Robust Backstepping Research Articles

Distributed Neurodynamics-Based Backstepping Optimal Control for Robust Constrained Consensus of Underactuated Underwater Vehicles Fleet.

Robust constrained formation tracking control of underactuated underwater vehicles (UUVs) fleet in 3-D space is a challenging but practical problem. To address this problem, this article develops a novel consensus-based optimal coordination protocol and a robust controller, which adopts a hierarchical architecture. On the top layer, the spherical coordinate transform is introduced to tackle the nonholonomic constraint, and then a distributed optimal motion coordination strategy is developed. As a result, the optimal formation tracking of UUVs fleet can be achieved, and the constraints are fulfilled. To realize the generated optimal commands better and, meanwhile, deal with the underactuation, at the lower-level control loop a neurodynamics-based robust backstepping controller is designed, and in particular, the issue of "explosion of terms" appearing in conventional backstepping-based controllers is avoided and control activities are improved. The stability of the overall UUVs formation system is established to ensure that all the states of the UUVs are uniformly ultimately bounded in the presence of unknown disturbances. Finally, extensive simulation comparisons are made to illustrate the superiority and effectiveness of the derived optimal formation tracking protocol.

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.

Design and real-time implementation of a robust backstepping non-singular integral terminal sliding mode attitude control for a quadrotor aircraft

This paper concerns the problem of robust attitude control of a quadrotor aircraft subjected to modeling inaccuracies and wind disturbances. First, the model dynamics and state space representation of the quadrotor system are designed by considering the impact of disturbances and uncertainties. Then, a novel robust backstepping non-singular integral terminal sliding mode control (BNITSMC) is synthesized for the quadrotor attitude with the aim of enhancing the tracking accuracy. To strengthen the system’s robustness and guarantee the reachability of the sliding surface while reducing chattering, the supertwisting algorithm (ST) is used. Closed-loop stability and state convergence are guaranteed via the Lyapunov theory. Some experimental flight tests have been executed to validate the workability of the developed flight control. The obtained results prove that the recommended technique can provide improved performance in terms of stabilization and tracking precision.

A Robust Backstepping Controller Based on Nonlinear Observer for Shunt Active Filters to Improve Power Quality in Four-Wire Distribution Systems

This article introduces a novel approach to enhance the performance of LCL based active power filters (APFs) in four-wire distribution systems by employing a nonlinear current control strategy. The strategy combines backstepping control (BSC) and a nonlinear disturbance observer (NDOB) to effectively manage harmonic and interharmonic grid currents. By situating the shunt active power filter (SAPF) at the point of common coupling (PCC) via the LCL filter, the technique ensures that grid connected currents remain balanced and purely sinusoidal. The integration of NDOB with BSC aims to fortify the resilience of BSC against disturbances. Consequently, any disturbances occurring within the system are precisely estimated by the NDOB and subsequently mitigated through the BSC mechanism. Notably, this approach showcases robust adaptability across diverse scenarios, encompassing external disturbances, variations in filter parameters, nonlinear loads laden with harmonics and interharmonics, load imbalances, and non-ideal grid voltages. Its performance remains robust and stable even when disturbances are present. Comparative analysis with linear-based methodologies underscores the advantages of this approach, revealing quicker and smoother transient responses. The efficacy of the proposed technique is demonstrated through comprehensive simulation studies, substantiating its potential for significantly advancing power quality in complex distribution systems.

Design and PIL implementation of a new robust backstepping based low-complexity voltage-oriented control method for four-leg rectifiers

This paper proposes a low computational complexity enhanced voltage-oriented control strategy (EVOC) based on robust backstepping controllers (BSC) in the synchronous rotating frame (dq0 frame) for a PWM four-leg voltage-source-rectifier (FLVSR). Unlike traditional VOC strategies, the suggested EVOC approach does not need any synchronization method and Park transformations, and it has the similar architecture and same features as the traditional VOC when it’s synchronization loop for grid voltage phase angle detection is properly operated. In addition to controlling the FLVSR, the suggested EVOC strategy is also used to develop the model of the three phase FLVSR in the dq0 frame using the concepts of direct instantaneous power control (DPC) theory, which combine the benefits of traditional DPC and traditional VOC with less computational complexity. The robust BSC is adopted for accurate regulation of FLVSR input currents and dc bus voltage simultaneously while taking into account the FLVSR parameter uncertainties. It produces sinusoidal currents with lower ripples and has high robustness against parametric variations. It is also simple to implement and has a relatively high grid voltage disturbance rejection ability. Finally, comparisons with both the traditional VOC strategy using PI controllers (VOC-PIC) and the EVOC strategy using PI controllers (EVOC-PIC) under various conditions demonstrate the superiority and benefits of the proposed EVOC-BSC strategy.

Model-Free Robust Backstepping Adaptive Cruise Control

This paper studies the model-free robust adaptive cruise control problem of a vehicle with unknown nonlinear dynamics and disturbances. First, under backstepping control framework, the position tracking errors with different spacing strategies are used to design a virtual control law, which provides a velocity reference. Then, a novel data-driven sliding surface whose parameters are updated by designing estimation algorithm is developed to handle the unknown uncertainties and disturbances. Finally, the model-free robust backstepping adaptive cruise control (MFRB-ACC) method including PI control, model-free control, and robust control is designed. The novelty of the proposed control technique lies in its strong robustness, which is not based on the precise vehicle model. The designed data-driven sliding surface releases the necessity for the accurate mathematical model of the vehicle and guarantees the inherent robustness of the controller, in particular to uncertainties, modelling error, or external disturbance. Moreover, the designed controller contains three terms such that it has an effective decoupling ability and strong robustness. The effectiveness and superiority of the designed MFRB-ACC method are validated on MATLAB, and the simulation results show that compared to the PID algorithm, the designed MFRB-ACC algorithm can track its preceding vehicle with lower tracking error under different spacing strategies, different operating conditions, and low sampling frequencies. Especially at a sampling frequency of 0.1 s, the error under the PID-ACC increases from 0.2 m at a sampling frequency of 0.01 s to 2 m, and the error under MFRB-ACC has little change compared to the error at a sampling frequency of 0.01 s.

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.

Control of DC–DC Buck Converters Using Robust Composite Backstepping and Integral Terminal Sliding Mode Approaches

This paper proposes a new composite scheme to design a robust voltage controller for DC-DC buck converters in which the composite structure combines the recursive backstepping approach with an integral terminal sliding mode controller (ITSMC). In this work, the proposed ITSMC is designed to overcome the one-degree limitation of existing ITSMCs and difficulties for the finite time convergence in standard sliding mode controllers (SSMCs) as it incorporates a quick reaching law. Moreover, the singularity problem in existing SSMCs is tackled using a modified integral sliding surface. The backstepping strategy is used to ensure the voltage monitoring with a higher degree of accuracy. The robustness of the proposed composite approach is ensured by capturing the variations in parameters, input voltage, and mismatch in the model; as all these factors are included in the dynamical model of the DC-DC buck converter based on which the proposed composite controller is designed. The robustness and stability of the proposed composite controller are simultaneously analyzed using the concept of the Lyapunov stability theory. The theoretical and analytical findings for the proposed composite robust backstepping ITSMC (RBITSMC) are further verified through extensive simulation studies in the MATLAB/Simulink platform. Performance comparisons of the proposed RBITSMC are also presented against an existing adaptive nonsingular fast terminal sliding mode controller (ANFTSMC). Finally, experimental results from the application of the proposed control strategy on a laboratory prototype are presented to justify its application on the practical system.

Robust backstepping control for maneuver aircraft based on event-triggered mechanism and nonlinear disturbance observer

PurposeThis study aims to achieve the post-stall pitching maneuver (PSPM) and decrease the deflection frequency of aircraft actuators controlled by the robust backstepping method based on event-triggered mechanism (ETM), nonlinear disturbance observer (NDO) and dynamic surface control (DSC) techniques.Design/methodology/approachTo estimate unsteady aerodynamic disturbances (UADs) to suppress their adverse effects, the NDO is designed. To avoid taking the derivative of the virtual control law directly and eliminate the coupling term of the system states and dynamic surface errors in the stability analysis, an improved DSC is developed. Combined with the NDO and DSC techniques, a robust backstepping method is proposed to achieve the PSPM. Furthermore, to decrease the deflection frequency of the aircraft actuators, a state-dependent ETM is introduced.FindingsAn ETM-and-NDO-based backstepping method with an improved DSC technique is developed to achieve the PSPM and decrease the deflection frequency of aircraft actuators. And simulation results are presented to verify the effectiveness of the proposed paper.Originality/valueFew studies have been conducted on the control of the PSPM in which the lateral and longitudinal attitude dynamics are coupled with each other considering the UADs. Moreover, the mechanism that can decrease the deflection frequency of aircraft actuators is rarely developed in existing research. This study proposes an ETM-and-NDO-based backstepping scheme to address these problems with satisfactory performance of the PSPM.

An Integrated Trajectory Planning and Motion Control Strategy of a Variable Rotational Speed Pump-Controlled Electro-Hydraulic Actuator

This article proposes an integrated two-loop motion control strategy of an electro-hydraulic actuator, in which the cylinder actuator is driven by a variable speed pump to track a desired trajectory. The control strategy combines constrained trajectory planning (outer loop) with nonlinear motion control (inner loop) to achieve accurate trajectory tracking of electro-hydraulic actuators under constraints. A nonlinear filter-type trajectory planner is utilized as the outer loop to synthesize the optimal trajectory, reaching the desired reference with the minimum time while fulfilling the constraints. A full-state constraints assignment approach is proposed, including motion and pressure state constraints. Furthermore, to accurately track the synthesized trajectory of the outer loop, a model-based adaptive robust backstepping motion controller is designed as the inner loop, which can realize guaranteed robustness and high accuracy of the trajectory tracking in the presence of dynamic nonlinearities and parametric uncertainties of the electro-hydraulic actuator. Experiments with contrast control strategies and practical trajectories are conducted, which comprehensively verify the advantages of the proposed integrated two-loop control strategy.

An adaptive robust backstepping improved control scheme for mobile manipulators robot

In this study, an approach with the position control scheme is proposed for the mobile manipulator robot, by applying the adaptive strategies with the backstepping control technique. In the proposed backstepping controller, the fixed problem of main control parameters has been improved by the adaptive self-updating process. In addition, this control method requires no prior knowledge of the control system, such as the unknown dynamics and disturbances. And, to relax uncertainties, an adaptive robust controller is also designed as a compensator for the main backstepping controller. Moreover, all adaptive updating algorithms are designed based on the Lyapunov theorem so that the proposed control system performances are guaranteed. The advantage of the improved control system will be evaluated via simulation results for the 3 - DOF MMR system.

Parameter identification of Duhem model based on antlion-fish swarm hybrid algorithm and robust backstepping sliding mode control for rate-dependent hysteresis of piezoelectric actuators

A new parameter identification method of Duhem model based on antlion-fish swarm hybrid algorithm is proposed to characterize the rate-dependent hysteresis. The unknown piecewise functions in Duhem model is identified by a hybrid algorithm. Antlion optimization (ALO) algorithm and artificial fish (AF) swarm algorithm are switched in order of execution and their iterative data are fused to form the antlion-fish swarm hybrid algorithm. The comparison experiment shows the hybrid algorithm has the advantages of fast convergence and high precision. In order to compensate the rate-dependent hysteresis of PEA, a robust backstepping sliding mode feedback controller with feedforward inverse Duhem model compensator are designed. The comparative experimental results of displacement tracking show that this method has good tracking performance. The practicability and effectiveness of the method are verified.

Design and analysis of robust backstepping controller for DC suppression of parallel UPS inverter system

AbstractHere, an improved control strategy is proposed, which adopts a non‐linear robust backstepping controller to eliminate DC circulating current in a parallel uninterruptible power supply (UPS) system. The traditional active and reactive power sharing control can ideally suppress the AC circulating current, but cannot effectively restrict the DC circulating current. Based on the traditional active power and reactive power sharing control (TAPRPSC) of the parallel UPS system, the proposed control strategy is used in each parallel inverter module to suppress the DC component disturbance in the inverter output voltage, which varies within a certain range. Hence the desirable steady‐state and dynamic performance of the system can be obtained. Moreover, the Lyapunov method is utilized to ensure the stability and robustness of the system. A parallel system of two UPS inverters with the proposed control strategy is built by Matlab/Simulink, and further experiments are carried out on the semi‐physical simulation platform of the Modelling Tech. Both the simulation and experimental results verify the effectiveness of the proposed control strategy for DC circulating current suppression and ideal output voltage tracking.

New Robust Backstepping Attitude Control Approach Applied to Quanser 3 DOF Hover Quadrotor in the Case of Actuators Faults

In this paper, a novel robust backstepping-based fault-tolerant control is designed, implemented and validated experimentally on a quadrotor unmanned aerial vehicle testbed under actuator fault conditions for tracking control. Backstepping is known as a robust method to maintain system performance and keep it insensitive to disturbances. The proposed nonlinear controller is mainly based on the advanced robust backstepping method to solve the system uncertainties caused by disturbances and actuator faults, which appear in the motor part of the system and are compensated without diagnostics or fault identification. The various parameters of the proposed approach are optimized using the particle swarm optimization (PSO) method. Owing to the minimized control effort to accommodate uncertainties compared to the conventional backstepping, the proposed approach can still maintain the system performance when severer faults occur. The proposed approach is validated, first, in a simulation using the nonlinear model of the quadrotor, then experimentally, using the Quanser 3DOF Hover quadrotor. Both theoretical and experimental analyses have demonstrated that the effectiveness of the proposed improved backstepping fault-tolerant control strategies faces significant loss of actuator efficiency.

Fuzzy based back stepping controller for glucose level regulation under meal disturbance

Diabetes is one of the most common and critical diseases around the world, which need insulin injections to control the body’s glucose rate. A robust back stepping (BS) controller design based on fuzzy system is introduced in this paper to control the glucose level with the presence of meal disturbance. The controller’s design is based on Bergman’s mathematical model. Different fuzzy controller structures are implemented (fuzzy PI, fuzzy PD, and fuzzy PID) controllers along with BS controller named as (BS-fuzzy PI, BS-fuzzy PD, BS-fuzzy PID) controllers. Simulation results using MATLAB/Simulink show efficiency and robustness of the proposed design in terms of controlling the insulin concentration level in blood under meal disturbance and retaining the glucose level to its Basal value.

Robust Backstepping Control Applied to UAVs for Pest Recognition in Maize Crops

In this paper, a robust control technique is developed to achieve the quadrotor stabilization against unmodeled matching vanishing dynamics. The synthesis of the proposed robust control is based on the Lyapunov approach and the backstepping method allowing to construct an iterative control algorithm. To compare the performance of the proposed controller, a Proportional Derivative (PD) controller is used to obtain experimental results in an outdoor environment. To compare the closed-loop system responses with both controllers, the Integral Absolute Error is computed and several tests are conducted to calculate the error standard deviation. Ultimately, employing the robust backstepping control approach in pest recognition in maize crops, which is a specific task of precision agriculture, demonstrates its effectiveness in improving the trajectory tracking of the vehicle while it captures images of the crops.

Quadcopter UAVs Extended States/Disturbance Observer-Based Nonlinear Robust Backstepping Control.

A trajectory tracking control for quadcopter unmanned aerial vehicle (UAV) based on a nonlinear robust backstepping algorithm and extended state/disturbance observer (ESDO) is presented in this paper. To obtain robust attitude stabilization and superior performance of three-dimension position tracking control, the construction of the proposed algorithm can be separated into three parts. First, a mathematical model of UAV negatively influenced by exogenous disturbances is established. Following, an extended state/disturbance observer using a general second-order model is designed to approximate undesirable influences of perturbations on the UAVs dynamics. Finally, a nonlinear robust controller is constructed by an integration of the nominal backstepping technique with ESDO to enhance the performance of attitude and position control mode. Robust stability of the closed-loop disturbed system is obtained and guaranteed through the Lyapunov theorem without precise knowledge of the upper bound condition of perturbations. Lastly, a numerical simulation is carried out and compared with other previous controllers to demonstrate the great advantage and effectiveness of the proposed control method.

Robust backstepping sliding mode aircraft attitude and altitude control based on adaptive neural network using symmetric BLF

In this paper, asymptotic control of attitude and altitude of the aircraft is proposed by employing robust backstepping sliding mode control (BSMC) in conjunction with adaptive radial basis function neural network (RBFNN). Accurate knowledge of the non-linear aerodynamic forces and moments, particularly high-fidelity models, is of paramount importance to arrive at such a control strategy under a continuous dynamic environment. Adaptive RBFNN is used to approximate such an unknown non-linear function by continuously updating the network weights in rapidly varying conditions. Further, adaptation laws are used concurrently with neural networks to update the control power derivatives. These adaptive neural networks are used within the architecture of backstepping, integrated with the sliding surfaces where angular rates act as the virtual controller. The postulation of such law requires only minimal information about the aerodynamic model beyond well-known physical features. Moreover, Barrier Lyapunov Function (BLF) candidate is employed to constrain the state of the plant from transgressing a specific limit. Closed-loop signals are theoretically proved to be semi-globally uniformly ultimately bounded in the sense of Lyapunov. Finally, the robustness of the designed flight control law is explored by appending uncertainties and bounded exogenous disturbances in the plant. The results obtained in the present study signify good control performance where output tracks the reference signals by forcing the system states to remain in the designed sliding surfaces.

Maximum Power Extraction from PV System using fast and Robust Backstepping Controller

Maximum power point tracking (MPPT) plays a pivotal role in enhancing output power extracted from photovoltaic (PV) system. The major obstacle against MPPT is occurrence of undesired chattering and environmental variations, which may affect desire objective. Hence, in this paper, the objective of MPPT is fulfilled by using a non-linear Fast and Robust Backstepping based on sliding mode controller (FRBSMC), which has less rise time, fast convergence and robust enough against uncertainties and variations. For MPPT, a reference voltage is generated using neural network, which is tracked by proposed controller to confirm the accuracy and efficiency of aforementioned controller. To ensure the effectiveness of proposed control scheme, a comparison is carried with Backstepping sliding mode controller (BSMC), Backstepping controller (BSC) and Perturb and Observe (P&O) controllers. Simulation of the mentioned controller is done in Simulink/MATLAB.

Anti-Windup Robust Backstepping Control for an Underactuated Reusable Launch Vehicle

The attitude control of an underactuated reusable launch vehicle (RLV) in the reentry phase involving nonminimum phase problem and control input constraints is investigated in this article. To address the nonminimum phase problem, an approach combining output redefinition and robust backstepping is proposed, where a synthetic output is constructed using the combination of the original output and the internal states to obtain stable zero dynamics, and then robust backstepping is performed on the new output. Besides, the ideal internal dynamics are obtained by using optimal bounded inversion, which are incorporated into the controller as the reference trajectories for the internal states to improve the output tracking accuracy. To cope with the control input constraints, a simple and useful anti-windup strategy is proposed by using feedback error clipping, which is shown to be very effective in mitigating control input saturation. Numerical simulations are given to validate the effectiveness of the proposed method.