Sliding Mode Control of Flexible Articulated Manipulator Based on Robust Observer

In this paper, a robust observer-based sliding mode control algorithm is proposed to address the modelling and measurement inaccuracies, load variations, and external disturbances of flexible articulated manipulators. Firstly, a sliding mode observer was designed with exponential convergence to observe system state accurately and to overcome the measuring difficulty of the state variables, unmeasurable quantities, and external disturbances. Next, a robust sliding mode controller was developed based on the observer, such that the output error of the system converges to zero in finite time. In this way, the whole system achieves asymptotic stability. Finally, the convergence conditions of the observer were theoretically analyzed to verify the convergence of the proposed algorithm, and simulation was carried out to confirm the effectiveness of the proposed method.

Weighted L 2-contractivity of Langevin dynamics with singular potentials

Convergence to equilibrium of underdamped Langevin dynamics is studied under general assumptions on the potential U allowing for singularities. By modifying the direct approach to convergence in L 2 pioneered by Hérau and developed by Dolbeault et al, we show that the dynamics converges exponentially fast to equilibrium in the topologies L 2(dμ) and L 2(W* dμ), where μ denotes the invariant probability measure and W* is a suitable Lyapunov weight. In both norms, we make precise how the exponential convergence rate depends on the friction parameter γ in Langevin dynamics, by providing a lower bound scaling as min(γ, γ −1). The results hold for usual polynomial-type potentials as well as potentials with singularities such as those arising from pairwise Lennard-Jones interactions between particles.

Legendre spectral collocation technique for fractional inverse heat conduction problem

For fractional inverse heat conduction problem (FIHCP), this paper introduces a numerical study. For the proposed FIHCP, in addition to the unknown function of temperature, the boundary heat fluxes are also unknown. Related to the two independent variables, the proposed scheme uses a fully spectral collocation treatment. Our technique is determined to be more accurate, efficient and practicable. The obtained results confirmed the exponential convergence of the spectral scheme.

Spectral solution to a problem on the axisymmetric nonlinear deformation of a cylindrical membrane shell due to pressure and edges convergence

A geometrically and physically nonlinear model of a membrane cylindrical shell, which has been built and tested, describes the behavior of a airbag made of fabric material. Based on the geometrically accurate relations of "strain-displacement", it has been shown that the equilibrium equations of the shell, written in terms of Biot stresses, together with boundary conditions acquire a natural physical meaning and are the consequences of the principle of virtual work. The physical properties of the shell were described by Fung’s hyper-elastic biological material because its behavior is similar to that of textiles. For comparison, simpler hyper-elastic non-compressible Varga and Neo-Hookean materials, the zero-, first-, and second-order materials were also considered. The shell was loaded with internal pressure and convergence of edges. The approximate solution was constructed by an spectral method; the exponential convergence and high accuracy of the equilibrium equations inherent in this method have been demonstrated. Since the error does not exceed 1 % when keeping ten terms in the approximations of displacement functions, the solution can be considered almost accurate. Similar calculations were performed using a finite element method implemented in ANSYS WB in order to verify the results. Differences in determining the displacements have been shown to not exceed 0.2 %, stresses – 4 %. The study result has established that the use of Fung, Varga, Neo-Hookean materials, as well as a zero-order material, lead to similar values of displacements and stresses, from which displacements of shells from the materials of the first and second orders significantly differ. This finding makes it possible, instead of the Fung material whose setting requires a significant amount of experimental data, to use simpler ones – a zero-order material and the Varga material