Backstepping Research Articles

Enhancing power generation via an adaptive neuro-fuzzy and backstepping maximum-power-point tracking approach for photovoltaic single-ended primary inductor converter system

Abstract The distinct characteristics of photovoltaic generators related to power and current present a complex problem in terms of optimizing their power output. To tackle this, maximum-power-point tracking techniques such as the adaptive neuro-fuzzy inference system are frequently utilized for their swift adaptability and reduced fluctuations. In addition, the backstepping controller is often selected to handle both linear and non-linear systems due to its exceptional reliability. The purpose of this research is to propose an innovative method that merges the adaptive neuro-fuzzy inference system and backstepping controller to refine the tracking of the optimal power point and to bolster the stability of the photovoltaic system in the face of unpredictable scenarios, such as those presented by the Ropp irradiance examination, which utilizes a single-ended primary inductor converter as a stage for power electronics adaptation. Simulations conducted using MATLAB®/Simulink® demonstrate that the combination of adaptive neuro-fuzzy inference system and backstepping controller achieves an impressive efficiency of 99.6% and exhibits fast, robust, and accurate responses compared with other algorithms such as artificial neural networks combined with the backstepping controller and conventional perturb and observe algorithm.

Safe Robust Adaptive Motion Control for Underactuated Marine Robots.

This article presents an innovative approach to the design of a safe adaptive backstepping control system. Tailored specifically for underactuated marine robots, the system utilizes simple sensors for enhanced practicality and efficiency. Given their operation in diverse oceanic environments fraught with various sources of uncertainties, ensuring the system's safe and robust behavior holds paramount importance in the control literature. To address this concern, this paper introduces a control strategy designed to ensure robustness at both the kinematic and dynamic levels. By emphasizing the compensation for the system uncertainties, the design integrates a straightforward fuzzy system structure. To further ensure the system's safety, a funnel surface is defined, followed by the design of a suitable nonlinear sliding surface as a function of the funnel and tracking error. Using Lyapunov theory, the study formally establishes the Semi-globally Practically Finite-time Stability of the closed-loop system, validated through simulations conducted on underactuated marine robots.

Efficient and robust control of a standalone PV-storage system: An integrated single sensor-based nonlinear controller with TSCC-battery management

The aim of this research undertaking is to investigate an integrated approach that extends the battery life of a single-stage off-grid photovoltaic system while simultaneously increasing the availability of solar photovoltaic power. This paper takes a synergistic approach to addressing these issues, in contrast to the numerous prior papers that have investigated them individually. In regard to the initial issue, this article proposes a hybrid MPPT solution which combines a backstepping controller with a distinct single-sensor MPPT approach. The aforementioned integrated system guarantees the exact attainment of the maximum power point (MPP) of the photovoltaic solar array, regardless of weather fluctuations. With regard to the second issue at hand, the effective management of charge for lead-acid batteries is accomplished by employing a three-stage charging controller (TSCC). The simulation results generated in MATLAB/Simulink indicate that MPPT tracking and battery charge control exhibit markedly improved performance across a range of weather conditions when the climatic conditions of El Jadida city, Morocco are taken into account. The hybrid method, as proposed, indisputable surpasses alternative MPPT approaches such as Inc-PI, FLC, PSO, RegP, and IMP-PO, with respect to convergence time (<3 milliseconds), variation (<0.19 watts), and tracking efficiency (over 99.86 %). Furthermore, the battery station is outfitted with secure and appropriate charging modes. In conclusion, the experimental validation of the proposed system against an actual experimental system in the laboratory verifies its hardware and practical viability.

Robustness of reaction–diffusion PDEs predictor-feedback to stochastic delay perturbations

This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction–diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The stabilization problem under consideration involves random perturbations modeled by a finite-state Markov process that further obstruct the actuation path at the controlled boundary of the infinite-dimension plant. This scenario is useful to describe several actuation failure modes in process control. Employing the recently introduced infinite-dimensional representation of the state of an actuator subject to stochastic input delay for ODEs (Ordinary Differential Equations), we convert the stochastic input delay into r+1 unidirectional advection PDEs, where r corresponds to the number of jump states. Our stability analysis assumes full-state measurement of the spatially distributed plant’s state and relies on a hyperbolic–parabolic PDE-PDE cascade representation of the plant plus actuator dynamics. Integrating the plant and the nominal stabilizing boundary control action, all while considering probabilistic delay disturbances, we establish the proof of mean-square exponential stability as well as the well-posedness of the closed-loop system when random phenomena weaken the nominal actuator compensating effect. Our proof is based on the Lyapunov method, the theory of infinitesimal operator for stability, and C0-semigroup theory for well-posedness. Our stability result refers to the L2-norm of the plant state and the H2-norm of the actuator state. Furthermore, our study presents a qualitative analysis of the maximum deviation of the stochastic disturbance relative to the nominal delay, which is expressed as a function of the severity of the plant instability, namely, the magnitude of the reactivity coefficientand the known upper bound of the transition rate of the underlying stochastic perturbations. Extensive simulation results illustrate the viability of the robustness study.

Leveraging MPPT capability for solar irradiance estimation: H-INC-IBS-based assessment of explicit models under real-world climatic conditions

This research investigates a low-cost method for estimating irradiance. The approach uses maximum power point tracking (MPPT) to easily estimate irradiance in a Photovoltaic (PV) system. Two main explicit mathematical models "IV-G" and "I-G" are examined for effective irradiance estimation. Given the requirement for MPPT, the examined PV system is powered by a hybrid-incremental conductance integral backstepping controller (H-INC-IBS), which enables proper maximum power point functioning. These models are evaluated using statistical indices such as the root mean square error (RMSE), mean absolute percentage error (MAPE), symmetrical mean absolute percentage error (SMAPE), and coefficient of correlation (R). The research tests these models using 37 climate patterns, demonstrating the influence of MPPT on model performance. In addition, the models are closely monitored in an experimental setup that includes two consecutive days of real-time climatic exposure. The experimental results show that the I-G model has the best accuracy measures, with worst MAE, MAPE, and SMAPE values of 18.81 W, 8.9039 %, and 4.7242 %, respectively. Thus, the article concludes that the I-G model is better suited for irradiance estimate in the context of MPPT. Furthermore, using evidence-based study outcomes, the paper proves that MPPT accuracy is proportional to estimating model accuracy. Given the little attention paid to this area of irradiance estimation, this work is intended to serve as a reference in the field.

Dynamics modeling and trajectory tracking control of a life support robot using sliding-mode control with extended state observer

This paper investigates the trajectory tracking control problem of a life support robot chassis under the slipping disturbances. First, a novel dynamics model for the robot chassis is proposed based on Lagrange equation. The constructed model incorporates the effects of rotational kinetic energy from the driving wheels, providing a more comprehensive representation of the chassis dynamics. Then, on the basis of the innovative framework, the dual-loop trajectory tracking control is derived for the chassis, via the kinematics-based backstepping controller and the dynamics-based sliding-mode controller. Moreover, an extended state observer is designed to reduce the influence caused by external disturbances. Finally, the effectiveness and superiority of the proposed tracking control approach are verified through simulation experiments.

Optimised backstepping control for the nonlinear strict-feedback system having unknown control dead-zone

In this article, the optimised backstepping (OB) strategy is extended to deal with the dead-zone control problem for a class of the nonlinear strict feedback systems. Since the dead-zone phenomenon is frequently encountered in the control of nonlinear strict feedback system, it is very necessary to consider the effect of dead-zone in the OB control. However, the published OB control methods are to rarely deal with the dead-zone problem because of the complex algorithm of reinforcement learning (RL). In this OB control, the dead-zone problem is effectively solved by utilising a simplified RL algorithm. For effective eliminating the effect of dead-zone, an adaptive compensation of dead-zone function's remainder is added to this RL. Since the RL under identifier-critic-actor architecture is implemented in every backstepping step, the requirement of complete dynamic acknowledge is released. Ultimately, the validity of this OB method is certified both theory and simulation.

Neural network adaptive switched fault-tolerant control of uncertain nonlinear systems with full state constraints

This paper studies the neural network adaptive fault-tolerant control (NNAFTC) for a class of uncertain nonlinear systems with full state constraints. It is the first time to introduce switched adaptive fault compensation strategy for the controller design process. On the one hand, the proposed method overcomes the limitation needed to be given a prescribed local restriction region of the traditional state constraint schemes, such as log-type, tan-type and integral-type. On the other hand, the full-state constraint and switched fault-tolerant problem is effectively solved even if the existence of actuator failures. Concomitantly, the novel switched tuning functions, the NN approximation technique and the integral barrier Lyapunov functions (IBLF) are combined to construct the backstepping controllers and adaptation laws. It can be proved that all the closed-loop states are restricted in the proper compact sets for any given initial values. Finally, A simulation is shown to demonstrate the validity and advantages of the presented control approach.

QCASBC: An algorithm for hardware-in-the-loop simulation of 3-link RRR robotic manipulator

In this paper, a quick convergence adaptive structure is proposed for trajectory tracking of an articulated type robotic manipulator using the Hardware in the Loop (HIL) simulation technique. A novel Nonlinear Quick Convergence Adaptive Sliding Backstepping Control (QCASBC) algorithm is implemented on a C2000 real-time controller board. The performance of the proposed control algorithm is inspected concerning the sliding mode PID (SM-PID) control technique to estimate its correlation with the proposed algorithm. The experimental part of the HIL simulation tests has been carried out on a simulated model of a three-link serial robot manipulator. A dynamic model of the robotic manipulator has been developed using Matlab Simulink software and its performance is analyzed using the HIL technique via a C2000 real-time controller for tracking the desired trajectory. Results show that the speed of convergence while tracking the desired trajectory of the manipulator is better in the proposed algorithm. It is also estimated that the positional error of the QCASBC algorithm is superior to the SM-PID control algorithm. The observed average angle error is improved by 14% and the average response time error is improved by 11% by using the proposed QCASBC algorithm compared to the SM-PID approach.

Trajectory tracking control of a flexible air-breathing hypersonic vehicle using Lyapunov-based model predictive control

Considering the constraints of inputs and angle of attack (AOA), the trajectory tracking control of a flexible air-breathing hypersonic vehicle (FAHV) is investigated. To solve the problem, the Lyapunov-based model predictive control (LMPC) is presented. Firstly, the virtual controller is designed by nonlinear backstepping control (BSC), and it is integrated into the Lyapunov contraction constraint in LMPC to ensure the stability of the closed-loop system. Secondly, LMPC law is obtained by optimizing the weighted summation performance index of the tracking error and the control. Within the LMPC framework, the input constraints and AOA constraints can be handled simply, and by designing the appropriate parameters of the virtual controller, closed-loop stability is achieved. The effectiveness and superiority of the proposed method are verified by comparing it with the BSC and traditional model predictive control.

Command filtered backstepping control of multiple transmission control protocol/active queue management networks with user datagram protocol flows

AbstractIn this study, the congestion control problem for multiple transmission control protocol/active queue management (TCP/AQM) networks with user datagram protocol (UDP) flows is investigated. Taking the UDP stream as the unknown interference and the maximum interference is obtained by the minimax theorem. A novel control algorithm is designed for multi‐TCP/AQM networks through backstepping control and command filtered technology. Simulation studies are carried out to verify the effectiveness and feasibility of the proposed method.

A novel approach to the FPIBSC strategy for an electric power steering system

The electric power steering system is used to improve comfort and steering feel for the user. In this article, we propose to use an integrated nonlinear control strategy for the electric steering system, which is described based on a complicated dynamic model. This work provides two new contributions. First, this control algorithm combines backstepping and proportional–integral (PI) techniques with parameters adjusted by a fuzzy algorithm, so it is called Fuzzy proportional–integral backstepping control (FPIBSC). The output of the PI algorithm is the input of the backstepping technique, while system stability is evaluated based on the Lyapunov function with virtual control variables. Second, road reaction torque is calculated based on a spatial dynamic model, which considers the influence of many other factors. Numerical simulation methods are used to evaluate the performance of the system. According to research findings, the value of the steering motor angle (controlled object) continuously tracks the desired value with negligible error. Under some specific conditions, the error between signals can be reduced to zero. In addition, other outputs that are obtained from the FPIBSC algorithm also tend to follow the reference signal with high accuracy. The phase difference phenomenon only occurs when using the conventional backstepping algorithm instead of FPIBSC. The assisted torque increases as speed decreases or the driver torque increases. In general, the system’s stability is always guaranteed under many different simulation conditions.

Active suspension hierarchical control with parameter uncertainty and external disturbance of electro-hydraulic actuators

In order to improve the ride comfort and handling stability of the electro-hydraulic active suspension system, a hierarchical control strategy is proposed. For the active suspension system with body mass uncertainty and safety constraints, an enhanced constraint adaptive backstepping controller is designed to generate the target force of body vertical motion. When dealing with constraints, nonlinear filters are introduced, backstepping technology and quadratic Lyapunov function are used to combine the control target and domain constraints, and the vertical displacement of the body and the suspension deflection control index are synthesized into a single controlled variable, so that the control variable converging to zero meets the suspension dynamic displacement limit. The ride comfort and safety of the active suspension system are improved. Secondly, stability analysis is conducted on the zero dynamic error system to ensure that all safety performance indicators are bounded. The effects of external disturbances, parameter uncertainties and modelling errors on the force tracking accuracy of asymmetric cylinder electrohydraulic systems are addressed. A backstepping dynamic surface control method based on a nonlinear perturbation observer is proposed, which estimates the composite perturbation terms such as modelling error and external perturbation, and uses the estimated value of the nonlinear observer to design a feedforward compensating control term to offset the effect of the composite perturbation on the system performance. In addition, the dynamic surface control method is used to calculate the derivative of the target force input, which avoids the derivative explosion phenomenon and reduces the computational complexity of the system. Simulation test results show that this method reduces the computational complexity of the system and improves the control performance. And under random and bumpy road conditions, the root-mean-square value of sprung mass acceleration performance index is reduced by 48.354 % and 72.677 % compared with passive suspension, which improves the ride comfort of the vehicle.

Switching control method for collaborative robots based on hybrid Petri nets

Abstract Aiming at the different working conditions of the mixed production process of collaborative robots, three kinds of controllers with the structure of sliding mode controller, backstepping controller and feedback linearisation are designed respectively, and a control structure switching method based on Petri net is proposed. The method is able to achieve better control performance by switching into different control methods to realise the relevant work tasks (tracked motion trajectories) according to the different work tasks (tracked motion trajectories) to be accomplished by the collaborative robots.

Comparing fuzzy logic and backstepping control for a buck boost converter in electric vehicles

Significant advances have been made in the control of DC/DC converters, owing to the effective combination of linear and nonlinear approaches. The above-mentioned approaches have greatly improved the efficiency as well as stability of the converter, even when faced with changing conditions. Nevertheless, the emergence of artificial intelligence has introduced new perspectives in the domain. The objective of the article is to examine two separate methodologies for controlling a boost-buck converter: using a nonlinear approach, especially backstepping, and utilizing artificial intelligence through fuzzy logic. The main aim of this work is to illustrate the inherent stability and robustness of fuzzy logic controllers compared to backstepping control in managing effectively various variations and challenges encountered in converter control.

Backstepping control based on adaptive neural network and disturbance observer for reconfigurable variable stiffness actuator

Reconfigurable variable stiffness actuator (RVSA) has attracted increasing attention in robotics due to its safety, compliance, and robustness. However, the control of the RVSA is challenging due to nonlinear factors such as high-order nonlinear dynamic, model uncertainties, time-varying model parameters, and disturbances. In this paper, firstly, a lightweight RVSA structure with both passive and active nonlinear variable stiffness characteristic is developed. Secondly, a dynamic surface backstepping control method based on a radial basis neural network and disturbance observer (DSBC-RBFNN-DOB) is proposed to achieve position control of the lightweight RVSA with matched and unmatched uncertainties. To address solve the “complexity explosion” and noise problems in traditional backstepping control, the dynamic surface backstepping control (DSBC) method is used to design the controller. Then, a method based on radial basis neural network (RBFNN) and disturbance observer (DOB) are used to compensate for the matched and unmatched uncertainties in the link and motor. In this method, the matched uncertainties are compensated using RBFNN, and the DOB is integrated to compensate RBFNN approximation errors and unmatched uncertainties. Through Lyapunov stability analysis, the semi-global boundedness of the controller is proven. Finally, the proposed method is simulated and actually implemented, verifying the effectiveness of the method. Simulation and experimental results show that the root mean square error (RMSE) of the proposed method is only 0.97277° and 0.6418°, respectively. Compared with PID, DSBC, and DSBC-RBFNN, the error reduction percentages in simulation (experiment) are 85.6 % (88.9 %), 49.4 % (88.4 %) and 36.1 % (80.0 %) respectively.

Distributed synchronization method of multi-motor driving system’s accelerated backstepping tracking control

This paper proposes a distributed synchronization control method and an accelerated backstepping tracking control scheme for the multi-motor driving system (MMDS). In the first step, we create a dynamic model of the MMDS with complex nonlinear dynamics, encompassing elements such as the dead zone, frictions, and disturbances. Next, in order to tackle the challenge of load tracking, we fuse a speed function, a cosine barrier function, a second-order tracking differentiator (TD), and a disturbance compensator into the backstepping approach. Lastly, to address potential issues related to diverse torque inputs, which could result in the overload occurrences, we put forward a novel distributed synchronization control scheme. This scheme aims to achieve torque synchronization for the MMDS while simultaneously ensuring superior load tracking performance. In the distributed synchronization control, a communication network is built to achieve the local coupling and improve the synchronization efficiency, and a corresponding mean deviation coupling synchronization control scheme is designed. Lyapunov theory is utilized to demonstrate the stability of the introduced control scheme. The simulation experimental results for the MMDS show the effectiveness of the proposed scheme.

Event-Triggered Adaptive Containment Control for Heterogeneous Stochastic Nonlinear Multiagent Systems.

This article investigates the event-triggered adaptive containment control problem for a class of stochastic nonlinear multiagent systems with unmeasurable states. A stochastic system with unknown heterogeneous dynamics is established to describe the agents in a random vibration environment. Besides, the uncertain nonlinear dynamics are approximated by radial basis function neural networks (NNs), and the unmeasured states are estimated by constructing the NN-based observer. In addition, the switching-threshold-based event-triggered control method is adopted with the hope of reducing communication consumption and balancing system performance and network constraints. Moreover, we develop the novel distributed containment controller by utilizing the adaptive backstepping control strategy and the dynamic surface control (DSC) approach such that the output of each follower converges to the convex hull spanned by multiple leaders, and all signals of the closed-loop system are cooperatively semi-globally uniformly ultimately bounded in mean square. Finally, we verify the efficiency of the proposed controller by the simulation examples.

Backstepping synchronization control for four-dimensional chaotic system based on DNA strand displacement

Backstepping control is an important nonlinear control design method, which realizes the control of complex systems by constructing control law step by step, and has significant advantages for dealing with complex nonlinear systems. This article proposes a synchronization technique for four-dimensional chaotic systems using a combination of backstepping control method and DNA strand displacement technology. By relying on theoretical knowledge of DNA molecules, five basic chemical reaction modules such as trigger reaction, reference reaction, catalytic reaction, annihilation reaction and degradation reaction are given to construct a four-dimensional DNA chaotic system. On the basis of the relevant theory of chaotic dynamics, the constructed system is analyzed by Lyapunov exponent diagram and spectral entropy complexity algorithm, and the results come to the conclusion that the system reveals extremely complex and varied dynamic behaviors. Combining DNA strand displacement technology with backstepping control method, four controllers are developed to ensure that the trajectories of two homogeneous chaotic systems are synchronized. The numerical simulation results validate the feasibility and applicability of the proposed method. The method proposed in this paper may provide some references in the field of DNA molecular chaos synchronization control.

An adaptive backstepping control strategy based on radial basis function neural networks for the magnetorheological semi-active suspension

Owing to nonlinear issues such as external disturbances and uncertain parameters within the semi-active suspension system (SASS), the vibration amplitude of the suspension system tends to increase, and the time required for the suspension system to reach a steady-state response is prolonged. Hence, this paper proposes an adaptive backstepping control strategy based on radial basis function neural networks (RBF-NNs). Firstly, the damping force characteristics of the magnetorheological (MR) damper are tested, and the experimental data are utilized for parameters identification and fitting of the Bouc-Wen model. To establish a connection between the controller and the forward model of the MR damper, the forward model of the MR damper, the inverse model of the MR damper, and the model of the MR-SASS are constructed. Secondly, the backstepping controller and the adaptive backstepping controller based on RBF-NNs are designed. The stability and reliability of the closed-loop suspension system are verified through stability analysis using Lyapunov function. Finally, the dynamic characteristics of the passive control, backstepping control, and adaptive backstepping control strategies based on RBF-NNs applied to MR-SASS are analyzed under B-Class road excitation and speed bump road excitation. The acceleration, suspension dynamic deflection, and tire dynamic load are selected as the evaluation indices. The results demonstrate that the adaptive backstepping controller based on RBF-NNs significantly enhances the ride comfort of the SASS.