.