A model-free terminal sliding mode control for robots: Achieving fixed-time prescribed performance and convergence.

This paper introduces a new control strategy for robot manipulators, specifically designed to tackle the challenges associated with traditional model-based sliding mode (SM) controller design. These challenges include the need for accurately computed system models, knowledge of disturbance upper bounds, fixed-time convergence, prescribed performance, and the generation of chattering. To overcome these obstacles, we propose the incorporation of a neural network (NN) that effectively addresses these issues by removing the constraint of a precise system model. Additionally, we introduce a novel fixed-time prescribed performance control (PPC) to enhance response performance and position-tracking accuracy, while effectively limiting overshoot and maintaining steady-state error within the predefined range. To expedite the convergence of the SM surface to its equilibrium point, we introduce a faster terminal sliding mode (TSM) surface and a novel fixed-time reaching control algorithm (RCA) with adaptable factors. By integrating these approaches, we develop a novel control strategy that successfully achieves the desired goals for robot manipulators. The effectiveness and stability of the proposed approach are validated through extensive simulations on a 3-DOF SAMSUNG FARA-AT2 robot manipulator, utilizing both Lyapunov criteria and performance evaluations. The results demonstrate improved convergence rate and tracking accuracy, reduced chattering, and enhanced controller robustness.

Real-Time Implementation of the Prescribed Performance Tracking Control for Magnetic Levitation Systems.

For magnetic levitation systems subject to dynamical uncertainty and exterior perturbations, we implement a real-time Prescribed Performance Control (PPC). A modified function of Global Fast Terminal Sliding Mode Manifold (GFTSMM) based on the transformed error of the novel PPC is introduced; hence, the error variable quickly converges to the equilibrium point with the prescribed performance, which means that maximum overshoot and steady-state of the controlled errors will be in a knowledge-defined boundary. To enhance the performance of Global Fast Terminal Sliding Mode Control (GFTSMC) and to reduce chattering in the control input, a modified third-order sliding mode observer (MTOSMO) is proposed to estimate the whole uncertainty and external disturbance. The combination of the GFTSMC, PPC, and MTOSMO generates a novel solution ensuring a finite-time stable position of the controlled ball and the possibility of performing different orbit tracking missions with an impressive performance in terms of tracking accuracy, fast convergence, stabilization, and chattering reduction. It also possesses a simple design that is suitable for real-time applications. By using the Lyapunov-based method, the stable evidence of the developed method is fully verified. We implement a simulation and an experiment on the laboratory magnetic levitation model to demonstrate the improved performance of the developed control system.

An Adaptive Prescribed Performance Tracking Motion Control Methodology for Robotic Manipulators with Global Finite-Time Stability.

In this paper, the problem of an APPTMC for manipulators is investigated. During the robot's operation, the error states should be kept within an outlined range to ensure a steady-state and dynamic attitude. Firstly, we propose the modified PPFs. Afterward, a series of transformed errors is used to convert "constrained" systems into equivalent "unconstrained" ones, to facilitate control design. The modified PPFs ensure position tracking errors are managed in a pre-designed performance domain. Especially, the SSE boundaries will be symmetrical to zero, so when the transformed error is zero, the tracking error will be as well. Secondly, a modified NISMS based on the transformed errors allows for determining the highest acceptable range of the tracking errors in the steady-state, finite-time convergence index, and singularity elimination. Thirdly, a fixed-time USOSMO is proposed to directly estimate the lumped uncertainty. Fourthly, an ASTwCL is applied to deal with observer output errors and chattering. Finally, an observer-based-control solution is synthesized from the above techniques to achieve PCP in the sense of finite-time Lyapunov stability. In addition, the precision, robustness, as well as harmful chattering reduction of the proposed APPTMC are improved significantly. The Lyapunov theory is used to analyze the stability of closed-loop systems. Throughout simulations, the proposed PPTMC has been shown to perform well and be effective.

A Novel Prescribed-Performance-Tracking Control System with Finite-Time Convergence Stability for Uncertain Robotic Manipulators.

Through this article, we present an advanced prescribed performance-tracking control system with finite-time convergence stability for uncertain robotic manipulators. It is therefore necessary to define a suitable performance function and error transformation to guarantee a prescribed performance within a finite time. Following the definitions mentioned, a modified integral nonlinear sliding-mode hyperplane is constructed from the transformed errors. By using the designed nonlinear sliding-mode surface and the super-twisting reaching control law, an advanced approach to the prescribed performance control was formed for the trajectory tracking control of uncertain robotic manipulators. The proposed controller exhibits improved properties, including estimated convergence speed and a predefined upper and lower limit for maximum overshoot during transient responses. Furthermore, the maximum allowable size of the control errors at the steady-state can be predefined and these errors will inevitably converge to zero within a finite time, while the proposed controller can provide a smooth control torque without the loss of its robustness. It is shown that the proposed control system is globally stable and convergent over a finite time. A comprehensive analysis of the effectiveness of the proposed control algorithm was already conducted via the simulation of an industrial robot manipulator.

A Novel Active Fault-Tolerant Tracking Control for Robot Manipulators with Finite-Time Stability.

Many terminal sliding mode controllers (TSMCs) have been suggested to obtain exact tracking control of robotic manipulators in finite time. The ordinary method is based on TSMCs that secure trajectory tracking under the assumptions such as the known robot dynamic model and the determined upper boundary of uncertain components. Despite tracking errors that tend to zero in finite time, the weakness of TSMCs is chattering, slow convergence speed, and the need for the exact robot dynamic model. Few studies are handling the weakness of TSMCs by using the combination between TSMCs and finite-time observers. In this paper, we present a novel finite-time fault tolerance control (FTC) method for robotic manipulators. A finite-time fault detection observer (FTFDO) is proposed to estimate all uncertainties, external disturbances, and faults accurately and on time. From the estimated information of FTFDO, a novel finite-time FTC method is developed based on a new finite-time terminal sliding surface and a new finite-time reaching control law. Thanks to this approach, the proposed FTC method provides a fast convergence speed for both observation error and control error in finite time. The operation of the robot system is guaranteed with expected performance even in case of faults, including high tracking accuracy, small chattering behavior in control input signals, and fast transient response with the variation of disturbances, uncertainties, or faults. The stability and finite-time convergence of the proposed control system are verified that they are strictly guaranteed by Lyapunov theory and finite-time control theory. The simulation performance for a FARA robotic manipulator proves the proposed control theory's correctness and effectiveness.

A Robust Observer-Based Control Strategy for n-DOF Uncertain Robot Manipulators with Fixed-Time Stability.

In this paper, a robust observer-based control strategy for n-DOF uncertain robot manipulators with fixed-time stability was developed. The novel fixed-time nonsingular sliding mode surface enables control errors to converge to the equilibrium point quickly within fixed time without singularity. The development of the novel fixed-time disturbance observer based on a uniform robust exact differentiator also allows uncertain terms and exterior disturbances to be proactively addressed. The designed observer can accurately approximate uncertain terms within a fixed time and contribute to significant chattering reduction in the traditional sliding mode control. A robust observer-based control strategy was formulated, according to a combination of the fixed-time nonsingular terminal sliding mode control method and the designed observer, to yield global fixed time stability for n-DOF uncertain robot manipulators. The proposed controller proved definitively that it was able to obtain global stabilization in fixed time. The approximation capability of the proposed observer, the convergence of the proposed sliding surface, and the effectiveness of the proposed control strategy in fixed time were fully confirmed by simulation performance on an industrial robot manipulator.

EARLY ESTIMATION OF REPRODUCTION NUMBER OF COVID-19 IN VIETNAM

Reproduction number is an epidemiologic indicator that reflects the contagiousness and transmissibility of infectious agents. This paper aims to estimate the reproduction number of in the early phase of COVID-19 outbreak in Vietnam.