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In this paper, an implicit discrete‐time fast terminal sliding mode (DFTSM) control with disturbance compensation is designed and analyzed for uncertain high‐order systems. First, a recursive discrete sliding surface is constructed based on implicit Euler technique, which can completely eliminate discretization chattering so as to significantly reduce the boundary layer of sliding mode motion. With the help of a high‐order disturbance compensator, the accuracy limitation of implicit DFTSM control systems is overcome by increasing the order of sliding mode. Then the finite‐time convergence of implicit DFTSM is proved for the first time, and the influence relationship of control parameters on the convergence speed and control accuracy of the algorithm is established. Finally, two numerical examples are provided to demonstrate the effectiveness and superiority of the proposed design approach. [ABSTRACT FROM AUTHOR]

The work presented in this brief describes the design of a discrete-time super-twisting algorithm based fractional-order observer for a class of non-linear fractional-order systems. The proposed observer is shown to achieve higher performance as compared to the conventional integer-order observers in terms of robustness and convergence time. It generalizes the design of observers for the class of non-linear fractional-order systems. The peaking phenomenon is observed to be less significant in the proposed approach. Chattering is suppressed with the Fractional Adams-Moulton Method, which is an implicit Euler discretization technique. The significance of the proposed observer is illustrated through a simulation example. [ABSTRACT FROM AUTHOR]

Noise reduction is one of the important issues for feedback control systems. Toward this problem, this paper proposes a new sliding mode filter, which is an improvement of Lv et al. ’s parabolic sliding mode filter. The proposed filter employs a first-order derivative feed-forward term for increasing both tracking and noise attenuating performances. Its discrete-time algorithm is derived by applying the implicit-Euler discretization, and it realizes exact convergence without producing chattering in discrete-time implementation. The effectiveness of the proposed filter is evaluated through an open-loop and a closed-loop numerical examples.

This paper presents a new quick-response sliding mode tracking differentiator (new TD) for feedback control of mechatronic systems. The new TD is an extension of Jin et al.’s sliding mode tracking differentiator (TD-J) by employing an exponential reaching term for balancing the trade-off between noise attenuating efficiency and convergence speed. The discrete-time algorithm of the new TD is derived by using the implicit-Euler discretization and an equivalent between a set-valued signum function and a saturation function, and it does not produce chattering, which has been one major challenge of implementing sliding mode technique in discrete-time. Simulations and experiments are conducted for validating the effectiveness of the new TD.

This brief proposes a discrete-time fractional-order differentiator based on the super-twisting algorithm for second-order systems. The differentiator achieves higher performance with respect to the classical ones of integer order in terms of convergence time and robustness. It relaxes the classical boundedness condition required to be satisfied by the second-order derivatives of the functions in conventional differentiators. The numerical integration is performed by an implicit Euler discretization technique based on the Fractional Adams-Moulton method, which significantly suppresses the chattering. The significance of the proposed differentiator is demonstrated through a simulation example, comparing with the classical ones. [ABSTRACT FROM AUTHOR]

This paper proposes a new sliding mode differentiator combined with a sliding mode filter for estimating first and second-order derivatives of noisy signals. The proposed differentiator can be seen as a version of Slotine et al.'s sliding mode observer extended with an additional non-Lipschitz property, which is intended to realize a faster reaching to the sliding mode. It behaves as a noise-reduction filter that is composed of first, second and third-order low-pass filter in the sliding mode, but also employs the filter that is composed of second, third and fourth-order low-pass filter out of the sliding mode. Moreover, the differentiator effectively removes impulsive noises by combining a sliding mode filter and its discrete-time implementation is based on the implicit (backward) Euler discretization, which does not result in chattering and realizes the exact sliding mode. Experiments show that the proposed algorithm has a better balance between the noise attenuation and small phase lag than the linear-filtered Euler differentiation and previous sliding mode differentiators. It was validated through experiments using optical encoder signals of industrial robots [ABSTRACT FROM AUTHOR]

We analyze the implicit Euler discretization for a class of convex linear-quadratic optimal control problems with control appearing linearly. Constraints are defined by lower and upper bounds for the controls, and the cost functional may depend on a regularization parameter ν . Without any structural assumption on the optimal control we prove convergence of order 1 w.r.t. the mesh size for the discrete optimal values. Under the additional assumption that the optimal control is of bang-bang type and the switching function satisfies a growth condition around their zeros we show that the solutions are calm functions of perturbation and regularization parameters. By applying this result to the implicit Euler discretization we improve existing error estimates for discretizations based on the explicit Euler method. Numerical experiments confirm the theoretical findings and demonstrate the usefulness of implicit methods and regularization in case of bang-bang controls. [ABSTRACT FROM AUTHOR]

The transient quantum drift diffusion model is derived from the isothermal quantum hydrodynamic model via a zero relaxation time limit. This yields a fourth-order nonlinear parabolic equation for the electron density, which is self-consistently coupled to the Poisson equation for the electrostatic potential. A stability analysis of the linearized system is performed by means of Hilbert space methods, which rely on a generalized Poincaré-type inequality. In the quantum case more states are linearly stable than in the classical one. The linear stability of an implicit Euler discretization for the nonlinear equations is proven and numerical results for a diode are presented, indicating that no maximum principle holds for the linearized system. [ABSTRACT FROM AUTHOR]