A family of smooth controllers for swinging up a pendulum

The paper presents a new family of controllers for swinging up a pendulum. The swinging up of the pendulum is derived from physical arguments based on two ideas: shaping the Hamiltonian for a system without damping; and providing damping or energy pumping in relevant regions of the state space. A family of simple smooth controllers without switches with nice properties is obtained. The main result is that all solutions that do not start at a zero Lebesgue measure set converge to the upright position for a wide range of the parameters in the control law. Thus, the swing-up and the stabilization problems are simultaneously solved with a single, smooth law. The properties of the solution can be modified by the parameters in the control law. Control signal saturation can also be taken into account using the Hamiltonian approach.     

Swing-up and stabilization of a Twin-Pendulum under state and control constraints by a fast NMPC scheme

In this paper, a real-time implementable Nonlinear Model Predictive Control scheme is proposed for the swing-up and the stabilization of a Twin-Pendulum system under control and state constraints. The basic feature lies in a particular parametrization of the set of candidate control profiles leading to a decision variable that may take only 3 admissible values. Simulations are proposed to assess the efficiency of the proposed feedback.     

An energy-balancing perspective of interconnection and damping assignment control of nonlinear systems

Stabilization of nonlinear feedback passive systems is achieved assigning a storage function with a minimum at the desired equilibrium. For physical systems a natural candidate storage function is the difference between the stored and the supplied energies—leading to the so-called energy-balancing control, whose underlying stabilization mechanism is particularly appealing. Unfortunately, energy-balancing stabilization is stymied by the existence of pervasive dissipation, that appears in many engineering applications. To overcome the dissipation obstacle the method of Interconnection and Damping Assignment, that endows the closed-loop system with a special—port-controlled Hamiltonian—structure, has been proposed. If, as in most practical examples, the open-loop system already has this structure, and the damping is not pervasive, both methods are equivalent. In this brief note we show that the methods are also equivalent, with an alternative definition of the supplied energy, when the damping is pervasive. Instrumental for our developments is the observation that, swapping the damping terms in the classical dissipation inequality, we can establish passivity of port-controlled Hamiltonian systems with respect to some new external variables—but with the same storage function.     

New integrability conditions for differential constraints

This paper discusses differential-form-based integrability conditions for dynamic constraints using the Frobenius theorem. The conditions can be used for the classification of holonomic and nonholonomic constraints. Some of the previous conditions used for this purpose are only sufficient. The conditions presented here are both necessary and sufficient.

The paper's main interest is on differential constraints for under-actuated mechanical systems. Different from many discussions in classical mechanics that deal with mostly on kinematics constraints, the constraints discussed here are from the Lagrange equations, which correspond to unactuated part of the system dynamics.     

Extension of impedance matching to nonlinear dynamics of robotic tasks

The concept of impedance matching for linear electric circuits is extended to nonlinear position-dependent circuits that express nonlinear dynamics of robotic tasks such as holding an object of soft material and handling a rigid object with soft fingers. At the first step, impedance control is realized by negative-feedback connection of two passive (hyper-stable) blocks, one is in the forward path expressing position control of the tool endpoint and the other is in the feedback path expressing force control of pressing the object. This negative-feedback framework is naturally introduced owing to the situation that both the tool mass and the nonlinear characteristics of reproducing force of the soft material are unknown. Extension of the concept of impedance matching to such nonlinear circuits is fulfilled by optimizing the regulation of impedance control and subsequently choosing optimal parameters from the viewpoint of both the transient and stead-state responses. The relations of this extension with the well-known theorem of maximum power supply and the H-infinity tuning for disturbance attenuation are also presented.     

Cardinality constraints in semantic data models

Constraints are central to the notion of a semantic data model. How well a model captures constraints affects its power and viability as a semantic data model. Cardinality constraints are an important subclass of general constraints. In this paper we provide formal definitions for cardinality constraints of several semantic models, as described in the literature. We construct a partial ordering of these constraints that shows the relative power expressed by each cardinality constraints. We discuss our results and offer possible extensions to contemporary cardinality constraint definitions. Our contributions include a collection and formal definition of existing cardinality constraints, a partial ordering of this set, and recommendations for cardinality constraint mechanisms in semantic data models.     

一种约束输入输出的隐式广义预测控制新算法

基于CARIMA模型提出了一种约束输入输出的隐式广义预测控制算法.针对广义预测控制问题,在整个预测时域和控制时域,对输入幅值,输入增量和输出幅值施加了约束,引入了输入输出柔化系数,从而简化了目标函数,减小了计算量,该算法不必求解逆矩阵;并采用了隐式广义预测自校正控制算法,利用并列预测控制器间的特点,直接辨识输出预测器中的参数,从而避免了在线求解Diophantine方程.该算法占用内存小,计算速度快,仿真结果表明该算法具有良好的控制性能.     

Rigid body attitude tracking without angular velocity feedback

In this paper, we revisit the classical problem of attitude tracking for a rigid body. The interesting difference in the formulation is the assumption that only attitude measurements are available. We proceed to construct globally stabilizing control laws in terms of a minimal set of three-dimensional kinematic parameters that enable the rigid body to track any specified trajectory without requiring angular velocity measurements. The results presented here complement and extend some recent developments available for the nonminimal case of Euler parameters (quaternions).     

Accuracy comparison of several common implicit solvent models and their implementations in the context of protein-ligand binding

In this study several commonly used implicit solvent models are compared with respect to their accuracy of estimating solvation energies of small molecules and proteins, as well as desolvation penalty in protein-ligand binding. The test set consists of 19 small proteins, 104 small molecules, and 15 protein-ligand complexes. We compared predicted hydration energies of small molecules with their experimental values; the results of the solvation and desolvation energy calculations for small molecules, proteins and protein-ligand complexes in water were also compared with Thermodynamic Integration calculations based on TIP3P water model and Amber12 force field. The following implicit solvent (water) models considered here are: PCM (Polarized Continuum Model implemented in DISOLV and MCBHSOLV programs), GB (Generalized Born method implemented in DISOLV program, S-GB, and GBNSR6 stand-alone version), COSMO (COnductor-like Screening Model implemented in the DISOLV program and the MOPAC package) and the Poisson-Boltzmann model (implemented in the APBS program). Different parameterizations of the molecules were examined: we compared MMFF94 force field, Amber12 force field and the quantum-chemical semi-empirical PM7 method implemented in the MOPAC package. For small molecules, all of the implicit solvent models tested here yield high correlation coefficients (0.87–0.93) between the calculated solvation energies and the experimental values of hydration energies. For small molecules high correlation (0.82–0.97) with the explicit solvent energies is seen as well. On the other hand, estimated protein solvation energies and protein-ligand binding desolvation energies show substantial discrepancy (up to 10 kcal/mol) with the explicit solvent reference. The correlation of polar protein solvation energies and protein-ligand desolvation energies with the corresponding explicit solvent results is 0.65–0.99 and 0.76–0.96 respectively, though this difference in correlations is caused more by different parameterization and less by methods and indicates the need for further improvement of implicit solvent models parameterization. Within the same parameterization, various implicit methods give practically the same correlation with results obtained in explicit solvent model for ligands and proteins: e.g. correlation values of polar ligand solvation energies and the corresponding energies in the frame of explicit solvent were 0.953–0.966 for the APBS program, the GBNSR6 program and all models used in the DISOLV program. The DISOLV program proved to be on a par with the other used programs in the case of proteins and ligands solvation energy calculation. However, the solution of the Poisson-Boltzmann equation (APBS program) and Generalized Born method (implemented in the GBNSR6 program) proved to be the most accurate in calculating the desolvation energies of complexes.     

Computing on rays: A parallel approach for surface mesh modeling from multi-material volumetric data

Ray representation (Ray-rep) of a solid has been studied and used in the solid modeling community for many years because of its compactness and simplicity. This paper presents a parallel approach for mesh surface modeling from multi-material volume data using an extended Ray-rep as an intermediate, where every homogeneous region is enclosed by a set of two-manifold surface meshes on the resultant model. The approach consists of three major algorithms: firstly, an algorithm is developed to convert the given multi-material volumetric data into a Ray-rep for heterogeneous solid; secondly, filtering algorithm is exploited to process the rays of heterogeneous solid in parallel; and lastly, the adaptive mesh surfaces are generated from the Ray-rep through a dual-contouring like algorithm. Here the intermediate surfaces between two constituent materials can be directly extracted without building the volumetric mesh, and the manifold topology is preserved on each surface patch. Furthermore, general offset surface can be easily computed in this paradigm by designing a special parallel operator for the rays.     

Zero-dynamics design and its application to the stabilization of implicit systems

We present a formula that computes the output of an R-controllable, regular, single-input linear time-invariant implicit system in such a way that it has prescribed relative degree and zeros. The formula is inspired on different generalizations of Ackermann’s formula.A possible application is in the context of sliding-mode control of implicit systems where, as the first step, one can use the proposed formula to design a sliding surface with desired dynamic characteristics and, as the second step, apply a higher-order sliding-mode controller to enforce a sliding motion along the resulting sliding surface.     

Free energies of ferroelectric crystals from a microscopic approach

The free energy of barium titanate is computed around the Curie temperature as a function of polarization from the first-principles derived Effective Hamiltonian of Zhong, Vanderbilt and Rabe [Phys. Rev. Lett. 73 (1994) 1861], through Molecular Dynamics simulations coupled to the method of the Thermodynamic Integration. The algorithms used to fix the temperature (Nosé-Hoover) and/or the pressure/stress (Parrinello-Rahman), combined with fixed-polarization molecular dynamics, allow to compute a Helmholtz free energy (fixed volume/strain) or a Gibbs free energy (fixed pressure/stress). The main feature of this approach is to calculate the gradient of the free energy in the 3-D space (Px, Py, Pz) from the thermal averages of the forces acting on the local modes, that are obtained by Molecular Dynamics under the constraint of fixed . This work extends the method presented in [Phys. Rev. B 79 (2009) 064101] to the calculation of the Gibbs free energy and presents new features about the computation of the free energy of ferroelectric crystals from a microscopic approach. A careful analysis of the states of constrained polarization is performed at T=280 K (≈15-17 K below Tc) especially at low order parameter. These states are found reasonably homogeneous for small supercell size (L=12 and L=16), until inhomogeneous states are observed at low order parameter for large supercells (L=20). The effect of this evolution towards multidomain configurations on the mean force and free energy curves is shown. However, for reasonable supercell sizes (L=12), the free energy curves obtained are in very good agreement with phenomenological Landau potentials of the literature and the states of constrained polarization are homogeneous. Moreover, the free energy obtained is quite insensitive to the supercell size from L=12 to L=16 at T=280 K, suggesting that interfacial contributions, if any, are negligible at these sizes around Tc. The method allows a numerical estimation of the free energy barrier separating the paraelectric from the ferroelectric phase at Tc (ΔG≈0.012-0.015 meV/5-atom cell). However, our tests evidence phase separation at low temperature and low order parameter, in agreement with the results of Tröster et al. [Phys. Rev. B 72 (2005) 094103]. Finally, the natural decomposition of the forces into onsite, short-range, dipole-dipole and elastic-local mode interaction allows to make the same decomposition of the free energy. Some parts of this decomposition can be directly calculated from the coefficients of the Effective Hamiltonian.     

Robust adaptive motion/force control for wheeled inverted pendulums

Previous works for wheeled inverted pendulums usually eliminate nonholonomic constraint force in order to make the control design easier, under the assumption that the friction force from the ground is as large as needed. Nevertheless, such an assumption is unfeasible in practical applications. In this paper, adaptive robust motion/force control for wheeled inverted pendulums is investigated with parametric and functional uncertainties. The proposed robust adaptive controls based on physical properties of wheeled inverted pendulums make use of online adaptation mechanism to cancel the unmodelled dynamics. Based on Lyapunov synthesis, the proposed controls ensure that the system outputs track the given bounded reference signals within a small neighborhood of zero, and guarantee the semi-global uniform boundedness of all closed loop signals. The effectiveness of the proposed controls is verified through extensive simulations.