Search Results (13)

In contrast to the majority of model-based terminal sliding mode control (TSMC) approaches that rely on the plant physical model and/or data-driven adaptive pointwise model, this study treats the unknown dynamic plant as a total uncertainty in a black box with enabled control inputs and attainable outputs (either measured or estimated), which accordingly proposes a model-free (MF) nonsingular terminal sliding mode control (MFTSMC) for higher-order dynamic systems to reduce the tedious modelling work and the design complexity associated with the model-based control approaches. The total model-free controllers, derived from the Lyapunov differential inequality, obviously provide conciseness and robustness in analysis/design/tuning and implementation while keeping the essence of the TSMC. Three simulated bench test examples, in which two of them have representatively numerical challenges and the other is a two-link rigid robotic manipulator with two input and two output (TITO) operational mode as a typical multi-degree interconnected nonlinear dynamics tool, are studied to demonstrate the effectiveness of the MFTSMC and employed to show the user-transparent procedure to facilitate the potential applications. The major MFTSMC performance includes (1) finite time ($2.5\pm 0.05$ s) dynamic stabilization to equilibria in dealing with total physical model uncertainty and disturbance, (2) effective dynamic tracking and small steady state error $0\pm 0.002$, (3) robustness (zero sensitivity at state output against the unknown bounded internal uncertainty and external disturbance), (4) no singularity issue in the neighborhood of TSM $\sigma =0$, (5) stable chattering with low amplitude ($\pm 0.01$) at frequency 50 mHz due to high gain used against disturbance $d(t)=100+30\sin (2\pi t)$). The simulation results are similar to those from well-known nominal model-based approaches. Full article

To address the formation control issue of multiple unmanned aerial vehicles (UAVs), a finite-time control scheme based on terminal sliding mode (TSM) is investigated in this paper. A quadcopter UAV with the vertical takeoff property is considered, with cascaded kinematics composed of rotational and translational loops. To strengthen the application in the low-cost UAV system, the applied torque is synthesized with an auxiliary rotational system, which can avoid utilizing direct attitude measurement. Furthermore, a terminal sliding mode surface is established and employed in the finite-time formation control protocol (FTFCP) as the driven thrust of multiple UAVs over an undirected topology in the translational system. To maintain the safe flight of the UAV clusters in an environment to avoid collision with obstacles or with other UAV neighbors, a pigeon-hierarchy-inspired obstacle avoidance protocol (PHOAP) is proposed. By imitating the interactive hierarchy that exists among the homing pigeon flocks, the collision avoidance scheme is separately enhanced to generate the repulsive potential field for the leader maneuver target and the follower UAV cluster. Subsequently, the collision avoidance laws based on pigeon homing behavior are combined with the finite-time sliding mode formation protocol, and the applied torque is attached as a cascaded structure in the attitude loop to synthesize an obstacle avoidance cooperative control framework. Finally, simulation scenarios of multiple UAVs to reach a desired formation among obstacles is investigated, and the effectiveness of the proposed approach is validated. Full article

We address the problems in the trajectory tracking control of a multi-joint robotic arm, including uncertainty in the internal modeling of its significant external unknown time-varying disturbances. With the control objective of tracking the desired trajectories of each joint stably and accurately, this paper proposes an adaptive non-singular terminal sliding mode control method based on a nonlinear disturbance observer (NDO). In order to speed up the convergence of the tracking error and avoid the singular value problem existing in the traditional terminal sliding mode (TSM), a non-singular terminal sliding mode (NTSM) surface is proposed in this paper. Given the system modeling uncertainty and external unknown time-varying disturbances, a nonlinear disturbance observer is used to observe the total set disturbance for feed-forward compensation. Secondly, the switching gain adaptive law is used to estimate the observation error of the total set disturbance and allow for the online adjustment of the switching gain weights. A robust gain adaptive law is also designed to reconverge quickly to the non-singular sliding mode surface when transient significant disturbances shock the system’s state variables out of the sliding phase. A simulation analysis of the spatial two-link robotic arm is carried out in Simulink. The results show that the adaptive non-singular terminal sliding mode control strategy based on the nonlinear disturbance observer proposed (PNDOANTSM) in this paper can reduce the average steady-state errors of robotic arm joints 1 and 2 by 36.58%, 38.40%, 44.68%, and 42.86%, compared with those observed in switching term adaptive law non-singular terminal sliding mode control based on a nonlinear disturbance observer (NDOANTSM) and non-singular terminal sliding mode control based on a nonlinear disturbance observer (NDONTSM). This paper provides a practical and feasible trajectory tracking control method for multi-joint robotic arms. Full article

This paper proposes a second-order terminal sliding mode (2TSM) approach to the trajectory tracking of the differential drive mobile robot (DDMR). Within this cascaded control scheme, the 2TSM dynamic controller, at the innermost loop, tracks the robot’s velocity quantities while a kinematic controller, at the outermost loop, regulates the robot’s positions. In this manner, chattering is greatly attenuated, and finite-time convergence is guaranteed by the second-order TSM manifold, which involves higher-order derivatives of the state variables, resulting in an inherently robust as well as fast and better tracking precision. The simulation results demonstrate the merit of the proposed control methods. Full article

Considering system uncertainties (e.g., gear backlash, unmodeled dynamics, nonlinear friction and parameters perturbation) coupling disturbances weaken the motion performance of robotic systems, an observer-based finite-time prescribed performance sliding mode control with faster reaching law is proposed for robotic manipulators equipped with dual-motor joints (DMJs). In the case where the backlash information is completely unknown, the backlash is maximally eliminated using a simple but efficient dual-motor adaptive anti-backlash strategy. Thus, the design of position tracking controllers for DMJs can be simplified. Then, to deal with the influence of disturbances and residual uncertainties (excluding backlash), a novel finite-time adaptive sliding mode disturbance observer (ASMDO) is proposed to practically estimate the lumped uncertainties where their upper bounds are assumed to be unknown. Finally, a finite-time composite fast non-singular terminal sliding mode (TSM) controller, integrated with the prescribed performance principle, is proposed in this paper. To enhance the convergence rate, a novel TSM-type reaching law has been developed. The controller ensures that the tracking error is not only stabilized within a finite-time convergence rate but also adheres to a predefined maximum transient-steady-state error. The proposed scheme is implemented through simulation and experimental results, demonstrating its superior performance. Full article

This paper studies the trajectory tracking issue for an underactuated autonomous underwater vehicle (AUV) in the horizontal plane. The desired velocity–tracking error relationship (DVTER) is constructed according to the kinematics and kinetic equation, which means that the expected velocities are built so that the position tracking errors converge to 0. Moreover, the limitation of obtaining the expected velocity by directly differentiating the desired position values is avoided. Then, the nonsingular fast terminal sliding mode (TSM) controller is developed to ensure that the velocities converge to the designed expected values in finite time, and tracking speed is improved by comparing with the traditional nonsingular terminal sliding mode method. It turns out that the expected trajectory can be tracked by an underactuated AUV. Finally, the efficiency of the constructed control mechanism is confirmed by simulation results. Full article

This paper presents an adaptive fixed-time fractional integral control for externally disturbed Euler–Lagrange systems. In the first step of the control design, the approach of fractional-order fixed-time integral nonsingular terminal sliding mode control (FoIFxTSM) is introduced. This scheme combines the benefits of fractional calculus with integral sliding mode control, resulting in fast convergence, smooth nonsingular control inputs, and fixed-time stability. By integrating an adaptive scheme, the proposed method is used to control the dynamical system in the presence of uncertainty and external perturbations. The findings of the fixed-time stability using Lyapunov analyses are provided for the closed-loop system. The simulation results are compared with the adaptive fractional-order sliding mode control scheme, and they show the better tracking and convergence performance of the proposed method. Full article

This paper addresses the issue of external unknown environmental interference affecting the trajectory tracking performance and driving stability of autonomous vehicles. This seriously impacts the performance and stability of the vehicle while driving. In order to provide precise, reliable, and safe trajectory tracking performance for autonomous vehicles, this paper proposes a recursive integral terminal sliding mode control (RITSMC) method. The proposed RITSMC combines the advantages of recursive integral sliding mode (RISM), terminal sliding mode (TSM), and adaptive algorithms, and can effectively achieve precise trajectory tracking and driving stability of autonomous vehicles. Furthermore, compared with traditional methods, an adaptive algorithm is introduced on the recursive sliding surface to enable real-time adaptation of the control parameters of the recursive controller, further improving the trajectory tracking accuracy and driving stability of autonomous vehicles. The stability of this control system is demonstrated by using a Lyapunov function. Finally, multiple simulation tests were conducted on different lane speeds on both wet and dry asphalt road sections. By comparing the simulation results, it was found that the proposed RITSMC exhibits excellent performance in terms of the precision of tracking trajectories and the stability of driving, in contrast to traditional sliding mode controllers (SMC) and integral terminal sliding mode controllers (ITSMC). Full article

Aiming at the trajectory tracking problem with unknown uncertainties, a novel controller composed of proportional-integral-differential sliding mode surface (PIDSM) and variable gain hyperbolic reaching law is proposed. A PID-type sliding mode surface with an inverse hyperbolic integral terminal sliding mode term is proposed, which has the advantages of global convergence of integral sliding mode (ISM) and finite time convergence of terminal sliding mode (TSM), and the control effect is significantly improved. Then, a variable gain hyperbolic approach law is proposed to solve the sliding mode approaching velocity problem. The variable gain term can guarantee different approaching velocities at different distances from the sliding mode surface, and the chattering problem is eliminated by using a hyperbolic function instead of the switching function. The redesign of the sliding mode surface and the reaching law ensures the robustness and tracking accuracy of the uncertain system. Adaptive estimation can compensate for uncertain disturbance terms in nonlinear systems, and the combination with sliding mode control further improves the tracking accuracy and robustness of the system. Finally, the Lyapunov stability principle is used for stability analysis, and the simulation study verifies that the proposed control scheme has the advantages of fast response, strong robustness, and high tracking accuracy. Full article

A nonlinear stiffness actuator (NSA) can achieve high torque/force resolution in the low stiffness range and high bandwidth in the high stiffness range. However, for the NSA, due to the imperfect performance of the elastic mechanical component such as friction, hysteresis, and unmeasurable energy consumption caused by former factors, it is more difficult to achieve accurate position control compared to the rigid actuator. Moreover, for a compliant robot with multiple degree of freedoms (DOFs) driven by NSAs, the influence of every NSA on the trajectory of the end effector is different and even coupled. Therefore, it is a challenge to implement precise trajectory control on a robot driven by such NSAs. In this paper, a control algorithm based on the Terminal Sliding Mode (TSM) approach is proposed to control the end effector trajectory of the compliant robot with multiple DOFs driven by NSAs. This control algorithm reduces the coupling of the driving torque, and mitigates the influence of parametric variation. The closed-loop system’s finite time convergence and stability are mathematically established via the Lyapunov stability theory. Moreover, under the same experimental conditions, by the comparison between the Proportion Differentiation (PD) controller and the controller using TSM method, the algorithm’s efficacy is experimentally verified on the developed compliant robot. The results show that the trajectory tracking is more accurate for the controller using the TSM method compared to the PD controller. Full article

This paper applies modified feedback technology to carry out the exact steady-state and fast transient in a high-performance alternating current (AC) power supply. The presented scheme displays the virtues of a finite-time convergence control (FTCC) and a discrete grey prediction model (DGPM). The FTCC, derived from a terminal sliding-mode (TSM) design principle, can produce the finite system-state convergence time and evade the singularity. It is noteworthy that the chattering/steady-state error around the FTCC may occur because of the overestimated or underestimated uncertainty bound. The DGPM with the bound estimate ability is integrated into the FTCC to cope with internal parameter variations and external load disturbances. The less chattering and steady-state error can be obtained, providing more robust performance in the AC power supply. The combination of the FTCC and the DGPM extends the standard TSM design for the purpose of faster singularity-free convergence, as well as introducing the grey modeling method in the case of a more exact uncertainty estimate. The modified control technology has a high-precision tracking performance and a fast convergent speed. Simulated and experimental results point out that the modified control technology can effectuate low total harmonic distortion (THD) and fast dynamic response in the presence of rectifier loads and abrupt step load changes. Full article

In order to improve the performance of the closed-loop Buck converter control system, a compound control scheme based on nonlinear disturbance observer (DO) and nonsingular terminal sliding mode (TSM) was developed to control the Buck converter. The control design includes two steps. First of all, without considering the dynamic and steady-state performances, a baseline terminal sliding mode controller was designed based on the average model of the Buck converter, such that the desired value of output voltage could be tracked. Secondly, a nonlinear DO was designed, which yields an estimated value as the feedforward term to compensate the lumped disturbance. The compound controller was composed of the terminal sliding mode controller as the state feedback and the estimated value as the feedforward term. Simulation analysis and experimental verifications showed that compared with the traditional proportional integral derivative (PID) and terminal sliding mode state feedback control, the proposed compound control method can provide faster convergence performance and higher voltage output quality for the closed-loop system of the Buck converter. Full article

The mobile satcom antenna (MSA) enables a moving vehicle to communicate with a geostationary Earth orbit satellite. To realize continuous communication, the MSA should be aligned with the satellite in both sight and polarization all the time. Because of coupling effects, unknown disturbances, sensor noises and unmodeled dynamics existing in the system, the control system should have a strong adaptability. The significant features of terminal sliding mode control method are robustness and finite time convergence, but the robustness is related to the large switching control gain which is determined by uncertain issues and can lead to chattering phenomena. Neural networks can reduce the chattering and approximate nonlinear issues. In this work, a novel B-spline curve-based B-spline neural network (BSNN) is developed. The improved BSNN has the capability of shape changing and self-adaption. In addition, the output of the proposed BSNN is applied to approximate the nonlinear function in the system. The results of simulations and experiments are also compared with those of PID method, non-singularity fast terminal sliding mode (NFTSM) control and radial basis function (RBF) neural network-based NFTSM. It is shown that the proposed method has the best performance, with reliable control precision. Full article