speed observation and position feedback stabilization of partially linearizable mechanical systems the problems of speed observation and position feedback stabilization of mechanical systems are addressed in this paper our interest is centered on systems that can be rendered linear in the velocities via a partial change of coordinates it is shown that the class is fully characterized by the solvability of a set of partial differential equations pdes and strictly contains the class studied in the existing literature on linearization for speed observation or control a reduced order globally exponentially stable observer constructed using the immersion and invariance methodology is proposed the design requires the solution of another set of pdes which are shown to be solvable in several practical examples it is also proven that the full order observer with dynamic scaling recently proposed by karagiannis and astolfi obviates the need to solve the latter pdes finally it is shown that the observer can be used in conjunction with an asymptotically stabilizing full state feedback interconnection and damping assignment passivity based controller preserving asymptotic stability

a globally exponentially stable speed observer for a class of mechanical systems experimental and simulation comparison with high gain and sliding mode designs abstractit is shown in the paper that the problem of speed observation for mechanical systems that are partially linearisable via coordinate changes admits a very simple and robust exponentially s

geometric criteria for the quasi linearization of the equations of motion of mechanical systems a linear transformation of velocity for a mechanical system is said to quasi linearize the equations of motion of the system if it eliminates all terms quadratic in the velocity it is well known that controller observer synthesis becomes tractable when the dynamics of a mechanical system are in quasi linearized form in this technical note we show that the quasi linearization property is equivalent to the property that the lie algebra of killing vector fields is pointwise equal to the tangent space to the configuration manifold with the riemannian metric induced by the mass tensor of the mechanical system a sufficient condition for this property is that the riemannian manifold be locally symmetric we further show that a necessary and sufficient condition for quasi linearizability on 2 d riemannian manifolds is that the scalar curvature is constant the above results extend the zero riemannian curvature condition that has been extensively applied since its introduction in 1992 moreover the local symmetricity condition and the constant scalar curvature condition can be easily verified using differentiation

algorithmic issues for three invariant hyperplastic critical state models implicit stress integration and the consistent tangents are presented for critical state hyperplasticity models which include a dependence on the third invariant of stress an elliptical deviatoric yielding criterion 43 is incorporated within the family of geotechnical models first proposed by collins and hilder 8 an alternative expression for the yield function is proposed and the consequences of different forms of that function are revealed in terms of the stability and efficiency of the stress return algorithm errors associated with the integration scheme are presented it is shown how calibration of the two new material constants is achieved through examining one dimesional consolidation tests and undrained triaxial compression data material point simulations of drained triaxial compression tests are then compared with established experimental results strain probe analyses are used to demonstrate the concepts of energy dissipation and stored plastic work along with the robustness of the integration method over twenty finite element boundary value problems are then simulated these include single three dimensional element tests plane strain footing analyses and cavity expansion tests the rapid convergence of the global newton raphson procedure using the consistent tangent is demonstrated in small strain and finite deformation simulations

reuleaux plasticity analytical backward euler stress integration and consistent tangent analytical backward euler stress integration is presented for a deviatoric yielding criterion based on a modified reuleaux triangle the criterion is applied to a cone model which allows control over the shape of the deviatoric section independent of the internal friction angle on the compression meridian the return strategy and consistent tangent are fully defined for all three regions of principal stress space in which elastic trial states may lie errors associated with the integration scheme are reported these are shown to be less than 3 for the case examined run time analysis reveals a 2 5 5 0 times speed up at a material point over the iterative newton raphson backward euler stress return scheme two finite element analyses are presented demonstrating the speed benefits of adopting this new formulation in larger boundary value problems the simple modified reuleaux surface provides an advance over mohr coulomb and drucker prager yield envelopes in that it incorporates dependencies on both the lode angle and intermediate principal stress without incurring the run time penalties of more sophisticated models

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

technical communique explicit convergence rates for mrac type systems it is well known since many years ago that for the linear time varying system email protected ae b t q email protected b t e with a hurwitz and b t bounded and globally lipschitz it is necessary and sufficient for global exponential stability that b t satisfy the so called persistency of excitation condition in this note we revisit this question and provide explicit bounds for the convergence rate and on the overshoot of the transient behaviour of the solutions e t q t as functions of the richness of b we believe that the result that we present is useful since knowing convergence rates aids in the construction of converse lyapunov functions moreover the type of systems that we study here appear for instance in model reference adaptive control mrac

non associated reuleaux plasticity analytical stress integration and consistent tangent for finite deformation mechanics analytical backward euler stress integration is presented for a volumetrically non associated pressure sensitive yield criterion based on a modified reuleaux triangle this advances previous work on associated reuleaux plasticity using energy mapped stress space the analytical solution is 2 4 times faster than a standard numerical backward euler algorithm the merit in transforming to and operating in this space is that the stress return is truly the closest point on the surface to the elastic trial state the paper includes a tension cut off formed by a second cone and describes the steps necessary to allow the model s incorporation within a finite deformation framework finite element results show a 59 runtime saving for a modified reuleaux model over a willam warnke cone giving comparable accuracy in a thick walled cylinder expansion problem the consistent tangent provides asymptotically quadratic convergence in the newton raphson scheme under both i small strain infinitesimal deformation and ii large strain finite deformation finite element simulations it is shown that the introduction of non associated flow changes the plastic deformation field and reduces the heave predicted in a plane strain rigid strip footing problem the proposed model offers a significant improvement over the drucker prager and mohr coulomb formulations by better reproducing the material dependence on the lode angle and intermediate principal stress at little extra computational effort

a high gain nonlinear observer with limited gain power in this note we deal with a new observer for nonlinear systems of dimension n in canonical observability form we follow the standard high gain paradigm but instead of having an observer of dimension n with a gain that grows up to power n we design an observer of dimension 2n 2 with a gain that grows up only to power 2

a systematic procedure for constructing critical state models in three dimensions abstract a general procedure for developing constitutive models for frictional materials possessing a critical state is developed in a three dimensional context the procedure starts from the laws of thermo dynamics so that the first and second laws of thermo dynamics are automatically satisfied there is hence no need to invoke any extraneous stability postulates the models involve a number of parameters which can be interpreted in terms of micro mechanical energy storage and dissipative mechanisms in most cases non associated flow rules are predicted and in some cases the yield surfaces are seen to have concave segments the procedure is more general than that traditionally used for materials with non associated flow rules in that plastic potentials are not needed and not presumed to exist in illustration examples of families of models are given in which the critical state surface is either the drucker prager or the matsuoka nakai cone

two globally convergent adaptive speed observers for mechanical systems a globally exponentially stable speed observer for mechanical systems was recently reported in the literature under the assumptions of known or no coulomb friction and no disturbances in this note we propose and adaptive version of this observer which is robust vis a vis constant disturbances moreover we propose a new globally convergent speed observer that besides rejecting the disturbances estimates some unknown friction coefficients for a class of mechanical systems that contains several practical examples

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

matched interface and boundary mib for the implementation of boundary conditions in high order central finite differences high order central finite difference schemes encounter great difficulties in implementing complex boundary conditions this paper introduces the matched interface and boundary mib method as a novel boundary scheme to treat various general boundary conditions in arbitrarily high order central finite difference schemes to attain arbitrarily high order the mib method accurately extends the solution beyond the boundary by repeatedly enforcing only the original set of boundary conditions the proposed approach is extensively validated via boundary value problems initial boundary value problems eigenvalue problems and high order differential equations successful implementations are given to not only dirichlet neumann and robin boundary conditions but also more general ones such as multiple boundary conditions in high order differential equations and time dependent boundary conditions in evolution equations detailed stability analysis of the mib method is carried out the mib method is shown to be able to deliver high order accuracy while maintaining the same or similar stability conditions of the standard high order central difference approximations the application of the proposed mib method to the boundary treatment of other non standard high order methods is also considered

lyapunov functions for persistently excited cascaded time varying systems application to consensus we present some results on stability of linear time varying systems with particular structures such systems appear in diverse problems which include the analysis of adaptive systems persistently excited observers and consensus of systems interconnected through time varying links the originality of our statements rely in the fact that we provide smooth strict lyapunov functions hence our proofs are constructive and direct moreover we establish uniform global exponential stability with explicit stability and decay estimates for illustration we address a brief but representative case study of consensus of lagrangian systems interconnected through unreliable links

improved explicit integration in plasticity the article presents a simple but efficient numerical scheme for the integration of non linear constitutive equations in which the principal reason for the inaccuracy of the classical explicit schemes for example forward euler scheme is effectively eliminated in the newly developed explicit scheme where there is no need for iteration the implementation simplicity of the forward euler scheme and accuracy of the approach which is using the backward euler scheme to integrate the constitutive equations are successfully combined computational performance of the proposed next increment corrects error nice integration scheme particularly regarding the accuracy and the cpu time consumption is first analysed on a case of complex loading of a material point when comparing it to the forward euler backward euler trapezoidal and midpoint integration schemes it turns out that because of its capability of a fast and relatively accurate integration of the constitutive equations the nice scheme is very convenient for the integration of constitutive models where a direct solution technique is used to solve a boundary value problem although the deduction of the new integration scheme is general its implementation for shell applications needs particular care namely in order to satisfy the zero normal stress condition during the whole integration a through thickness strain increment has to be adequately chosen in each integration step the nice scheme which was also implemented into abaqus explicit via user material subroutine vumat interface platform has been additionally compared with the abaqus explicit default integration scheme backward euler and forward euler scheme two loading case studies namely the bending of a square plate and the stretching of a specimen including the onset of necking are considered with two constitutive models the von mises and gtn material model being adopted generally the nice scheme has demonstrated to be advantageous in cases where reasonable accuracy and very fast integration of the constitutive model is demanded which is mostly the case in engineering computations with a direct solution method for example explicit dynamics and metal forming process simulations copyright 2009 john wiley sons ltd

integration methods for complex plastic constitutive equations abstract this paper shows new results concerning the finite element computations with complex plastic and viscoplastic constitutive equations the integration procedure then needs special numerical treatments when a large number of internal variables are present or for stiff non linearities implicit and explicit integration methods are compared the general solution proposed can be applied either in plasticity or in viscoplasticity for isotropic or anisotropic materials several options are proposed in the numerical scheme and for the completion step for the semi implicit scheme numerical tests are performed in order to compare the relative performances of the various approaches

accurate finite difference schemes for solving a 3d micro heat transfer model in an n carrier system with the neumann boundary condition in spherical coordinates in this study we propose a 3d generalized micro heat transfer model in an n carrier system with the neumann boundary condition in spherical coordinates which can be applied to describe the non equilibrium heating in biological cells two improved unconditionally stable crank nicholson schemes are then presented for solving the generalized model in particular we delicately adjust the location of the interior grid point that is next to the boundary so that the neumann boundary condition can be applied directly without discretization as such a second order accurate finite difference scheme without using any fictitious grid points is obtained the convergence rates of the numerical solution are tested by an example results show that the convergence rates of the present schemes are about 2 0 with respect to the spatial variable r which improves the accuracy of the crank nicholson scheme coupled with the conventional first order approximation for the neumann boundary condition

nurbs plasticity yield surface representation and implicit stress integration for isotropic inelasticity in numerical analysis the failure of engineering materials is controlled through specifying yield envelopes or surfaces that bound the allowable stress in the material however each surface is distinct and requires a specific equation describing the shape of the surface to be formulated in each case these equations impact on the numerical implementation specifically relating to stress integration of the models and therefore a separate algorithm must be constructed for each model this paper presents for the first time a way to construct yield surfaces using techniques from non uniform rational basis spline nurbs surfaces such that any isotropic convex yield envelope can be represented within the same framework these surfaces are combined with an implicit backward euler type stress integration algorithm to provide a flexible numerical framework for computational plasticity the algorithm is inherently stable as the iterative process starts and remains on the yield surface throughout the stress integration the performance of the algorithm is explored using both material point investigations and boundary value analyses demonstrating that the framework can be applied to a variety of plasticity models

on global uniform asymptotic stability of nonlinear time varying systems in cascade abstract in this short paper we deal with the stability analysis problem of nonautonomous nonlinear systems in cascade in particular we give sufficient conditions to guarantee that i a globally uniformly stable gus nonlinear time varying nltv system remains gus when it is perturbed by the output of a globally uniformly asymptotically stable guas nltv system under the assumption that the perturbing signal is absolutely integrable ii if in addition the perturbed system is guas it remains guas under the cascaded interconnection iii two guas systems yield a guas cascaded system under some growth restrictions over the lyapunov function our proofs rely on the second method of lyapunov roughly speaking on a e stability analysis

a globally exponentially stable tracking controller for mechanical systems using position feedback a solution to the problem of global exponential tracking of mechanical systems without velocity measurements is given in the technical note the proposed controller is obtained combining a redesign of the recently reported exponentially stable immersion and invariance velocity observer and a new state feedback passivity based controller which assigns to the closed loop a port hamiltonian structure with a desired energy function the result is applicable to a large class of mechanical systems including those with unbounded inertia matrix and possible presence of friction forces unlike previous results that rely on the presence exact knowledge and pervasiveness of these forces our design treats them as disturbances which are suitably compensated

a new high accuracy two level implicit off step discretization for the system of three space dimensional quasi linear parabolic partial differential equations we present a new two level compact implicit numerical scheme based on off step discretization for the solution of the system of three space dimensional quasi linear parabolic partial differential equations subject to suitable initial and boundary conditions further we derive the estimates of first order space derivatives of the solution the proposed methods are fourth order accurate in space and second order accurate in time and involve 19 spatial grid points of a single compact cell also we develop the alternating direction implicit adi scheme for a linear parabolic equation with variable coefficients which is shown to be unconditionally stable for the heat equation in polar coordinates the methods so proposed do not require any modification when applied to the singular problems at the point of singularity unlike the numerical scheme proposed earlier in mohanty and jain 1994 and mohanty 1997 2003 the proposed methods are directly applicable to parabolic equations with singular coefficients this is the main highlight of our work the method successfully works for the navier stokes equations of motion in polar coordinates many physical problems are solved to illustrate the accuracy of the proposed methods

robust energy shaping control of mechanical systems the problem of robustness improvement vis a vis external disturbances of energy shaping controllers for mechanical systems is addressed in this paper first it is shown that if the inertia matrix is constant constant disturbances both matched and unmatched can be rejected simply adding a suitable integral action interestingly not at the passive output for systems with non constant inertia matrix additional damping and gyroscopic forces terms must be added to reject matched disturbances and moreover enforce the property of integral input to state stability with respect to matched disturbances the stronger property of input to state stability this time with respect to matched and unmatched disturbances is ensured with further addition of nonlinear damping finally it is shown that including a partial change of coordinates the controller can be significantly simplified preserving input to state stability with respect to matched disturbances

nurbs plasticity yield surface evolution and implicit stress integration for isotropic hardening this paper extends the non uniform rational basis spline nurbs plasticity framework of coombs et al 2016 to include isotropic hardening of the yield surfaces the approach allows any smooth isotropic yield envelope to be represented by a nurbs surface the key extension provided by this paper is that the yield surface can expand or contract through the movement of control points linked to the level of inelastic straining experienced by the material the model is integrated using a fully implicit backward euler algorithm that constrains the return path to the yield surface and allows the derivation of the algorithmic consistent tangent to ensure optimum convergence of the global equilibrium equations this provides a powerful framework for elasto plastic constitutive models where unlike the majority of models presented in the literature the underlying numerical algorithm and implemented code remains unchanged for different yield surfaces the performance of the algorithm is demonstrated and validated using both material point and boundary values simulations including plane stress plane strain and three dimensional examples for different yield criteria

on global asymptotic stability of x ϕ t ϕ t x with ϕ not persistently exciting abstract we study global convergence to zero of the solutions of the n th order differential equation x t t x we are interested in the case when the vector is not persistently exciting which is a necessary and sufficient condition for global exponential stability in particular we establish new necessary conditions on t for global asymptotic stability of the zero equilibrium of the unexcited system a new sufficient condition that is strictly weaker than the ones reported in the literature is also established unfortunately it is also shown that this condition is not necessary

second order sliding mode observer for mechanical systems the super twisting second order sliding mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems the finite time convergence of the observer is proved thus the observer can be designed independently of the controller a discrete version of the observer is considered and the corresponding accuracy is estimated

cam clay plasticity part iii extension of the infinitesimal model to include finite strains the infinitesimal version of the modified cam clay model of critical state soil mechanics is reformulated to include finite deformation effects central to the formulation are the choice of a hardening law that is appropriate for cases involving large plastic volumetric strains and the use of a class of two invariant stored energy functions appropriate for cam clay type models that includes as special cases the constant elastic shear modulus approximation as well as the pressure dependent shear modulus elastic model the analytical model is cast within the framework of finite deformation theory based on a multiplicative decomposition of the deformation gradient for the fully elasto plastic case return mapping is done implicitly in the space defined by the invariants of the elastic logarithmic principal stretches which requires the solution at each stress point of no more than three simultaneous non linear equations a finite element analysis of a strip footing problem is presented to illustrate a prototype example where finite deformation effects significantly impact the predicted response