Adaptive Nonsingular Terminal Sliding Mode Control Research Articles

Application of cell mapping to control optimization for an antenna servo system on a disturbed carrier

Abstract. The cell-mapping method, due to its global optimality, has been applied to solve multi-objective optimization problems (MOPs) and optimal control problems. However, the curse of dimensionality limits its application in high-dimensional systems. In this paper, the multi-parameter sensitivity analysis is investigated to reduce the parameter space dimension, which broadens the application of cell mapping to MOPs in high-dimensional parameter space. A post-processing algorithm for MOPs is introduced to help choose proper control parameters from the Pareto set. The proposed scheme is applied successfully in the control parameter optimization of an adaptive nonsingular terminal sliding-mode control for an antenna servo system on a disturbed carrier. Moreover, as the existing global optimal tracking control with an adjoining cell-mapping method may generate tracking-phase differences, an optimal-sliding-mode combined-control strategy is proposed. By using the combined-control strategy, the azimuth and pitch angles of the antenna system are controlled to catch up to a target trajectory with the minimum cost function and to keep high-precision tracking after that.

Machining control of non-axisymmetric aspheric surface based on piezoelectric fast tool servo system

Non-axisymmetric aspheric machining is increasingly important in photoelectric industry. The machining process requires an external feeding device mounted to a machine tool to achieve fast-tool servo (FTS) function. In this study, a piezoelectric (PZT, Lead zirconate titanate) FTS was used to perform non-axisymmetric aspheric machining by control methods. In the beginning, system identification of the PZT tool holder was conducted to obtain the mathematical model of the system and then the simulations were performed for various controllers, including the PID (Proportional-integral-derivative), sliding mode control (SMC), non-singular terminal sliding mode control (NTSMC), and adaptive NTSMC. The simulation results showed that the NTSMC and the adaptive NTSMC had excellent control performances with the tracking errors of 0.0 and 3.1 nm, respectively. Then, control practices without machining were performed with the PV (Peak-to-valley) tracking errors of 0.96 μm, 0.77 μm, and 0.95 μm obtained by the PID controller, NTSMC, and adaptive NTSMC, correspondingly. The large PV errors were found due to the low sampling rate of position commands. Finally, experiments of non-axisymmetric aspheric machining with the implemented controllers were performed for a workpiece of oxygen-free copper (OFC) having 5 mm diameter. The measured results of the machined surfaces were with the PV form errors of 7.2 μm, 2.8 μm, and 3.8 μm in corresponding to the usual machining, using NTSMC and adaptive NTSMC. The effectiveness of the implemented controllers was demonstrated, and the NTSMC showed the best performance. Future works are to examine the repeatability of various controllers with a large hardware memory size and improved environment.

Fault-Tolerant Control for N-Link Robot Manipulator via Adaptive Nonsingular Terminal Sliding Mode Control Technology

An adaptive nonsingular terminal sliding mode control (ANTSMC) scheme for the n-link robot manipulator is presented in this study, which can achieve faster convergence and higher precision tracking compared with the linear hyperplane-based sliding mode control. Novel adaptive updating laws based on the actual tracking error are employed to online adjust the upper bound of uncertainty, which comprehensively consider both the tracking performance and chattering eliminating problem. The stability analysis of the proposed ANTSMC is verified using the Lyapunov method with the existence of the parameter uncertainty and the actuator faults. Numerical simulation studies the comparison of performance between ANTSMC and the conventional nonsingular terminal sliding mode control (NTSMC) scheme to validate the advantages of the proposed control algorithm.

Adaptive super-twisting non-singular terminal sliding mode control for tracking of quadrotor with bounded disturbances

In this research, a novel adaptive non-singular terminal sliding mode control (ANTSMC) is proposed for finite-time attitude and altitude tracking of aircraft system considering the bounded disturbances. By utilizing this structure, the desired reference is tracked in finite-time. Afterward, a new adaptive super-twisting sliding mode control (ASTSMC) is presented to decrease the control signals' chattering effect. This approach combines with the ANTSMC to compose this study's proposed approach as adaptive super-twisting non-singular terminal sliding mode control (ASTNTSMC). Additionally, an adaptive-regulation strategy is designed for estimating the unknown bounds of the disturbances. Finally, for evaluating the proposed strategies' ability, some simulations are performed based on quadrotor real parameters and confirmed the presented controllers' appropriate performances compared to other techniques.

Adaptive Non-singular Terminal Sliding Mode Control for an Unmanned Underwater Vehicle: Real-time Experiments

This research work focuses on the design of a robust-adaptive control algorithm for a 4DOF Unmanned Underwater Vehicle (UUV). The proposed strategy is based in a Non-Singular Terminal Sliding Mode Control (NTSMC) with adaptive gains, where the proposed adaptation mechanism ensures that the gains remain bounded. In this control strategy a non-singular terminal sliding surface is proposed to obtain a faster convergence of the tracking errors. The NTSMC ensures Practical Finite-Time Stability for the closed-loop system as well as exhibits a chattering reduction. In order to demonstrate the satisfactory performance of the proposed controller, a set of experiments was performed with a Non-Singular Terminal Sliding Mode Controller and an Adaptive Non-Singular Terminal Sliding Mode Control (ANTSMC) in real time for trajectory tracking in the X-Y plane, the graphs showed that the ANTSMC converges faster to a smaller region and reduces oscillations.

Adaptive Optimal Parameter Estimation and Control of Servo Mechanisms: Theory and Experiments

Most of classical adaptive laws used in adaptive control have been developed based on the gradient descent algorithm to minimize the control error. Hence, the sluggish convergence of tracking error may affect the online learning, making accurate parameter estimation difficult. The aim of this article is to present a new adaptive law to achieve optimal parameter estimation, and then to showcase its application to adaptive control for a benchmark servo system to retain simultaneous convergence of both the estimation error and tracking error. For this purpose, an auxiliary filter is introduced to extract the estimation error, which is used to drive the adaptive law with a time-varying gain to minimize a cost function of the estimation error to achieve fast, accurate parameter estimation. Finally, this new adaptation is incorporated into an adaptive nonsingular terminal sliding-mode control for the considered servo system to obtain tracking control and parameter estimation simultaneously. The effectiveness of the developed method is validated by means of comparative simulations and experiments.

An Adaptive Nonsingular Terminal Sliding Mode Control for Bidirectional DC–DC Converter in Hybrid Energy Storage Systems

In order to improve transient response and robust tracking performance, an adaptive nonsingular terminal sliding mode control (ANTSMC) strategy is developed for bidirectional dc–dc converter (BDC) of hybrid energy storage systems (HESSs). By using the adaptive rules, the estimated values of load variations, external input voltage, input current, and output voltage can be obtained. Then, the voltage tracking error can be calculated based on the estimated value and the actual value. The fast terminal SMC strategy is proposed such that the tracking error converges in a finite time. Simulation results, compared with conventional PID, second-order sliding mode, show that output voltage can robustly track the reference voltage with fast response.

Adaptive Nonsingular Terminal Sliding Mode Control for Attitude Tracking of Spacecraft With Actuator Faults

In this paper, an adaptive nonsingular terminal sliding mode control (ANTSMC) is investigated for attitude tracking of spacecraft with actuator faults. First, a nonsingular fast terminal sliding mode surface is designed to avoid the singularity. Finite-time attitude control is developed using the nonsingular terminal sliding mode technique, which can make the attitude and angular velocity tracking errors converge to zero in finite time in the presence of uncertainties and external disturbances. Second, the total uncertainty is deduced to be bounded. The adaptive laws are incorporated to develop the ANTSMC, removing the restriction on the upper bound of the lumped uncertainty. The finite-time convergence of the closed-loop system with ANTSMC is proved using the Lyapunov stability theory. Finally, the simulation results are presented to demonstrate the performance of the proposed controllers.

Two Novel Approaches of NTSMC and ANTSMC Synchronization for Smart Grid Chaotic Systems

The presence of uncertainties and external disturbances is one of the unavoidable problems with various practical systems which might be unavailable in real-time. Sliding Mode Control (SMC) is one of the effective robust control methods to deal with these uncertainties and external disturbances. In this paper, two novel controllers are designed by using Nonsingular Terminal SMC (NTSMC) and Adaptive Nonsingular Terminal SMC (ANTSMC) methods for synchronization of dual smart grid chaotic systems with various uncertainties and external disturbances. Indeed, both adaptive and non-adaptive controllers based on NTSMC are proposed to provide two alternatives which can adjust by changing operating conditions and dynamics. The concept of SMC method guarantees controller robustness against various uncertainties and external disturbances. Elimination of the undesirable chattering phenomenon is addressed in this study which is one of the common deficiencies with conventional SMC method. Additionally, finite time concept is used to speed up the convergence rate. Finite time stability proof is performed by using Lyapunov stability theory. The numerical simulation is carried out in Simulink/MATLAB to reveal the validity of the proposed controllers for the smart grid chaotic system. A comprehensive comparison is made by performing simulation for the Fractional Order Adaptive Sliding Mode Control (FOASMC) controller and defining three performance criteria, among the proposed controllers in this study and FOASMC controller.

Nonsingular terminal sliding mode control of underwater remotely operated vehicles

This study investigates the nonsingular terminal sliding mode control (NTSMC) method for the four-degree-of-freedom (4-DOF) trajectory tracking control problem of underwater remotely operated vehicles (ROVs) in the presence of parametric uncertainties and external disturbances. Two new control algorithms have been developed for ROVs. The first one, combining a nonsingular sliding surface with a fast terminal sliding mode (FTSM) type reaching law, is nonsingular and chattering-free. The second one, introducing adaptive methodology to compensate for lumped uncertainties, is an improved version of the first algorithm and can be called adaptive NTSMC (ANTSMC). The adaptive methodology effectively reduces the chattering problem. Meanwhile, it also provides better robustness and higher tracking precision compared with the first algorithm. A corresponding stability analysis is presented using Lyapunov stability theory, and some comparative numerical simulation results are presented to show the effectiveness of the proposed approaches.

Adaptive non‐singular integral terminal sliding mode tracking control for autonomous underwater vehicles

This study proposes an adaptive non-singular integral terminal sliding mode control (ANITSMC) scheme for trajectory tracking of autonomous underwater vehicles (AUVs) with dynamic uncertainties and time-varying external disturbances. The ANITSMC is first proposed for a first-order uncertain non-linear dynamic system to eliminate the singularity problem in conventional terminal sliding mode control (TSMC) and avoid the requirement of the bound information of the lumped system uncertainty. The time taken to reach the equilibrium point from any initial error is guaranteed to be finite. The proposed ANITSMC is then applied to trajectory tracking control of AUVs. It guarantees that the velocity tracking errors locally converge to zero in finite time and after that the position tracking errors locally converge to zero exponentially. The designed ANITSMC of AUVs avoids the requirement of the prior knowledge of the lumped system uncertainty bounds as opposite to the existing globally finite-time stable tracking control (GFTSTC), provides higher tracking accuracy than the existing GFTSTC and adaptive non-singular TSMC (ANTSMC) and offers faster convergence rate and better robustness against dynamic uncertainties and time-varying external disturbances than the adaptive proportional-integral sliding mode control (APISMC). Comparative simulation results are presented to validate the superiority of the ANITSMC over the APISMC.

Multivariable Output Feedback Adaptive Terminal Sliding Mode Control for Underwater Vehicles

AbstractFor the four degrees of freedom (4‐DOF) trajectory tracking control problem of underwater vehicles in the presence of parametric uncertainties and external disturbances, a novel multivariable output feedback adaptive nonsingular terminal sliding mode control (ANTSMC) approach is proposed based on the equivalent output injection adaptive sliding mode observer (ASMO) and ANTSMC method. The ASMO is applied to reconstruct the full states in finite time and the ANTSMC method is designed to stabilize the trajectory tracking error to a small field in finite time. The proposed output feedback ANTSMC approach, using the adaptive technology, does not require the bound information of parametric uncertainties or external disturbances which successfully achieves the decrease of undesired chattering effectively. Corresponding stability analysis is presented. Comparative numerical simulation results are presented to validate the effectiveness of the proposed approach.

Finite‐time attitude stabilization for rigid spacecraft

SUMMARYThis paper investigates the finite‐time attitude stabilization problem for rigid spacecraft in the presence of inertia uncertainties and external disturbances. Three nonsingular terminal sliding mode (NTSM) controllers are designed to make the spacecraft system converge to its equilibrium point or a region around its equilibrium point in finite time. In addition, these novel controllers are singularity‐free, and the presented adaptive NTSM control (ANTSMC) laws are chattering‐free. A rigorous proof of finite‐time convergence is developed. The proposed ANTSMC algorithms combine NTSM, adaptation and a constant plus power rate reaching law. Because the algorithms require no information about inertia uncertainties and external disturbances, they can be used in practical systems, where such knowledge is typically unavailable. Simulation results support the theoretical analysis.Copyright © 2013 John Wiley & Sons, Ltd.