Backstepping Research Articles

Adaptive neural network fault‐tolerant control for uncertain non‐strict feedback nonlinear system with actuator faults and state constraints

SummaryThis article studies a neural network (NN)‐based adaptive fault‐tolerant control (FTC) scheme for uncertain non‐strict feedback systems with time‐varying state constraints and actuator faults. The introduction of asymmetric Barrier‐Lyapunov function (BLF) makes controller design more difficult due to the emergence of actuator faults and state constraints. Therefore, this article designs a fault‐tolerant controller with constraint compensation information under the backstepping control design framework to solve the state constraint asymmetry problem caused by actuator failure. By designing an improved asymmetric time‐varying BLF, the design of the state‐constrained controller will become more realistic and the constraints will be weakened. In the design process, the characteristics of the radial basis function neural network are used to avoid the algebraic ring problem. Actuator failure in this article considers deviation failure and loss of effectiveness. Based on the properties of the exponential function, the improved BLF can make the bounds of the state constraints smaller and smaller, and the bounds of the constraints can change with the desired trajectory. Simulation verified the feasibility of this control method.

A nonlinear design method of robust PI control by using adaptive backstepping control for web winding system of reversible cold rolling mill

A nonlinear design method of robust PI control by using adaptive backstepping control for web winding system of reversible cold rolling mill

Designing robust hybrid controllers for enhancing output voltage regulation in CPL feed boost converters through backstepping and nonsingular fast terminal sliding mode approaches

This paper presents a novel and robust hybrid controller that combines the backstepping controller with the nonsingular fast terminal sliding mode controller (NFTSMC) for DC-DC boost converters (DDBCs) operating alongside constant power loads (CPLs). The primary aim of the controller is to enhance the stability of the DC-bus voltage while consistently delivering power to the CPL. To achieve this objective, the exact feedback linearization approach is applied to transform the nonlinear dynamical model of the DDBC into Brunovsky’s canonical forms. The incorporation of matched uncertainties into the dynamical model illustrates the robustness of the proposed control approach. The hybrid controller is formulated based on this model, leveraging Lyapunov stability theory to ensure large signal stability under the designated control law. Significantly, the NFTSMC effectively addresses the singularity problem associated with sliding mode controllers (SMCs). The effectiveness and resilience of the proposed controller are validated under variations in input voltage, reference voltage, and power demand. Comparative analysis is conducted by contrasting simulation results with those obtained using conventional SMC (CSMC) and a typical PI controller (PIC). The results unequivocally highlight the superiority of the proposed controller in terms of ensuring system stability and providing a rapid response across various operating modes. Furthermore, to authenticate the practical applicability of the proposed controller, processor-in-loop (PIL) validation is employed, confirming its effectiveness in real-world scenarios.

Adaptive Fuzzy Backstepping Control for Itô-Type Nonlinear Switched Systems Subject to Unknown Hysteresis Input

The adaptive fuzzy backstepping control problem is studied for Itô-type nonlinear switched systems subject to unknown hysteresis input. Compared with existing works, the unknown hysteresis and stochastic disturbances are considered in the pure-feedback switched systems. The mean value theorem tackles the non-affine functions. The backstepping technique introduces an auxiliary virtual controller. In addition, the Nussbaum function is employed to solve the difficulty caused by the unknown hysteresis under arbitrary switching. Based on a fuzzy logic system and backstepping technique, a new adaptive control proposal is obtained, which ensures that the system states satisfy semiglobally uniformly ultimately bounded (SGUUB) in probability and that the tracking error converges to a region of the origin. Finally, we provide two examples to show the validity of the presented scheme.

Distributed Robust Learning-Based Backstepping Control Aided With Neurodynamics for Consensus Formation Tracking of Underwater Vessels.

This article addresses distributed robust learning-based control for consensus formation tracking of multiple underwater vessels, in which the system parameters of the marine vessels are assumed to be entirely unknown and subject to the modeling mismatch, oceanic disturbances, and noises. Toward this end, graph theory is used to allow us to synthesize the distributed controller with a stability guarantee. Due to the fact that the parameter uncertainties only arise in the vessels' dynamic model, the backstepping control technique is then employed. Subsequently, to overcome the difficulties in handling time-varying and unknown systems, an online learning procedure is developed in the proposed distributed formation control protocol. Moreover, modeling errors, environmental disturbances, and measurement noises are considered and tackled by introducing a neurodynamics model in the controller design to obtain a robust solution. Then, the stability analysis of the overall closed-loop system under the proposed scheme is provided to ensure the robust adaptive performance at the theoretical level. Finally, extensive simulation experiments are conducted to further verify the efficacy of the presented distributed control protocol.

Entirely Coupled Recurrent Neural Network-Based Backstepping Control for Global Stability of Power System Networks

In an interconnected power system network, global performance is affected by various unknown power system parameters subjected to system uncertainties. These unknown parameters in the control expression deteriorate the performance of the power system network. Therefore, these terms associated with the control expression must be estimated precisely. This paper proposes an adaptive backstepping scheme using an entirely coupled recurrent neural network (ECRNN) to estimate these control terms. Three continuous differentiable functions are used to design control input, virtual signals, and adaptive control laws to achieve global performance. The objective of ECRNN is to reduce the control complexity by estimating the associated nonlinear term in the control expression. It will facilitate the complex formulation of the controller and improve system performance. The robust functional estimation ability of ECRNN will make the system immune to uncertainties that may appear due to external disturbances. In ECRNN, feedback loops are added to each neuron layer to achieve additional estimation accuracy. The proposed adaptive law enhances the online weight update speed and accuracy. Verification of the proposed scheme is carried out in MATLAB/Simulink. It is also verified in the real-time digital simulator (RTDS) platform using the IEEE standard New England 39-bus, 10-machine power system model. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the existing limitations in the global performance of a multimachine power system network due to uncertainty in the system parameters. Uncertainties in the power system network primarily appeared due to penetration of renewable power sources, load uncertainty, or occurrence of an uncertain fault in the network. As power system networks are complex nonlinear interconnected systems, these perturbations in the generator states may cause economic losses, load demand uncertainty, or electric scarcity. Thus, a control scheme is required to address the global performance of such networks. This article proposes uniform ultimate bounded stability of synchronous generators in a multimachine power system network with a robust ECRNN-based backstepping control design. The other available technique has not adequately addressed the global performance under uncertainties. The efficacy of the proposed scheme is verified in a real-time environment via a real-time digital simulator which may be a feasible solution for designing excitation control for the synchronous machine in an extensive industrial network.

Finite-Time Adaptive Fuzzy Backstepping Control for Quadrotor UAV With Stochastic Disturbance

This paper proposes an adaptive fuzzy output feedback control approach for quadrotor unmanned aerial vehicles (QUAV) with stochastic disturbances, besides which we consider the unmeasurable states and unknown nonlinear functions. The QUAV system contains stochastic terms which are not bounded and not differentiable. By combining the It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\hat{\rm \textbf{o}}$</tex-math> </inline-formula> differential equation with finite-time theory, a novel stochastic finite-time stability controller for QUAV is raised for the first time. The fuzzy logic system (FLS) is utilized to approximate the unknown nonlinear functions in the model. Dynamic surface control technology is introduced to reduce the complexity of differential. Furthermore, an observer with FLS is designed through the adaptive backstepping technique to estimate the immeasurable states. It is proved that this control approach can ensure that all states of the closed-loop QUAV system are semi-global and finite-time stable in probability. Meanwhile, the errors of system outputs and observer converge to a small neighborhood of origin. The simulation results show the effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In practical applications, many systems are often affected by internal and external disturbances, and not all of them can be described by mathematical models, so they are called stochastic disturbances. Taking the QUAV as an example, when the system is disturbed by internal parameters, external environment, system input, sensor error, and other stochastic factors, the deterministic system can no longer accurately describe the controlled object. In this paper, the QUAV is regarded as a stochastic system for the first time, and a novel controller is designed to solve the above problems. In addition, the QUAV needs fast action in some applications, such as emergency collision avoidance, which has high requirements for the convergence performance of the controller. Therefore, studying the finite-time control for QUAV systems with stochastic disturbances is necessary. At the same time, this paper also considers the problem that the state is not measurable and the system contains unknown nonlinear equations.

Anti-unwinding adaptive robust backstepping attitude maneuver control for rigid spacecraft

In this paper, an anti-unwinding adaptive robust backstepping control law is proposed to solve the attitude control problem of rigid spacecraft with external disturbances and inertia uncertainties. A new variable based on hyperbolic sine functions is designed to prevent the unwinding phenomenon, and then a novel robust backstepping controller is developed. Initially, a nonlinear tracking law is designed to obtain the desired angular velocity and to ensure that the attitude maneuvering system could have two equilibrium points. Subsequently, an adaptive robust control law is devised, which incorporates the adaptive estimation method to update the inertial parameters in real-time. Moreover, the bounded external disturbances are taken into account in the design of the control law, and thus the robustness of the attitude control system is improved. Furthermore, the global asymptotic stability of the attitude control system is verified by the Lyapunov-Krasovskii theorem. Finally, numerical simulations are carried out to demonstrate the effectiveness and robustness of the proposed control law, as well as the anti-unwinding characteristics are perfectly validated during the attitude maneuver of rigid spacecraft.

Dynamical Analysis, Circuit Design, and Fuzzy Prescribed Performance Backstepping Control of the FO Weakly Coupled MEMS Resonators

Dynamical Analysis, Circuit Design, and Fuzzy Prescribed Performance Backstepping Control of the FO Weakly Coupled MEMS Resonators

Anti-Interference Control Method of Buck–Boost Converter Based on High-Order Nonlinear Disturbance Observer

A compound anti-interference control method based on a high-order nonlinear disturbance observer (HONDO) is proposed to address the impact of system disturbances on output voltage when applying the Buck–Boost converter in a microgrid to provide power to loads. Initially, the dynamic circuit model of the Buck–Boost converter is formulated, taking into account the system disturbance. Subsequently, HONDOs are designed to provide real-time estimates of uncertain factors in both the voltage loop and current loop of the circuit. These estimates are then utilized to design backstepping controllers aimed at effectively tracking the load output voltage set point. The simulation and experimental findings indicate that, when faced with load mutations, input voltage variations, and uncertainties in system parameters, the proposed compound anti-interference control method outperforms traditional control techniques by offering superior response speed, broader disturbance estimation capabilities, and enhanced dynamic performance of the Buck–Boost converter.

Adjustable backstepping fuzzy controller for a 7 DOF anthropomorphic manipulator

Adjustable backstepping fuzzy controller for a 7 DOF anthropomorphic manipulator

Adaptive backstepping control for uncertain semiconductor refrigeration systems considering even-order input

Temperature control technique has received much attention in the field of semiconductor thermal management. This paper presents a novel adaptive backstepping-based temperature control strategy for semiconductor refrigeration systems considering unmodeled dynamics. The inherent non-affine problem caused by the even-order input signal is solved by combining a novel smooth function into the command filtered backstepping method. And then, the adaptive observer is also employed to improve the system performance under unmodeled dynamic deviations. The stability of the closed-loop system is analyzed based on the Lyapunov theory, and simulation experiments are given to verify our control method. The simulation results show that the method can realize the accurate control of temperature under unmodeled dynamics. Under the disturbance of ambient temperature changes and model errors, the steady state error of the system remains below 0.1 °C. In comparison with the traditional control methods, our strategy has a stronger ability to suppress the uncertainty effects.

An optimal hybrid quadcopter control technique with MPC-based backstepping

Quadcopter unmanned aerial vehicle is a multivariable, coupled, unstable, and underactuated system with inherent nonlinearity. It is gaining popularity in various applications and has been the subject of numerous research studies. However, modelling and controlling a quadcopter to follow a trajectory is a challenging issue for which there is no unique solution. This study proposes an optimal hybrid quadcopter control with MPC-based backstepping control for following a reference trajectory. The outer-loop controller (backstepping controller) regulates the quadcopter’s position, whereas the inner-loop controller (Model Predictive Control) regulates its attitude. The translational and rotational dynamics of the quadcopter are analyzed utilizing the Newton-Euler method. After that, the backstepping controller (BC) is created, which is a recurrent control method according to Lyapunov’s theory that utilizes a genetic algorithm (GA) to choose the controller parameters automatically. In order to apply a linear control technique in the presence of nonlinearities in the quadcopter dynamics, Linear Parameter Varying (LPV) Model Predictive Control (MPC) structure is developed. Simulation validated the dynamic performance of the proposed optimal hybrid MPC-based backstepping controller of the quadcopter in following a given reference trajectory. The simulations demonstrate the fact that using a command control input in trajectory tracking, the proposed control algorithm offers suitable tracking over the assigned position references with maximum appropriate tracking errors of 0.1 m for the �� and �� positions and 0.15 m for the �� position.

Adaptive asymptotic tracking control of uncertain fractional-order nonlinear systems with unknown control coefficients and actuator faults

For uncertain fractional-order nonlinear systems (UFONS) with unknown control coefficients and intermittent actuator faults, the asymptotic tracking control problem is investigated in this paper. Firstly, to weaken the influence of virtual control coefficients and intermittent actuator faults, a smooth fractional-order projection operator-based adaptive compensation mechanism is presented. Additionally, a fractional-order nonlinear filter is constructed to replace the fractional-order derivative of virtual control functions approximately, which not only avoids the issue of complexity explosion existed in backstepping control frame, but fully compensates the effects of boundary errors caused by the employed filter in spite of the unknown virtual control coefficient. By constructing a fractional Lyapunov function from the property of projection operator, it is proved that all signals in the closed-loop system are bounded, and the asymptotic tracking control object is achieved. Definitively, a simulation study is presented to verify the availability of the presented method.

Fault detection and fault-tolerant control of dual-motor autonomous steering system

In order to improve the safety of autonomous ground vehicle (AGV) and the accuracy of trajectory tracking, a fault detection (FD) scheme of steering system and a fault-tolerant control (FTC) method are proposed. First, this paper analyzes the causes of steering motor failure and designs a passive fault-tolerant controller to ensure that the torque motor under coordinated control can still follow the angle when a slight fault occurs in the angle motor. Second, the corresponding FD schemes are designed for different motor faults, and the unknown input observer (UIO) of the steering resistance moment is designed considering the uncertainty of the steering system caused by the fault motor. The active fault-tolerant controller composed of backstepping control and global sliding mode control (SMC) is further combined to control the fault-free motor. Finally, simulation and HiL test results show the effectiveness of the proposed FD scheme and FTC strategy.

Research on Compliance Control of Electro-Hydraulic Loading Experimental System

This article discusses the challenges in preventing workpiece damage due to impacts in electro-hydraulic loading systems, especially in unknown environments. We propose an innovative compliance control strategy, synergizing a series elastic actuator with impedance control to significantly mitigate impact forces between the mechanism and test workpieces. The controller consists of two loops: an internal loop and an outer loop. The internal loop integrates a position loop utilizing a radial basis function observer within a backstepping control framework, effectively countering the nonlinear dynamics of hydraulic actuators and ensuring precise trajectory tracking. The outer loop advances traditional impedance control by adaptively modifying the damping coefficient, resulting in a straightforward and easily implementable damping control law. For the unknown environment parameters, our system employs a parameter estimation law to estimate the unknown environmental stiffness and position parameters. The effectiveness of this strategy has been verified through comparative simulation with traditional impedance control, indicating that the proposed method can not only effectively reduce contact shock in unknown environments, improve response speed, and reduce overshoot, but also improve steady-state accuracy. We provided a feasible control scheme for similar systems to ensure precise and safe operation.

Fuzzy backstepping control for enhanced stability of a quadrotor unmanned aerial vehicle

This paper presents a robust fuzzy backstepping control approach to enhance the stability and maneuverability of a Quadrotor Unmanned Aerial Vehicle (UAV). The proposed design combines the robustness of backstepping control with the adaptability of fuzzy logic to address uncertainties and disturbances commonly encountered in UAV dynamics. By incorporating fuzzy logic, the controller can adapt to changing environmental conditions, ensuring reliable performance in various flight scenarios. The backstepping technique enables systematic handling of nonlinear dynamics and achieves precise tracking of desired trajectories. Extensive simulations demonstrate the effectiveness of the proposed control strategy in stabilizing the UAV and enabling agile maneuvers, even in the presence of disturbances and model uncertainties. These results highlight the potential of the proposed approach to enhance the robustness and agility of Quadrotor UAVs in real-world applications.

Robust dynamic surface control of series elastic actuators based on reduced-order extended state observer

The compliance of series elastic actuators (SEAs) is significant for ensuring safe human–machine interaction. However, in practical applications, the SEA is inevitably encountered with unknown disturbances, such as parameter uncertainties, unmodeled dynamics, and environmental interferences. In this paper, a robust dynamic surface control scheme is presented to address the high-precision trajectory tracking problem of the SEA. Firstly, a reduced-order extended state observer (RESO) with only link-side position measurements is designed to estimate the unknown lumped disturbance and unmeasurable system states. Based on the estimated values from the RESO, a robust dynamic surface controller is proposed for the trajectory tracking of the SEA. Additionally, the finite-time filter is introduced to overcome the “explosion of complexity” in the backstepping controller, and the filtering error in the dynamic surface controller is reduced compared with the conventional first- and second-order filters. The stability of the closed-loop system is guaranteed by the Lyapunov theory. Finally, the effectiveness and superiority of the proposed control algorithm are verified through simulations and experiments.

Using Fractional-order Technique and Non-linear Surface to Improve the Performance of the Backstepping Control of Multi-rotor Wind Power Systems

In this study, an effective solution is given to overcome the drawbacks of backstepping command (BC) for a doubly-fed induction generator based on multi-rotor wind power system, where both fractional calculus and non-linear surface were used for this purpose. This suggested approach differs from the classical BC method and demonstrates strong efficacy, displaying resilience against both external and internal factors of the system. This command was suggested to command the machine-side inverter to increase power quality and reduce steady-state error (SSE). Therefore, the characteristics of this suggested BC were verified compared with the conventional BC method using MATLAB in different operating situations. This proposed strategy demonstrates a distinctive performance in improving system characteristics, as evidenced by the reduction rates compared to the BC technique. Active power undulations were minimized by 47.36% in the first test and 41.74% in the second test compared to BC. Also, The SSE value of reactive power was minimized by approximately 41.66% and 45.83% in both tests compared to the BC strategy. Moreover, the value of harmonic distortion improved significantly compared to the BC, with high ratios estimated at 68.57% and 55.30% in the same testes. These ratios indicate that the current quality is high when the suggested command is used. This indicates that in the future, this control method is poised to become one of the leading solutions trusted in the field of control.

Chattering analysis of an electro-hydraulic backstepping velocity controller

This paper focuses on the chattering analysis in a backstepping controller used to drive an electro-hydraulic servo system. The chattering phenomenon, well known in sliding mode control, strongly reduces operating performance while causing premature wear of the system. Four cases are studied to highlight the factors influencing the chattering in the backstepping control. In the first case, the effect of the unmodeled fast servo valve dynamics is analysed by comparing a reduced-order backstepping controller with a full-order controller. The second case analyses the sensitivity to the tuning gains of the backstepping controller. The third case emphasises the influence of the parameter of sign function approximation. The last case analyses the sensitivity of the parameter of the time derivative of the virtual controls. The simulation results in the Matlab/Simulink show that the chattering is mitigated by an appropriate gains tuning but above all an appropriate calculation of the derivatives of the virtual controls, particularly for high-order systems.