Adaptive Backstepping Sliding Mode Control Research Articles

Adaptive Backstepping Sliding Mode Control for ABS with Nonlinear Disturbance Observer

Adaptive Backstepping Sliding Mode Control for ABS with Nonlinear Disturbance Observer

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.

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.

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.

Fault Diagnosis and Fault Tolerant Control for Manipulator with Actuator Multiplicative Fault

In this paper, a new fault diagnosis and fault tolerant control algorithm for manipulators with actuator multiplicative fault is proposed. The dynamic model of the manipulator with disturbance is taken as the research object. When faults occur in the actuator, a nonlinear observer based on radial basis function (RBF) neural network is used to estimate the fault information. After the fault information is obtained, an adaptive back-stepping sliding mode controller is used to control the manipulator to reach the desired trajectory. At last, an illustrated example is given to demonstrate the efficiency of the proposed algorithm, and satisfactory results have been obtained.

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.

Incomplete differentiation-based improved adaptive backstepping integral sliding mode control for position control of hydraulic system

In the hydraulic systems, the non-structural uncertainties such as the nonlinear friction will reduce the tracking accuracy for the hydraulic servo system. In this paper, an incomplete differential-based improved adaptive backstepping integral sliding mode control (ID-BIABISMC) is proposed to realize the position control for the hydraulic servo system based on the friction compensation. The backstepping-based control being integrated the integral sliding mode surface-based sliding mode control with the friction compensation are used to solve the problem of non-structural uncertainty of the hydraulic system. The incomplete differential is introduced to the adaptive update law, by which the low-pass filtering behavior in the incomplete differential is capable of effectively suppressing the interference caused by the pure differential mutation signal. Compared with the traditional adaptive backstepping control (ABC), adaptive sliding mode control (ASMC), the adaptive backstepping sliding mode control (ABSMC) and the proposed adaptive backstepping integral sliding mode control (IABISMC), the experimental results verify the high accuracy tracking performance of the proposed the incomplete differential-based improved adaptive backstepping integral sliding mode control (ID-BIABISMC). For the responses of the sinusoidal signal 40sin(0.2πt+1.5π)+40mm and step signal with 30 mm, the corresponding tracking accuracy for ID-BIABISMC are 0.005 mm and 2.15 mm, respectively.

Adaptive Neural Backstepping Sliding Mode Heading Control for Underactuated Ships with Drift Angle and Ship-Bank Interaction

In order to track the desired path under unknown parameters and environmental disturbances, an adaptive backstepping sliding mode control algorithm with a neural estimator is proposed for underactuated ships considering both ship-bank interaction effect and shift angle. Using the features of radial basis function neural network, which can approximate arbitrary function, the unknown parameters of the ship model and environmental disturbances are estimated. The trajectory tracking errors include stabilizing sway and surge velocities errors. Based on the Lyapunov stability theory, the tracking error will converge to zero and the system is asymptotically stable. The controlled trajectory is contractive and asymptotically tends to the desired position and attitude. The results show that compared with the basic sliding mode control algorithm, the overshoot of the adaptive backstepping sliding mode control with neural estimator is smaller and the regulation time of the system is shorter. The ship can adjust itself and quickly reach its desired position under disturbances. This shows that the designed RBF neural network observer can track both the mild level 3 sea state and the bad level 5 sea state, although the wave disturbance has relatively fast time-varying disturbance. The algorithm has good tracking performance and can realize the accurate estimation of wave disturbance, especially in bad sea conditions.

Adaptive Backstepping Sliding Mode Control of the Hybrid Conveying Mechanism with Mismatched Disturbances via Nonlinear Disturbance Observers

An adaptive backstepping sliding mode controller combined with a nonlinear disturbance observer is designed for trajectory tracking of the electrically driven hybrid conveying mechanism with mismatched disturbances. A nonlinear disturbance observer is constructed for estimation and compensation of the mismatched and matched disturbances. Then, a hybrid control scheme is designed by combining the adaptive backstepping sliding mode controller and the mentioned observer. The Lyapunov candidate functions are utilized to derive the control and adaptive law. According to the simulation and experimental results, superior tracking performance could be obtained through the presented control scheme compared with conventional backstepping sliding mode control. Meanwhile, the presented control scheme can effectively reduce the chattering problem and improve tracking precision.

Adaptive Backstepping Sliding Mode Control of Trajectory Tracking for Robotic Manipulators

To achieve precise trajectory tracking of robotic manipulators in complex environment, the precise dynamic model, parameters identification, nonlinear characteristics, and disturbances are the factors that should be solved. Although parameters identification and adaptive estimate method were proposed for robotic control in many literature studies, the essential factors, such as coupling and friction, are rarely mentioned as it is difficult to build the precise dynamic model of the robotic manipulator. An adaptive backstepping sliding mode control is proposed to solve the precise trajectory tracking under external disturbances with complex environment, and the dynamic response characteristics of a two-link robotic manipulator are described in this paper. First, the Lagrange kinetic method is used to derive the precise dynamic model which includes the nonlinear factor with friction and coupling. Moreover, the dynamic model of two-link robotic manipulator is built. Second, the estimate function for the nonlinear part is selected, and backstepping algorithm is used for analyzing the stabilities of the sliding mode controller by using Lyapunov theory. Furthermore, the convergence of the proposed controller is verified subject to the external disturbance. At last, numerical simulation results are reported to demonstrate the effectiveness of the proposed method.

A finite time adaptive back‐stepping sliding mode control for instantaneous active‐reactive power dynamics based DFIG‐wind generation towards improved grid stability

AbstractIn this paper, a low computational, robust nonlinear feedback control is proposed as independent distributed generation controller (IDGC) for doubly fed induction generator (DFIG) based wind power generation system (WPGS). WPGS integration as distributed generation (DG) to grid point of common coupling (PCC) is reflecting high power loss profile in terms of low frequency oscillations under grid operational contingencies and have high instability hazard under unbounded uncertainties like unintentional islanding operation. Thus, to improve the stability margin of DFIG‐WPGS integration fast DG dynamic relations are obtained, where instantaneous active‐reactive power (P‐Q) formulation is proposed to avoid unnecessary phase locked loop (PLL) angle (ω) estimation. The feedback path is designed with proposed finite time adaptive backstepping sliding mode control (FTABSMC) for IDGC operation according to ISA‐95 standards. The FTABSMC is ensured with bounded/unbounded uncertainty handling capability by incorporating backstepping based dynamic error profile depletion and with enhanced stability margin by finite time sliding surface based error trajectory to equilibrium. Further, the adaptive sliding surface estimation is proposed in terms of dynamic uncertainty (energy fluctuation) for robust unbounded uncertainty handling. The stability improvement is established with small‐signal (SS) based closed loop analysis of considered DFIG‐WPGS. The uncertainty handling capability is presented thought rigorous case studies in MATLAB based simulation environment and TMS 320 digital signal processor (DSP) based processor‐in‐loop (PIL) validation.

Consensus tracking of multi-agent systems using constrained neural-optimiser-based sliding mode control

In this paper, an optimal Sliding-Mode Control (SMC) technique based on Projection Recurrent Neural Network (PRNN) is proposed to solve the tracking consensus for the robotic multi-agent system. Based on a connection topology between the leader and agents and relative degree of the system, the sliding surfaces are defined in terms of the error signals. Then, a performance index is defined to realise the exponential reaching law and minimum control effort. By considering the actuator limits, a constrained Quadratic Programming (QP) problem is derived. The solution of the QP is calculated using PRNN, which is developed based on Variational Inequality (VI) problem. The structure of PRNN is composed of a dynamic and an algebraic equation, in which a projection operator acts as an activation function. The convergence analysis of PRNN as a numerical optimiser has been performed using Lyapunov theorem. Moreover, the sufficient conditions are derived for ensuring the robust stability of the closed-loop system. The performance of the proposed algorithm has been investigated by applying it to a robotic multi-agent system and has been compared with an adaptive backstepping SMC.

Adaptive fractional-order backstepping sliding mode controller design for an electrostatically actuated size-dependent microplate

In this article, adaptive backstepping sliding mode controller and adaptive fractional backstepping sliding mode controller methods are proposed to control an electrostatic microplate with a piezoelectric layer. Based on the modified couple stress theory, a size-dependent mathematical model is proposed, in which the microplate is modeled using the Kirchhoff plate theory. To take into account the geometric nonlinearities, the von Kármán nonlinear strains are considered in the mathematical model. The Hamilton’s principle is used to obtain the nonlinear equation of motion of the system, which is then converted into a nonlinear ordinary differential equation via the Galerkin technique. The validity of the results obtained from the proposed reduced-order model is checked through direct numerical simulation of the partial differential equation using the finite element method. Finally, two Lyapunov-based control approaches that are adaptive backstepping sliding mode and adaptive fractional backstepping sliding mode are applied to the system. In the adaptive fractional backstepping sliding mode controller method, the adaptive control law is used to evaluate the upper bound of uncertainties and random disturbances. The fractional-order form of sliding surface is used to reduce the amount of chattering and also to improve the tracking error. In the results section, first, numerical studies are conducted to study the effect of system parameters, such as material length scale parameter, aspect ratio, fractional order, and robustness of the controller, on the performance of the system. In addition, the performances of the two control methods are compared, and the merits and demerits of each method are discussed.

Design of Air-Wake Rejection Control for Longitudinal Automatic Carrier Landing Cyber-Physical System

ABSTRACT The automatic carrier landing system (ACLS) is an indispensable component of modern aircraft carriers, and it can be considered a special cyber-physical system. However, the disturbance of the carrier air-wake in the final approach is detrimental to the landing safety and complicates the design of the ACLS. An air-wake rejection control strategy can be designed by analyzing the signal flow chart. To suppress the air-wake disturbance, the ACLS in this study is designed based on an adaptive backstepping sliding mode control. This design compensates and restrains the flight performance deviation, and it can also ensure the robustness of the system. Compared with the conventional ACLS design, the capability to restrain the flight performance deviation is significantly enhanced. The simulation results show that the system robustness is improved significantly. Moreover, the proposed design can achieve strict control of the ideal glide slope tracking and realize safe landing under the air conditions of the final approach.

An Adaptive Backstepping Sliding Mode Controller to Improve Vehicle Maneuverability and Stability via Torque Vectoring Control

To improve the maneuverability and stability of a vehicle and fully leverage the advantages of torque vectoring technology in vehicle dynamics control, a finite-time yaw rate and sideslip angle tracking controller is proposed by combining a second-order sliding mode (SOSM) controller with the backstepping method in this paper. However, existing research indicates that first-order sliding mode (FOSM) control suffers from the chattering problem, while the traditional SOSM controller requires knowing the bound of the uncertain term in advance to obtain the switching gain, which is difficult in practice. To address these problems, this paper proposes an adaptive second-order sliding mode (ASOSM) controller based on the backstepping method by adding the high-frequency switching term to the first derivative of the sliding mode variable, which implies that the actual control can be acquired after an integration process. The switching gain in the ASOSM controller is obtained by an adaptive algorithm without knowing any information of the uncertainty. The proposed algorithm is compared with FOSM and SOSM in different scenarios to demonstrate its applicability and robustness. Simulation results show that the bandwidth of the vehicle transient response can be improved by 21%. In addition, ASOSM and SOSM controllers are insensitive to vehicle mass and tire type, implying their robustness to such disturbances. Furthermore, ASOSM requires less control action because of the adaptive law when it performs similarly with SOSM and FOSM.

Robust adaptive backstepping sliding mode control for motion mode decoupling of two‐axle vehicles with active kinetic dynamic suspension systems

SummaryA mode decoupling control strategy is proposed for the active Kinetic Dynamic Suspension Systems (KDSS) with electrohydrostatic actuator (EHA) to improve the roll and warp mode performances. A matrix transfer method is employed to derive the modes of body and wheel station motions for full vehicle with active KDSS. The additional mode stiffness produced by the active KDSS is obtained and quantitatively described with the typical physical parameters. A new hierarchical feedback control strategy is proposed for the active KDSS to improve the roll and warp motion performances and simultaneously accounting for nonlinear dynamics of the actuators with hydraulic uncertainties. H∞ static output‐feedback control is employed to obtain the desirable mode forces, and a new projection‐based adaptive backstepping sliding mode tracking controller is designed for EHA to deal with address the nonlinearity and parameters uncertainty. This controller is used to realize the desirable pressure difference of EHA required from the target mode forces. Numerical simulations are presented to compare the roll and warp performances between the active KDSS, conventional spring‐damper suspension, and suspension with antiroll bar under typical excitation conditions. The evaluation indices are normalized and compared with radar chart. The obtained results illustrate that the proposed active KDSS with proposed controller does not produce additional warp motion for vehicle body, and has achieved more reasonable tire force distribution among wheel stations, the roll stability, road holding, and significantly improved ride comfort simultaneously.

Proton exchange membrane fuel cell-powered bidirectional DC motor control based on adaptive sliding-mode technique with neural network estimation

Proton exchange membrane fuel cell (PEMFC), according to its merits of high energy density, zero emission, and low noise, has been widely applied in industrial appliances. A full bridge converter is used to implement PEMFC-powered DC motor bidirectional rotation in this paper. For the sake of the regulations of DC motor angular velocity as well as bus voltage, an adaptive backstepping sliding-mode control (ABSMC) technique integrated with Chebyshev neural network (CNN) is proposed. Based on the equivalent-circuit method, the control-oriented model of the PEMFC-powered motor system is structured. By constructing Lyapunov function, the adaptive laws and control laws can be obtained to achieve bus voltage and angular velocity regulations simultaneously. Moreover, the proposed neural network is applied to estimate the uncertainties of the system through orthogonal basis Chebyshev polynomials. To highlight the advantages of proposed technique, a proportional-integral (PI) control was introduced subsequently and two controllers were compared via numerical simulations. The simulation results demonstrate that CNN estimation method in conjunction with backstepping sliding-mode shows fast and accurate response even though the existence of system uncertainties and external disturbances.

Online Estimation and Control for Feed Drive Systems With Unmeasurable Parameter Variations

This paper develops an online parameter estimation and control method for both rigid and flexible feed drive systems with unmeasurable parameter variations. The perturbations of the state-space model caused by the parameter variations are formulated, thereby making it possible to obtain the parameter variations in real-time by estimating the perturbations. To estimate the perturbations, they are regarded as the extended states and estimated through the extended-state-observer. With the estimation method, a novel state feedback control structure with double integrators is further proposed, which can eliminate the steady-state tracking error at constant velocities. The H$_\infty $ optimization technique is used to design the proposed state feedback controller. A simulation is conducted that integrates the estimator and the controller for a ball screw setup with mass-dependent resonant modes, where several proposed state feedback controllers are linearly interpolated into a gain-scheduling controller and scheduled by the estimated mass. The results demonstrate that the designed gain-scheduling state feedback controller outperforms a linear-time-invariant state feedback controller and an adaptive backstepping sliding mode controller. The proposed method is experimentally validated on a rigid linear-motor-driven motion stage, of which the results indicate the proposed estimation method can accurately estimate the parameter variations.