Backstepping Sliding Mode Control Research Articles

Load frequency control in power systems by a robust backstepping sliding mode controller design

This paper presents a novel sliding-mode load frequency control (LFC) strategy for two-area thermal interconnected power system. Backstepping technique is utilized to design the controller. The sliding control method can be motivated heuristically by reasoning that one would expect better tracking performance exposed to parametric uncertainties and load disturbances. The controlled system’s asymptotic stability and the robustness of the controlled system are proved mathematically utilizing the Lyapunov theorem. Moreover, it is shown numerically that the proposed controller can diminish the intensity of the frequency oscillations caused by the load disturbance. The advantages of the proposed control approach are shown by comparing the results of proposed controller based on backstepping sliding mode control (BSMC) and other control approaches designed with the second order smc (SOSMC), observer-based BSMC (OBSMC) and port-Hamiltonian system and cascade system based proportional integral derivative (PHPID) controllers.

Design and implementation of an adaptive neural network observer–based backstepping sliding mode controller for robot manipulators

Robot manipulators as an indispensable part of automatic operation are becoming increasingly important in intelligent manufacturing systems, such as grinding and assembly. Although control methods of robot manipulators have been extensively studied, high-precision robots still face new challenges from uncertainties caused by changes in the environment and enhancement of interference. As a consequence, the neural network-based observer is utilized to reduce the influence of uncertainties and external disturbances. In this work, a new kind of nonlinear disturbance observer is designed which could well function with observed states. To improve the control efficiency and response characteristic, a kind of new integral sliding manifold is devised and the control input is generated via backstepping techniques. The stability is proved with Lyapunov theory, and the experimental results are given to demonstrate the effectiveness of the proposed controller.

Optimization of wind energy extraction for variable speed wind turbines using fuzzy backstepping sliding mode control based on multi objective PSO

This study addresses the problem of designing a nonlinear feedback control strategy for horizontal axis variable speed wind turbines in the below-rated wind speed operating region (whether the wind turbine is offshore or onshore). The objective is to operate the wind turbines to maximum wind energy extraction while reducing the mechanical load. To overcome both issues, a robust nonlinear control strategy based on sliding mode control (SMC) is proposed which tries to seek for an improved performance. The proposed controller has been developed to compensate for negative consequences of external disturbances, measurement noises and unmodeled dynamics. This control strategy exploits a tracking controller that keeps an optimal value for the ratio between the rotor angular speed and the wind speed. For maximum wind energy extraction, the control algorithm employs the sliding mode state output feedback torque controller to provide robustness, combined with backstepping scheme to ensure better performance in the presence of matched and mismatched uncertainties. Next, a fuzzy logic system (FLS) approach is introduced to the backstepping sliding mode controller (BSMC) to achieve better mechanical loads prevention suffered by the transmission shaft by adjusting the parameters of the controller. Finally, multi-objective particle swarm optimization (MOPSO) algorithm is used to find the optimal values for the adjustable parameters of the proposed fuzzy BSMC (FBSMC). To validate the proposed control structure, FAST aeroelastic simulator is used. The obtained results illustrate that the presented control scheme has satisfactory performance.

Bioinspired backstepping sliding mode control and adaptive sliding innovation filter of quadrotor unmanned aerial vehicles

Quadrotor unmanned aerial vehicles have become the most commonly used flying robots with wide applications in recent years. This paper presents a bioinspired control strategy by integrating the backstepping sliding mode control technique and a bioinspired neural dynamics model. The effects of both disturbances and system and measurement noises on the quadrotor unmanned aerial vehicle control performance have been addressed in this paper. The proposed control strategy is robust against disturbances with guaranteed stability proven by the Lyapunov stability theory. In addition, the proposed control strategy is capable of providing smooth control inputs under noises. Considering the modeling uncertainties, the adaptive sliding innovation filter is integrated with the proposed control to provide accurate state estimates to improve tracking effectiveness. Finally, the simulation results demonstrate that the proposed control strategy provides satisfactory tracking performance for a quadrotor unmanned vehicle operating under disturbances and noises.

Stability enhancement of battery energy storage and renewable energy-based hybrid AC/DC microgrids using terminal sliding mode backstepping control approaches

In this paper, a terminal sliding mode backstepping controller (TSMBC) has been proposed for various components of a hybrid AC/DC microgrid (HADMG) to enhance its dynamic stability. The proposed control technique is employed to generate switching control signals for converters, which serve as the primary interface between the DC bus and the AC bus in a hybrid microgrid. Additionally, this technique facilitates the interface of PMSG-based wind generators, solar photovoltaic generators, and battery energy storage systems with the DC bus. Through the implementation of the composite control technique, the global stability of the microgrid is ensured by driving all the states of the HADMG associated with various components to converge towards their intended values. Afterward, the Lyapunov control theory has been used to analyze the converter and inverter’s large-signal stability while ensuring the robustness of the proposed robust composite controller. Finally, an extensive simulation study was conducted on a hybrid microgrid to verify the efficacy of the designed controller in maintaining power balance amidst variations in the system’s operational regimes. Moreover, the effectiveness of the controller’s practical implementation is confirmed by real-time processor-in-the-loop analysis. Simulation results clearly show that the proposed TSMBC improves the overall dynamic performance of the hybrid microgrid with less overshoot (0%) and settling time (110 ms) in DC bus voltage when compared to the existing sliding mode controller.

A Novel Control Method for Unmanned Agricultural Tractors: Composite Back-stepping Sliding Mode Path Tracking

A composite back-stepping sliding mode controller is explored in the paper to address the under-actuated, input saturated, and time-varying disturbances, as well as model-dependent issues that bother the path tracking control of unmanned agricultural tractors. Specifically, the path tracking error model is introduced. The extended state observers (ESO) with time-varying parameters are employed to handle the lump disturbances resulting from the external disturbances and model nonlinearity. A novel composite path tracking controller is proposed based on back-stepping and active disturbance rejection control and sliding mode control, whose effectiveness is elaborated by simulations and experiments. According to the results, the proposed controller, whose stability is elucidated in the appendix, outperforms the fuzzy pure pursuit control in reducing the lateral offset.

Observer based incremental backstepping terminal sliding-mode control with learning rate for a multi-vectored propeller airship

The problem of finite-time trajectory tracking control for a multivectored propeller airship with model parameter uncertainties and unknown disturbances is addressed in the paper. In order to obtain a fast transient response and finite time convergence without singularity, an incremental backstepping nonsingular terminal sliding mode controller is designed to track desired trajectory within finite time. To overcome the limitation of backstepping terminal sliding-mode control design being dependant on prior knowledge, a nonlinear disturbance-observer is designed to estimate the external observable disturbances. Meanwhile, to reduce system chattering when the tracking error reaches the sliding mode surface, an adaptive learning rate design is proposed for the terminal sliding mode controller such that the tracking error approaches the sliding mode surface at a low speed and so the system chattering is restrained. The closed-loop trajectory tracking control system is proved to be stable and finite time convergence by using Lyapunov theory. The results are compared with traditional backstepping sliding mode control and different learning rate based control design, and they demonstrate the averaged tracking error in altitude and pitch motion is reduced more than 30% by using the disturbance-observer based incremental backstepping terminal sliding mode controller for the multivectored propeller airship to execute a realistic trajectory tracking mission, even in the presence of aerodynamic coefficient uncertainties, unknown disturbances.

Terminal and Backstepping Sliding Mode Control with Genetic Algorithms for Robot Manipulators

Terminal and Backstepping Sliding Mode Control with Genetic Algorithms for Robot Manipulators

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.

Spherical Joint Actuator with Backstepping Sliding Mode Control for Robotic Manipulator Rigid-Flexible Coupling System

At present, the output shaft of a permanent magnet spherical actuator (PMSA) is a rigid structure, which has the problems of small load weight ratio and high energy consumption. It is difficult to meet the application requirements of lightweight, high speed, and low energy consumption. In this paper, a PMSA is proposed as the driving motor for the rigid-flexible coupling system (R-FCS) of the robotic manipulator, and a flexible mechanical arm is used to replace the rigid output shaft of the PMSA to connect the hand claw to form a spherical joint. Firstly, the partial differential dynamics model of the robotic manipulator in the coordinate system is established based on the Hamilton method, and the R-FCS is constructed according to the momentum conservation equation combined with the rigid axis dynamics model of the PMSA. Then, a backstepping sliding mode controller (BSMC) is designed to form a closed-loop control system by selecting an appropriate nonlinear gain function to estimate the unknown disturbances of the system, and the stability of the controller is guaranteed by the Lyapunov theory. Finally, the simulation and experimental results verify that the R-FCS can achieve better trajectory tracking and provide an effective driving method for robotic manipulator spherical joint.

Discrete-Time Backstepping Sliding Mode Control for a 2-DOF PAM-Based Exoskeleton

This study aims to propose a discrete-time backstepping sliding mode control technique (BSMC) for regulating a pneumatic artificial muscle (PAM)-based exoskeleton used in rehabilitating human lower extremities. The PAM system is challenging to control due to its high nonlinearity, parameter uncertainty, and significant delay resulting from using compressed air. A backstepping control method is a recursive approach that systematically designs control laws for nonlinear and complicated systems. This technique ensures stable and robust system control, even in uncertain circumstances. Furthermore, the backstepping controller can handle high-order systems and guarantee high-precision tracking of a desired trajectory. The incorporation of sliding mode control is aimed at enhancing the performance of the robot PAM system by reducing chattering and reaching time. The algorithm employs Lyapunov functions and sliding surfaces to design the control signal for operating the system. The study concludes with experimental scenarios demonstrating the effectiveness of the proposed approach.

Multi-AUV Formation Predictive Control Based on CNN-LSTM under Communication Constraints

For the problem of hydroacoustic communication constraints in multi-AUV leader follower formation, this paper designs a formation control method combining CNN-LSTM prediction and backstepping sliding mode control. First, a feedback linearization method is used to transform the AUV nonlinear model into a second-order integral model; then, the influence of hydroacoustic communication constraints on the multi-AUV formation control problem is analyzed, and a sliding window-based formation prediction control strategy is designed; for the characteristics of AUV motion trajectory with certain temporal order, the CNN-LSTM prediction model is selected to predict the trajectory state of the leader follower and compensate the effect of communication delay on formation control, and combine the backstepping method and sliding mode control to design the formation controller. Finally, the simulation experimental results show that the proposed CNN-LSTM prediction and backstepping sliding mode control can improve the effect of hydroacoustic communication constraints on formation control.

Generalized Super-Twisting Backstepping Sliding Mode Control for Electro-Hydraulic Servo Systems Considering the Coexistence of Matched and Mismatched Uncertainties

Aiming at the problem of the coexistence of matching and mismatching uncertainties in electro-hydraulic servo systems, disturbance observers and a backstepping sliding mode controller based on the generalized super-twisting algorithm (GSTA) are proposed in this paper. First, in order to compensate for the uncertainty in the controller, two generalized super-twisting disturbance observers (GSTDOs) are constructed to effectively reduce the discontinuous gain of the controller. Then, the GSTA is introduced to optimize the backstepping sliding mode controller to obtain a better control effect. Finally, the proposed control strategy is compared and simulated on the electro-hydraulic servo system. The experimental results verify that the proposed control strategy has better tracking performance. The effect of asymptotic tracking in the presence of parameter uncertainties and disturbances is achieved, while transient tracking performance and final tracking accuracy are guaranteed in the presence of time-varying uncertain nonlinearities.

Neural network optimization algorithm based non-singular fast terminal sliding-mode control for an uncertain autonomous ground vehicle subjected to disturbances

As computer computing capabilities increase, optimization algorithms are becoming more useful for solving engineering problems. Up to now, several metaheuristic algorithms have been exploited in control engineering. However, this effort remains weak in addressing the autonomous ground vehicles (AGVs) trajectory tracking problem. This research presents a novel optimal approach merging the robust non-singular fast terminal sliding-mode control method (NFTSMC) and the neural network optimization algorithm (NNA) for automatic lane changing. First, a reference double lane-change path (DLC) is designed, and the robust non-singular fast terminal sliding-mode steering controller is developed, according to Lyapunov stability theory, to suppress the lateral deviation and ensure the yaw stability. Then, the control strategy is optimized by the NNA algorithm to adjust the steering controller optimally while avoiding local optimums. A comparison, under the same conditions, with the particle swarm optimization algorithm (PSO) revealed the superiority of the control law resulting from the NNA-based optimization. Furthermore, the proposed approach shows its excellent tracking performance versus the integrated backstepping sliding-mode controller (IBSMC) and the adaptive sliding-mode control (ASMC) under severe conditions typical of real-world lane changes.

Back-stepping sliding mode control for libration control of large swing angles of electrodynamic tether system

Due to its widespread use in the field of space exploration, the electrodynamic tether system has undergone intensive research and is expected to pave the way for future developments in space technology. It has been demonstrated that, if not carefully regulated, the electrodynamic tether system easily deviates from equilibrium positions during a mission. The system works well in this instance because the equilibrium points of the cable near the vertical can be considered the “working equilibrium positions.” It implies that the in-plane and out-of-plane libration motion will mirror the cable's swing dynamics. The primary goal of this article is to alter the tether current and out-of-plant thrust in order to get the tether close to the vertical. A nonlinear control law using back-stepping control law in conjunction with sliding mode control can reduce the tether's attitude angles and increase robustness taking into account the extremely nonlinear and coupled properties of the system. The in-plane angle control subsystem, the out-of-plane angle control subsystem, and the auxiliary stabilization subsystem make up the control scheme. To confirm the efficacy of the suggested control methods and the stability of the control system, numerical simulations were run.

Backstepping sliding mode control for an active hydraulically interconnected suspension

This paper presents a backstepping sliding mode control (BSMC) method for an active anti-roll hydraulically interconnected suspension (HIS) system. The proposed control strategy enables the active HIS system tracking desired anti-roll moment within the working area. Based on the tracking error, the BSMC controller calculates the flowrate of the control cylinder. This flowrate successively changes the pressure in the accumulators and cylinder chambers, and finally determines the output anti-roll moment of the HIS. The HIS system parameters uncertainty and the system’s nonlinear characteristic are both considered in the proposed BSMC controller. To comprehensively design and validate the proposed control method, a 4-DOF half car model and a corresponding nonlinear active anti-roll HIS model are firstly established. Next, a linear quadratic regulator (LQR) upper layer controller is designed to optimize the vehicle’s roll motion, and the result of the LQR controller is set as a tracking target. Thereafter, the proposed BSMC bottom layer controller is designed to track the target moment. Finally, numerical simulation and experiments on the test bench are conducted to validate the proposed control method. The simulation and bench test results indicate that the proposed active HIS performs well in tracking target and tolerating disturbance. The proposed active HIS expands about additional ±1000 N/m dynamic anti-roll moment compared to a passive HIS at each roll angle, and the response time is less than 70 ms. The field test results show that the active HIS with proposed control method improves anti-roll property compared with a passive HIS by 23.3% in the double lane change test.

An Improved Sliding Mode Controller for MPP Tracking of Photovoltaics

Maximum power point tracking (MPPT) through an effective control strategy increases the efficiency of solar panels under rapidly changing atmospheric conditions. Due to the nonlinearity of the I–V characteristics of the PV module, the Sliding Mode Controller (SMC) is considered one of the commonly used control approaches for MPPT in the literature. This paper proposed a Backstepping SMC (BSMC) method that ensures system stability using Lyapunov criteria. A fuzzy inference system replaces the saturation function, and a modified SMC is used for MPPT to ensure smooth behavior. The proposed Fuzzy BSMC (FBSMC) parameters are optimized using a Particle Swarm Optimization (PSO) approach. The proposed controller is tested through various case studies on account of MPP’s dependence on temperature and solar radiation. The controller performance is assessed in partial shading conditions as well. The simulation results show that less settling time, a small error, and enhanced power extraction capability are achieved by applying the PSO-based FBSMC approach compared to the conventional BSMC- and ABC-based PI control presented in previous research in different scenarios. Moreover, the proposed approach provides faster adaptation to temperature and solar radiation variation, ensuring faster convergence to the MPP. Finally, the robustness of the proposed controller is validated by providing variation within the system components. The result of the proposed controller clearly indicates the lowest value of RMSE measured between PV voltage and the reference voltage, as well as the RMSE between PV power and maximum power. The results also show that the proposed MPPT controller exhibits the highest dynamic efficiency and mean power.

Group Coevolution and Immigration Pigeon-Inspired Optimized Dual-layer Controller for Aerial Manipulator Trajectory Tracking

The aerial manipulator expands the scope of unmanned aerial vehicle (UAV)’s application as well as increases the difficulties in the design of the controller. To better control the aerial manipulator for different trajectories tracking under different conditions, a new dual-layer controller is designed in this paper. The integral backstepping sliding mode controller (IBSMC) is applied to the outer-loop controller and backstepping controller (BC) is applied to the inner-loop controller. To improve the performance of the system, an improved pigeon-inspired optimization (PIO) algorithm called group coevolution and immigration pigeon-inspired optimization (GCIPIO) algorithm is proposed to optimize the controller parameters of IBSMC. GCIPIO algorithm utilizes the group coevolution and immigration mechanisms. A series of simulations are conducted to show the advantage of the proposed method. The results illustrate that the proposed method ensures the closed-loop system has less end-effector tracking error.

Spatial Trajectory Tracking of Wall-Climbing Robot on Cylindrical Tank Surface Using Backstepping Sliding-Mode Control

Wall-climbing robots have been well-developed for storage tank inspection. This work presents a backstepping sliding-mode control (BSMC) strategy for the spatial trajectory tracking control of a wall-climbing robot, which is specially designed to inspect inside and outside of cylindrical storage tanks. The inspection robot is designed with four magnetic wheels, which are driven by two DC motors. In order to achieve an accurate spatial position of the robot, a multisensor-data-fusion positioning method is developed. The new control method is proposed with kinematics based on a cylindrical coordinate system as the robot is moving on a cylindrical surface. The main purpose is to promote a smooth and stable tracking performance during inspection tasks, under the consideration of the robot's kinematic constraints and the magnetic restrictions of the adhesion system. The simulation results indicate that the proposed sliding mode controller can quickly correct the errors and global asymptotic stability is achieved. The prototype experimental results further validate the advancement of the proposed method; the wall-climbing robot can track both longitudinal and horizontal spatial trajectories stably with high precision.

Integral Backstepping Sliding Mode Control for Unmanned Autonomous Helicopters Based on Neural Networks

In this paper, we propose an adaptive control approach to deal with the problems of input saturation, external disturbances, and uncertainty in the unmanned autonomous helicopter system. The dynamics of the system take into account the presence of input saturation, uncertainty, and external disturbances. Auxiliary systems are built to handle the input saturation. The neural networks are applied to approximate the uncertain terms. The control scheme combining integral backstepping and sliding mode control is developed in position and attitude subsystems, respectively. In the closed-loop system, the boundedness of the signals is proved by means of the Lyapunov theory. The simulation demonstrates that the approach has good robustness and tracking performance.