Adaptive Backstepping Sliding Mode Research Articles

Adaptive fuzzy-neural network effectively disturbance compensate in sliding mode control for dual arm robot

In this study, an Adaptive Backstepping Sliding Mode Controller (ABSMC) is introduced based on the Radial Basis Function (RBF) neural network and a fuzzy logic modifier. The proposed method is used to control a Dual-Arm Robot (DAR) – a nonlinear structure with unstable parameters and external disturbances. The control aims to track the motion trajectory of both arms in the flat surface coordinate within a short time, maintaining stability, and ensuring that the tracking error converges in finite time, especially when influenced by unforeseen external disturbances. The nonlinear Backstepping Sliding Mode Control (BSMC) is effective in trajectory tracking control; however, undesired phenomena may occur if there are uncertain disturbances affecting the system or model parameters change. It is proposed to use a neural network to estimate a nonlinear function to handle unknown uncertainties of the system. The neural network parameters can be adaptively adjusted to optimal values through adaptation rules derived from Lyapunov's theorem. Additionally, fuzzy logic theory is also employed to adjust the controller parameters to accommodate changes or unexpected impacts. The performance of the Fuzzy Neural Network Backstepping Sliding Mode Control (FNN-BSMC) is evaluated through simulation results using Matlab/Simulink software. Two simulation cases are conducted: the first case assumes stable model parameters without uncertain disturbances affecting the joints, while the second case considers a model with changing parameters and disturbances. Simulation results demonstrate the effective adaptability of the proposed method when the system model is affected by various types of uncertainties from the environment

Adaptive Fuzzy Backstepping and Backstepping Sliding Mode Controllers Based on ICD Observer: A Comparative Study

Adaptive Fuzzy Backstepping and Backstepping Sliding Mode Controllers Based on ICD Observer: A Comparative Study

Adaptive backstepping fast terminal sliding mode control of dynamic positioning ships with uncertainty and unknown disturbances

Considering the complexity of the operating environment of marine ships, higher demands are placed on the positioning accuracy and positioning performance of Dynamic Positioning (DP) systems. This paper designs an Adaptive Backstepping Fast Terminal Sliding Mode Control (ABFTSMC) to solve the problems of low positioning accuracy, slow convergence, and poor anti-interference performance in ship positioning due to uncertainty of dynamic model parameters and unknown time-varying environmental disturbances. A Fast Terminal Sliding Mode Control (FTSMC) is combined with backstepping techniques to ensure the robustness of the system to uncertainties and disturbances. Meanwhile, an adaptive law is used to estimate the unknown uncertainty terms. Moreover, the Lyapunov stability criterion is used to prove the convergence and stability of the designed controller. Multiple simulation results show that ABFTSMC has better control performance compared with Adaptive Backstepping Control (ABC) and Adaptive Backstepping Sliding Mode Control (ABSMC). All the comparisons could fully verify the effectiveness and superiority of the proposed control method.

Optimized Cooperative Control of Error Port-Controlled Hamiltonian and Adaptive Backstepping Sliding Mode for a Multi-Joint Industrial Robot

Robot joints driven by permanent magnet synchronous motors (PMSM) often cannot have both superior accuracy and rapidity when they track target signals. The robot joints have fine dynamic characteristics and poor steady-state characteristics when the signal controller is used, or they have fine steady-state characteristics and poor dynamic characteristics when the energy controller is used. It is hard to make robot joints that have both superior dynamic and steady-state characteristics at once using a single control method. In order to solve this problem, the strategy of optimized cooperative control is proposed. First, an error port-controlled Hamiltonian (EPCH) energy controller and an adaptive backstepping sliding mode (ABSM) signal controller are designed. Second, an optimized cooperative control coefficient based on the position error of a robot joint is designed; this enables the system to switch smoothly between the EPCH energy controller and ABSM signal controller. Next, the strategy of optimized cooperative control is designed. In this way, robot systems can combine the advantages of the EPCH energy controller and the ABSM signal controller. Finally, simulation results demonstrate that using the strategy of optimized cooperative control gives robot joints outstanding control performance in terms of tracking accuracy and response rapidity.

Multiple Constraints-Based Adaptive Three-Dimensional Back-Stepping Sliding Mode Guidance Law against a Maneuvering Target

This paper addresses the issue of a complex three-dimension (3-D) terminal guidance process that is used against maneuvering targets while considering both the terminal impact angle (TIA) and field-of-view (FOV) angle constraints. According to the highly coupled and nonlinear 3-D terminal guidance model, an adaptive back-stepping sliding-mode guidance law algorithm is proposed in order to guarantee the stability and robustness of the guidance system. Considering the explicit expression of the line-of-sight (LOS) angle in the kinematics and dynamics of the terminal guidance process, the TIA constraint is transformed into an LOS constraint based on their well-known relationship. In view of the challenges in obtaining the motion information of maneuvering targets, an adaptive law design is introduced in order to estimate and compensate for external disturbances caused by the maneuvering of the target and modeling uncertainty. In addition, because the FOV angle represented by the overall leading angle is not a state variable in the sliding-mode guidance system, it is decoupled into two partial leading angles based on a specific transformation relation, so the 3-D terminal guidance control problem is converted into separate tracking system control issues in the pitch and yaw planes. Then, the Lyapunov stability theory is utilized to substantiate the stability of the guidance system, where the Lyapunov functions in both of the subsystems consist of the LOS and partial FOV state error terms. Finally, a series of simulations of various motion states of maneuvering targets under different terminal cases were carried out. It was proved that the terminal guidance design based on the strategies presented above was able to obtain the desired LOS constraints with satisfying the FOV limitation, and the simulation results verified the effectiveness, universality, and significance for practical applications of the proposed guidance design method.

Adaptive Finite-Time Backstepping Sliding Mode Control for PMSM System With Backlash

The rapid tracking stabilization problem of the servo system with gear backlash and unmatched unknown disturbance is investigated. In this article, a novel finite-time sliding mode surface with a faster convergence rate is proposed to improve the anti-interference of the gear transmission servo system. This surface not only can adaptively and dynamically regulate the integral capability together with disturbances and tracking error variations, but also does not create singularity issues. An adaptive fixed-time reaching law (AFTRL) is proposed, which performs a faster convergence rate and chattering-free performances. The adaptive mechanism ensures the continuous property of the control output and dynamically regulates the fixed-time convergence rate regardless of initial states. The dSPACE platform is employed to validate the excellent tracking performance of the gear transmission servo system.

Adaptive Backstepping Sliding Mode Control of Vehicle-Mounted Parallel Stabilized Platform

This paper researches an accurate and cooperative stability control method for the vehicle-mounted parallel stabilized platform to isolate the external random interference caused by rugged terrains. An adaptive backstepping sliding mode controller is designed by combining the adaptive method and backstepping design method. The position and pose of the platform are calculated in real time as feedback quantity and a closed-loop controller overall pose is designed. Simulation and experimental results show that the vehicle-mounted parallel stabilized platform can quickly and accurately adjust the pose of the upper platform to keep horizontal when the vehicle runs on rugged terrains.

Constrained Adaptive Backstepping Sliding Mode Control for Inertial Stable Platform

Constrained Adaptive Backstepping Sliding Mode Control for Inertial Stable Platform

Adaptive Optimal Multi-Surface Back-Stepping Sliding Mode Control Design for the Takagi-Sugeno Fuzzy Model of Uncertain Nonlinear System With External Disturbance

This paper proposes a novel scheme of the multi-objective robust control design for a class of uncertain nonlinear systems in strict-feedback-form based on Takagi–Sugeno fuzzy model (TSFM). The nonlinear system contains both the matched and the unmatched uncertainties and also subjected to the external disturbances. The TSFM provides the generalization of the linear systems concepts to the nonlinear systems field in a convex framework. First, a new sliding surface is defined using a convex combination of the surfaces which are defined for each fuzzy rule consequence local linear subsystems. Then, their gains are designed optimally via a generalized eigenvalue problem (GEVP). Also, the upper-bounds of the matched and unmatched uncertainties are estimated using the adaptive update laws. The multi-objective control aims not only to satisfy the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> -optimization performance, but also, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stability region is formulated to improve the transient response performance. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> -optimization characterization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stability design conditions are derived in terms of new linear matrix inequalities (LMIs) conditions. Finally, the effectiveness of the proposed approach is demonstrated by considering a comparative practical example.

Adaptive variable impedance control for a modular soft robot manipulator in configuration space

Compliance is a strong requirement for human–robot interactions. Soft-robots provide an opportunity to cover the lack of compliance in conventional actuation mechanisms, however, the control of them is very challenging given their intrinsic complex motions. Therefore, soft-robots require new approaches to e.g., modeling, control, dynamics, and planning. One of the control strategies that ensures compliance is the impedance control. During the task execution in the presence of coupling force and position constraints, a dynamic behavior increases the flexibility of the impedance control. This imposes some additional constraints on the stability of the control system. To tackle them, we propose a variable impedance control in configuration space for a modular soft robot manipulator (MSRM) in the presence of model uncertainties and external forces. The external loads are estimated in configuration space using a momentum-based approach in order to reduce the calculation complexity, and the adaptive back-stepping sliding mode (ABSM) controller is designed to guard against uncertainties. Stability analysis is performed using Lyapunov theory which guarantees not only the exponential stability of each state under the designed control law, but also the global stability of the closed-loop system. The system performance is benchmarked against other conventional control methods, such as the sliding mode (SM) and inverse dynamics PD controllers. The results show the effectiveness of the proposed variable impedance control in stabilizing the position error and diminishing the impact of the external load compared to SM and PD controllers.

Fault tolerant control of wind turbines with simultaneous actuator and sensor faults using adaptive time delay control

In this paper, a new Active Fault Tolerant Control (AFTC) is proposed using adaptive fractional-based Terminal Back-stepping Sliding Mode (TBSM) control strategy for pitch angle control of a variable speed wind turbine in the presence of actuator and sensor faults. In order to detect, isolate and accommodate the faults, Time Delay Estimation (TDE) is used as an online fault estimation algorithm. To eliminate the chattering of conventional sliding mode, supper twisting sliding mode algorithm is applied, which also ensures finite time convergence and high precision. Moreover, wind speed profiles are generated using TurbSim, and the controller is implemented on a simplified two-mass wind turbine model. To verify the validity of the proposed scheme, the simulations are also performed in FAST environment, and finally, the simulation results are presented which reveal the effectiveness of the proposed controller in the presence of faults, uncertainties and turbulent wind fields.

Research on Pneumatic Muscle Position Control Based on Adaptive Backstepping Sliding Mode

Aiming at the nonlinearity and uncertainty of pneumatic muscles, an adaptive backstepping sliding mode control method is proposed. Using the three-element model of pneumatic muscles, an adaptive backstepping sliding mode controller for pneumatic muscles is designed, which is proved by Lyapunov theory. For the stability of the system, a simulation test platform is built in MATLAB. The simulation results show that the designed controller has fast convergence speed and strong robustness.

Adaptive Backstepping Sliding Mode Control for ABS with Nonlinear Disturbance Observer

Adaptive Backstepping Sliding Mode Control for ABS with Nonlinear Disturbance Observer

Event-Triggered Adaptive Neural Network Backstepping Sliding Mode Control for Fractional Order Chaotic Systems Synchronization With Input Delay

This paper investigates the fractional order chaotic systems synchronization with input delay. To reduce the utilization of communication resources and achieve system synchronization, an adaptive neural network backstepping sliding mode controller is proposed based on event-triggered scheme without Zeno behavior. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. The sliding term is introduced to enhance robustness. The Pade delay approximation method is used to handle the input delay, which can reduce the analysis complexity of fractional order chaotic systems with input delay. The unknown nonlinear functions and uncertain disturbances are approximated by the RBF neural network. An observer is used for state estimation of the fractional order system. By applying the Lyapunov stability theory, we can prove that the all closed-loop signals are bounded. Examples and simulations prove the feasibility of the proposed control method.

Design of a Fixed-Wing UAV Controller Based on Adaptive Backstepping Sliding Mode Control Method

In this paper, an advanced control method is proposed for a fixed-wing unmanned aerial vehicle (UAV) to maintain the stabilization of its altitude, attitude, and velocity. The mathematical model of a fixed-wing UAV is very complicated because of its characteristics of nonlinearity and large extent of multi-variable coupling. Thus, to design the relevant controller is also difficult. In addition, during the operation of a fixed-wing UAV, various uncertainties and disturbances will occur, which will make the control process harder to accomplish. To solve these problems, this study designs a variable-structure controller with multiple algorithm fusion. The design mainly adopts the backstepping sliding mode control method to simplify the complex nonlinear mathematical model, and an adaptive law is introduced to estimate the uncertainty and disturbance of the system. Subsequently, the tracking error of the controller is proved to converge to zero using Lyapunov’s second method. Finally, it is verified that the controller has the ability to stably control a fixed-wing UAV by numerical simulation and can overcome the disturbance and uncertainty. The buffeting also can be eliminated by an adaptive law.

Adaptive Backstepping Sliding Mode Tracking Control for Underactuated Unmanned Surface Vehicle With Disturbances and Input Saturation

This paper presents an adaptive backstepping sliding mode tracking control method for underactuated unmanned surface vehicle. The tracking controller is designed by combining backstepping and adaptive sliding mode control technology. The virtual control law is used to replace the control strategy of position error, and the position tracking control is transformed into velocity control, which can effectively avoid the input saturation and singular value problem existing in the design of traditional backstepping control law. The neural shunt model method is used to solve the differential explosion problem caused by virtual control law. The adaptive technology based on backstepping sliding mode theory is introduced to compensate the model uncertainty and time-varying disturbances of the system, and the robustness of the underactuated USV is enhanced by this method in the unknown environment. Based on the Lyapunov stability theory, it is proved that the control system error is ultimately uniformly bounded. The simulation results show that the proposed adaptive backstepping sliding mode tracking control method can achieve stable tracking in the case of system parameter uncertainty and time-varying disturbances, so it can be concluded that this method is reasonable and effective.

Improved Vector Control of a Counter-Rotating Wind Turbine System Using Adaptive Backstepping Sliding Mode

The vector control (VC) method based on proportional-integral (PI) controllers of a doubly fed induction generator (DFIG) integrated in a counter rotating wind turbine (CRWT) system have many problems, such as low dynamic performances, coupling effect between the d-q axes and weak robustness against variation parametric. In order to resolve these problems, this research work proposes an adaptive backstepping sliding mode (ABSM) controller. The proposed control strategy consists in using dynamic-gains that ensures a better result than a conventional VC method. Stability of the proposed ABSM control approach has been proved by the Lyapunov method. Simulation results depicted in this research paper have confirmed the good usefulness and effectiveness of the proposed ABSM control.

Adaptive Backstepping Sliding Mode Control of Uncertain Semi-Strict Nonlinear Systems and Application to Permanent Magnet Synchronous Motor

A disturbance observer (DOB) based-backstepping sliding mode control scheme is discussed for a class of semi-strict nonlinear system with unknown parameters and mismatched uncertainty. Firstly, adaptive technique and DOB are respectively applied to tackle the unknown parameters and mismatched uncertainty, where the DOB can effectively alleviate the chattering problem of sliding mode control (SMC). Then, exponential sliding mode surface is proposed to improve the convergence rate of the sliding mode state. The ‘explosion of complexity’ problem inherent in conventional backstepping control is overcome by designing the novel first-order filter. The stability of the closed-loop system is analyzed in the framework of Lyapunov stability theory, in which the tracking error converges to an arbitrarily small neighborhood around zero (ASNZ). At last, two examples are given to illustrate the effectiveness of the proposed control strategy.

Synchronous Reluctance Motor with Load Vibration Perturbation: Analysis, Electronic Implementation and Adaptive Backstepping Sliding Mode Control

Dynamical analysis and chaos control of a synchronous reluctance motor (SynRM) with a constant and sinusoidal load torque are studied in this paper. The SynRM with load vibration perturbation exhibits pitchfork bifurcation, steady state behavior, double-scroll chaotic attractor and coexistence of attractors between steady state behavior and double-scroll chaotic attractors. Furthermore, an analog circuit is designed and implemented in OrCAD-PSpice software to validate the dynamical behaviors found in the SynRM with load vibration perturbation during the numerical simulations. Finally, an adaptive backstepping sliding mode control is used to suppress the chaotic oscillations in the SynRM with load vibration perturbation. Numerical simulations confirm the effectiveness of the proposed controller.

Adaptive Backstepping Sliding Mode Control of Tractor-trailer System with Input Delay Based on RBF Neural Network

In this paper, an adaptive sliding mode neural network(NN) control method is investigated for input delay tractor-trailer system with two degrees of freedom. An uncertain camera-object kinematic tracking error model of a tractor car with n trailers with input delay is proposed. Radial basis function neural networks(RBFNNs) are applied to approximate the unknown functions in the error model. A sliding mode surface with variable structure control is designed by using backstepping method. Then, an adaptive NN sliding mode control method is thus obtained by combining Lyapunov-Krasovskii functionals. The controller realizes the global asymptotic trajectories tracking of the kinematics system. The stability of the closed-loop system is strictly proved by the Lyapunov theory. Matlab simulation results demonstrate the feasibility of the proposed method.