Conventional Terminal Sliding Mode Control Research Articles

Cascaded robust fixed-time terminal sliding mode control for uncertain cartpole systems with incremental nonlinear dynamic inversion

This paper proposes a cascaded fixed-time terminal sliding mode controller (TSMC) for uncertain underactuated cartpole dynamics using incremental nonlinear dynamic inversion (INDI). Leveraging partial linearization and prioritizing pole dynamics for internal tracking, the proposed controller achieves efficient stabilization of the cart upon convergence of the pole. Stability analysis is carried out using Lyapunov stability theorem, proving that the proposed controller stabilizes the state variables to an arbitrarily small neighborhood of the equilibrium in fixed-time, along with the suboptimality (steady-state error), existence and uniqueness of the solutions. The INDI is also integrated into TSMC to further improve the robustness while suppressing the conservativeness of conventional TSMC. The stability of INDI is rigorously proved using sampling-based Lyapunov function under sampling-based control realm. The simulation results illustrate the superiority of the proposed method with comparison and ablation studies.

Novel distributed event/self-triggered sliding-mode control: Application to practical fixed-time consensus of second-order multi-agent systems

This paper presents a novel terminal sliding-mode control (SMC) protocol to accomplish the practical fixed-time (PFXT) consensus of second-order multi-agent systems (MASs) through event-triggered scheme (ETS). The main challenge is the digitization of SMC which prevents the controlled system from reaching an ideal sliding phase and the singularity problem in terminal sliding-mode controllers. Firstly, a novel method of PFXT stability is proposed, which guarantees the non-singularity for the controller. Secondly, based on the proposed PFXT control method, a practical non-singular terminal SMC strategy is designed to accomplish the PFXT consensus of MASs through ETS. Besides, a strictly positive minimal triggering interval of each follower is given to exclude the Zeno phenomenon. Different with conventional terminal SMC, maintaining the sliding trajectory constrained on the sliding manifold is not a premise to guarantee the system stability. Then, to eliminate the requirement of continuous monitoring for ETS, the SMC strategy is generalized to the self-triggered approach. At last, a numerical example is presented to validate the developed methods.

Barrier-Function-Based Adaptive Fast-Terminal Sliding-Mode Control for a PMSM Speed-Regulation System

Barrier-function-based adaptive fast-terminal sliding-mode control approaches have been devised to enhance the precision of speed regulation of permanent magnet synchronous motors (PMSMs). Firstly, the speed loop utilizes fast-terminal sliding-mode control, which contributes to a faster convergence rate and enhances the robustness of the system. By adopting this control technique, the system can quickly reach the desired speed setpoint and effectively handle disturbances. Secondly, an adaptive law based on the barrier function is employed to adjust the control gain adaptively. The proposed adaptive law considers the magnitude of the disturbance and effectively mitigates chattering resulting from excessive switching gain. Unlike conventional control methods, the design of the adaptive fast-terminal sliding-mode control does not require attaining the upper limit of the lumped disturbances. Experimental results are presented to validate the proposed approach. These results demonstrate that the proposed method outperforms the conventional terminal sliding mode control technique in terms of handling both external and internal disturbances.

Robust Nonsingular Terminal Sliding Mode Control of a Buck Converter Feeding a Constant Power Load

In recent years, DC microgrid systems feeding constant power loads (CPLs) have been given a particular focus due to their effect on the overall system stability caused by their electrical characteristics behaving as negative incremental impedance. To address this issue, this paper investigates the stabilization of a DC bus voltage in a DC microgrid (MG) feeding a CPL. The output voltage of the main DC bus is stabilized by using a robust nonsingular terminal sliding mode controller that is characterized by the elimination of the singularity problem that arises from the conventional terminal sliding mode controller. The CPL is emulated by a boost converter where its output voltage is tightly regulated. The system is investigated in terms of voltage following and disturbance rejection. The robustness and effectiveness of the proposed control strategy are assessed against input voltage fluctuations and power demand variations. The proposed controller is validated through simulations and an experimental setup.

Distributed fixed-time sliding mode control of time-delayed quadrotors aircraft for cooperative aerial payload transportation: Theory and practice

This paper investigates a cooperative fixed-time control for networked-delayed and disturbed quadrotors in payload transportation missions. First, the input time-delayed tracking error system is adequately transformed into a delay-free system via Artstein’s reducing transformation. Second, a novel Distributed Cooperative Fixed-Time Stable Control Protocol (DCFTSCP) is proposed for the multi-quadrotor system to stabilize the geometrical spatial formation while carrying the payload. Furthermore, a disturbance observer is incorporated into the control framework to counteract the lumped disturbances and achieve the transportation task with a minimal swing. Overall, the designed DCFTSCP is able to stabilize the delayed tracking states at the origin in fixed-time uniformly to the Initial Conditions (ICs). It is worth mentioning that the proposed controller belongs to the homogeneous sliding mode control class. The reported related works rely on the bi-limit approximation method to prove the fixed-time convergence of the states. Nevertheless, this method suffers from a crucial shortcoming where it is unable mathematically to provide an explicit expression on the settling (convergence) time. In contrast, in the present study, the stability analysis is thoroughly investigated based on the algebraic Lyapunov tools, namely, Algebraic Lyapunov Equation (ALE) and Lyapunov Quadratic Function (LQF). Consequently, the upper-bound on the convergence-time is explicitly derived for the first time for time-delayed quadrotors aircraft used in cooperative payload transportation. MATLAB® simulations and real flight experiments are conducted to corroborate the theoretical studies of the paper. Overall, the results show that the proposed control protocol yields performance improvement regarding fixed-time tracking stability featuring fast transient, strong robustness, and high steady-state precision. In addition, the undesirable chattering problem of regular linear sliding mode control is noticeably attenuated. Furthermore, unlike conventional terminal sliding mode control techniques, the control input is singularity-free. Finally, several challenging issues in cooperative fixed-time control for networked-delayed quadrotors are highlighted for future research.

Combination of terminal sliding mode and finite-time state-dependent Riccati equation: Flapping-wing flying robot control

A novel terminal sliding mode control is introduced to control a class of nonlinear uncertain systems in finite time. Having command on the definition of the final time as an input control parameter is the goal of this work. Terminal sliding mode control is naturally a finite-time controller though the time cannot be set as input, and the convergence time is not exactly known to the user before execution of the control loop. The sliding surface of the introduced controller is equipped with a finite-time gain that finishes the control task in the desired predefined time. The gain is found by partitioning the state-dependent differential Riccati equation gain, then arranging the sub-blocks in a symmetric positive-definite structure. The state-dependent differential Riccati equation is a nonlinear optimal controller with a final boundary condition that penalizes the states at the final time. This guides the states to the desired condition by imposing extra force on the input control law. Here the gain is removed from standard state-dependent differential Riccati equation control law (partitioned and made symmetric positive-definite) and inserted into the nonlinear sliding surface to present a novel finite-time terminal sliding mode control. The stability of the proposed terminal sliding mode control is guaranteed by the definition of the adaptive gain of terminal sliding mode control, which is limited by the Lyapunov stability condition. The proposed approach was validated and compared with state-dependent differential Riccati equation and conventional terminal sliding mode control as independent controllers, applied on a van der Pol oscillator. The capability of the proposed approach of controlling complex systems was checked by simulating a flapping-wing flying robot. The flapping-wing flying robot possesses a highly nonlinear model with uncertainty and disturbance caused by flapping. The flight assumptions also limit the input law significantly. The proposed terminal sliding mode control successfully controlled the illustrative example and flapping-wing flying robot model and has been compared with state-dependent differential Riccati equation and conventional terminal sliding mode control.

Neural network–based adaptive fractional-order terminal sliding mode control

This paper proposes an adaptive fractional-order (FO) terminal sliding mode control (TSMC) scheme to the robust current control of active power filter (APF) using a recurrent meta-cognitive fuzzy neural network (RMCFNN). An FO TSMC is developed by considering that the parametric perturbations and the external disturbances of APF are bounded. Compared with conventional TSMC approach, the proposed scheme, with an FO sliding surface, can obtain enhanced finite-time high-precision tracking performance due to another degree of freedom. Then, a novel observer-based FO TSMC is derived to achieve an absorbing model-free feature arising from RMCFNN. To improve the capabilities in managing the uncertainties, the specific online updating schemes for the structure and parameters of RMCFNN are designed. Meanwhile, closed-loop stability and finite-time convergence characteristic can be achieved using Lyapunov theory. Finally, simulation and experimental results indicate that the proposed observer-based FO TSMC can be easily implemented by microcontroller and has superior control performance compared with other existing schemes.

Time‐varying nonsingular terminal sliding mode control for uncertain second‐order nonlinear systems with prespecified time

AbstractThis article proposes a time‐varying nonsingular terminal sliding mode (TSM) control for a class of uncertain second‐order nonlinear system and its application to n‐links rigid robotic manipulators. First, a time‐varying nonsingular terminal sliding manifold is developed by incorporating a piecewise‐defined function of time into a nonsingular TSM manifold. As a result, the singularity problem is avoided and the reaching phase existing in conventional TSM control is totally suppressed which ensures the global robustness of the system against uncertainties and disturbances. Moreover, adaptive tuning laws are developed to omit the requirement of prior knowledge of the upper bound of the lumped uncertainty. In particular, an effective method is provided for the parameters selection to meet a prespecified convergence time. Hence, the convergence time to the origin of the tracking errors can be specified in advance according to the mission requirements. The formulation of the controllers and the stability analysis are verified by Lyapunov theory. Simulation results and comparative studies are presented to demonstrate the effectiveness and the superiority of the proposed algorithms.

Neuro-adaptive fixed-time non-singular fast terminal sliding mode control design for a class of under-actuated nonlinear systems

This paper presents a fixed-time neuro-adaptive control design for a class of uncertain under-actuated nonlinear systems (UNS) using a non-singular fast terminal sliding mode control (TSMC) with a radial basis function (RBF)-based estimator to achieve the convergence and robustness against the uncertainties. The mathematical model of the considered class is reduced into an equivalent regular form. A fast TSMC is designed for the transformed form to improve the control performance and annihilate the associated singularity problem of the conventional TSMC. Lyapunov stability theory ensures the steering of the sliding manifold and system states in fixed time. RBF neural networks are adaptively estimate the nonlinear drift functions. The theoretical design, analysis, and simulations of cart-pendulum and quadcopter demonstrate the feasibility and benefits of the regular form transformation and the designed control design. Comparing the proposed synthesis with the standard literature presents the attractive nature of proposed method for such a class.

Robust Terminal Sliding Mode Control on SE(3) for Gough–Stewart Flight Simulator Motion Platform with Payload Uncertainty

This work proposes a robust terminal sliding mode control scheme on Lie group space SE(3) for Gough–Stewart flight simulator motion systems with payload uncertainty. A complete dynamic model with geometric mechanical structures and a computer dynamic model built in the MATLAB/Simulink package are briefly presented. The robust control strategy on the Lie group SE(3) is applied at the workspace level to counteract the effects of imperfect compensation due to model simplification and payload uncertainty in flight simulator application. With exponential coordinates for configuration error and adjoint operator on Lie algebra se(3), the robust control strategy is designed to guarantee almost global finite-time convergence over state space through the Lyapunov stability theory. Finally, a describing function and a step acceleration response to characterize the performance of a flight simulator motion base are employed to compare the robustness performance of the proposed controller on SE(3) with the conventional terminal sliding mode controller on Cartesian space. The comparison experimental results verify that the proposed controller on SE(3) provides better robustness than the conventional controller on Cartesian space, which means higher bandwidth in two degrees of freedom and faster response with smaller tracking error in six degrees of freedom.

Robust trajectory tracking with non-singular terminal sliding mode control of a mobile manipulator

This effort addresses and uses a robust-trajectory-tracking control system for kinematically redundant location tracking of a mobile manipulator (mobman) in its task space in the presence of parameter uncertainties and external disturbances. It consists of a serial manipulator with four degrees of freedom (DOF) fixed on three DOF mobile bases. A robust tracking control is achieved using the configuration of a non-singular terminal sliding mode (NSTSM) control for the entire non-linear model of a mobman. Because of the non-linear added term in the linear sliding surface, which reflects in the non-linear sliding mode known as terminal sliding mode (TSM), this control preparation satisfies systems states finite time convergence. Similarly, conventional terminal sliding mode control (CTSMC) entail singularity trouble, which is tackled by the control scheme. (Computer based) simulations are used to demonstrate the convenience, feasibility, and robustness of given techniques.

Design of a non-singular fast terminal sliding mode control for second-order nonlinear systems with compound disturbance

This paper investigates a new disturbance observer based non-singular fast terminal sliding mode control technique for the path tracking and stabilization of non-linear second-order systems with compound disturbance. The compound disturbance is comprised of both parametric and non-parametric uncertainties. While warranting fast convergence rate and robustness, it also dominates the singularity and complex-value number issues associated with conventional terminal sliding mode control. Furthermore, due to the estimation properties of the observer, knowledge about the bounds of the uncertainties is not required. The simulation results of two case studies, the velocity and path tracking of an autonomous underwater vehicle and the stabilization of a chaotic Φ6-Duffing oscillator, validate the efficacy of the proposed method.

Adaptive type‐II fuzzy nonsingular fast terminal sliding mode controller using fractional‐order manifold for second‐order chaotic systems

AbstractA novel fuzzy adaptive finite‐time controller is designed for synchronization and control of the Duffing–Holmes and the gyroscope systems in the presence of uncertainty and external disturbance. The fractional‐order fast nonsingular terminal sliding mode manifold is used to ensure the finite‐time control, speed up the convergence rate, and address the singularity problem of the conventional terminal sliding mode controller. Also, the novel control law successfully reduces the chattering phenomenon. Adaptive biased type‐II fuzzy inference system is used to determine the optimal values of the switching control term. The adaptation rules of the novel fuzzy inference system are achieved based on Lyapunov stability theorem. Finally, by using numerical simulations, the effectiveness and superiority of the proposed control scheme are verified against some other methods.

Non-singular terminal sliding mode control for redundantly actuated parallel mechanism

In this article, the trajectory tracking control is developed by implementing a non-singular terminal sliding mode control for the redundantly actuated parallel mechanism system. The proposed control scheme could guarantee that the tracking errors converge to zero asymptotically. The problem of singularity with regard to conventional terminal sliding mode control scheme can be eliminated with the presented novel non-singular terminal sliding mode surface as well. The corresponding stability of the proposed control scheme has also been proved theoretically in terms of Lyapunov method. In addition, simulations and experiments are conducted for trajectory tracking to validate the effectiveness of the proposed scheme. The illustrative results demonstrate that the proposed scheme is available to solve the uncertainties and external disturbances with self-tuning in real time. Furthermore, the prominent characteristics of the presented control scheme are quick convergence, high accuracy, and high robustness, which can achieve excellent tracking performance as compared with computed torque control scheme and conventional sliding mode control scheme.

Finite-Time Control for Piezoelectric Actuators With a High-Order Terminal Sliding Mode Enhanced Hysteresis Observer

Piezoelectric actuators (PZTs) are essential elements in high-precision systems. However, the hysteresis nonlinearity introduced by PZTs degrades the control accuracy. In this paper, a high-order terminal sliding mode enhanced hysteresis observer is designed, which compensates the error between the Bouc-Wen model and the actual hysteresis. Subsequently, a novel terminal sliding mode control (TSMC) is proposed. Unlike the conventional TSMC, the novel TSMC method makes the tracking error in the sliding mode converge to the origin within a finite time regardless of the initial conditions, which improves the performance of conventional TSMC. The stability of the proposed control method is verified through the Lyapunov theory. Finally, simulations and experiments are implemented to validate the effectiveness of the proposed control method. Experimental results demonstrate that the proposed method has a more superior performance than conventional TSMC.

Implementation of an Adaptive Neural Terminal Sliding Mode for Tracking Control of Magnetic Levitation Systems

In this article, an adaptive neural terminal sliding mode is implemented for tracking control of magnetic levitation systems with the presence of dynamical uncertainty and exterior perturbation. By proposing a novel fast terminal sliding manifold function with the dynamic coefficients, the system state variables quickly converge the equilibrium point on the manifold function. Besides, an adaptive, robust reaching control law combined with radial basis function neural network compensator drives the system fast approaching the sliding manifold function regardless of whether the initial value is near or far from the sliding manifold and reduces the chattering of the conventional terminal sliding mode control. With a design approach based on the combination of the proposed sliding manifold and the combined control law, the implemented control method provides a control performance with significant improvement in the terms of chattering reduction, high tracking accuracy, fast convergence along with simple design for real applications. The experimental work is implemented for a real magnetic levitation system to demonstrate the superior efficiency of the proposed terminal sliding mode control. The stable evidence of the proposed method is also completely verified by Lyapunov-based method.

A Novel Fault-Tolerant Control Method for Robot Manipulators Based on Non-Singular Fast Terminal Sliding Mode Control and Disturbance Observer

In this study, a novel Fault-Tolerant Control Methodology (FTCM) is developed for robot manipulators. First, to overcome singularity glitch and to enhance convergence time of conventional Terminal Sliding Mode Control (TSMC), a new Fast Terminal Sliding Mode Surface (FTSMS) is constructed. Next, to reduce the computation complexity and to provide requirements about undefined nonlinear functions for the control system, a Disturbance Observer (DO) to estimate uncertain dynamics, external disturbances, or faults. Besides, a Super-Twisting Reaching Control Law (STRCL) is designed to compensate for the estimated error of disturbance observer with chattering rejection. Final, a novel, robust, FTCM was developed for robot manipulators to obtain the stability goal of the system, to reach the prescribed performance, and to overcome the effects of disturbances, nonlinearities, or faults. Accordingly, the proposed FTCM has remarkable features, such as fast convergence speeds, robust precision, high tracking performance, significant alleviation of chattering behavior, and finite-time convergence. The position tracking computer simulations were implemented to exhibit the effectiveness and feasibility of the suggested FTCM compared with other control algorithms.

Research on trajectory tracking control of manipulator based on modified terminal sliding mode with double power reaching law

This article proposes a control strategy that combines the double power reaching law with the modified terminal sliding mode for tracking tasks of rigid robotic manipulators quickly and accurately. As a significant novelty, double power reaching law can reach the sliding surface in finite time when the system is in any initial state. At the same time, modified terminal sliding surface guarantees the system that position and velocity error converge to be zero approximately. In other words, the control law is able to make the system slip to the equilibrium point in a finite time and improves the speed of the system approaching and sliding modes. The simulation results demonstrate the practical implementation of the control strategy, verify its robustness of more accurate tracking and faster disturbance rejection, and weaken the chattering phenomenon more effectively compared with the conventional terminal sliding mode controller.

Finite-time nonsingular terminal sliding mode control: A time setting approach

This article proposes a combination of linear and nonlinear sliding surfaces to design a new structure for terminal sliding mode control, capable of accepting a definite final time as an input data. The structures of both single-input-single-output and multi-input-multi-output systems are expressed. The controller operates in two modes: first, reaching the states to linear sliding surface, defining control parameters and rise time; second, switching to nonlinear sliding surface and defining a convergence time. Sum of rise time and convergence time, both of which as inputs, sets the final time. The control gains are adaptively tuned and parameter uncertainty in dynamics is considered in the design. The proposed method is implemented theoretically and experimentally on Scout robot in point-to-point motion and trajectory tracking. The results are compared to conventional terminal sliding mode control and finite-time state-dependent Riccati equation to assess the improvement.

An Adaptive Terminal Sliding Mode Control for Robot Manipulators With Non-Singular Terminal Sliding Surface Variables

This paper presents an adaptive terminal sliding mode control (TSMC) algorithm for robot manipulators. The contribution of our control method is that the suggested controller can enable the advantages of non-singular TSMC such as non-singularity, high robustness, small transient error, and finite time convergence. To develop the suggested system, a non-singular terminal sliding variable is selected and does not have any complex-value or constraints of the exponent in conventional TSMC. Therefore, it prevents the singularity that occurs in the conventional TSMC and eliminates the reaching phase glitch. Accordingly, the suggested system can ensure that the controlled variables reach the desired values within a randomly known finite time using an efficiently smooth and chattering-free definite control input. In addition, sliding motion in finite time can be achieved by employing the adaptive self-tuning rules with no prior information regarding the upper bounds of undefined parameters (e.g., friction, disturbances, and uncertainties). Furthermore, the finite-time convergence and global stability of the proposed algorithm are proved by the Lyapunov stability theory. Finally, the proposed control algorithm is applied to the joint position tracking control simulation for a 3-DOF PUMA560 robot. The trajectory tracking performance of the proposed method is compared with those of the conventional terminal sliding mode control and the conventional continuous sliding mode control. This comparison shows the efficiency and superiority of the proposed algorithm.