Conventional Backstepping Control Research Articles

Application of Backstepping Control With Nonsingular Terminal Sliding Mode Surface Technique to Improve the Robustness of Stator Power Control of Asynchronous Generator-Based Multi-Rotor Wind Turbine System

The conventional backstepping control (CBC) technique for the asynchronous generator (AG) incorporated in a multi-rotor wind turbine (MRWT) system faces several challenges, including torque and stator power ripples, lack of robustness, and low-quality stator currents. Furthermore, the CBC performs poorly under distorted grid voltage conditions. To address these issues, this study proposes applying backstepping nonsingular terminal sliding mode control (BNTSMC). The controller design involves incorporating a NTSMC into the control law of the CBC technique, where Lyapunov theory was used to analyze the stability of the suggested approach. The synthesis of the suggested controller revolves around two sliding mode surfaces, specifically the stator powers of the AG, which are used to determine the final control laws. The advantages of this technique are excellent robustness against internal and external disturbances based on NTSMC, and the controller exhibits asymptotic stability based on the backstepping technique. Simulation tests in MATLAB software on a 1.5 MW AG-based MRWT system clearly demonstrate the advantages of BNTSMC over CBC.

Adaptive Fractional-Order Backstepping Control for a General Class of Nonlinear Uncertain Integer-Order Systems

In this paper, we consider the adaptive fractional-order backstepping control problem for a class of high-order integer-order systems with uncertainties and unknown external disturbance. To obtain enhanced control performance, fractional-order calculus is integrated within the conventional backstepping controller design procedure. Theoretical proof is provided based on the Lyapunov stability theorem to ensure the global stability of the closed-loop system in the sense that all the closed-loop signals are uniformly ultimately bounded and the output tracking error to a reference signal converges to an adjustable arbitrarily small range by tuning certain design parameters. Both numerical simulation and experimental results verify the efficacy of the proposed adaptive fractional-order backstepping control scheme.

Finite-Time Attitude Optimization Maneuver Control for Coupled Spacecraft Under Attitude Measurement Errors and Actuator Faults

The large-angle attitude maneuver trajectory design and tracking control for flexible spacecraft with slosh structure under attitude measurement errors and actuator faults are investigated in this article. Considering that rapid attitude maneuvers can lead to severe flexible vibrations and liquid sloshing, which in turn affects system stability. Therefore, under the requirement of fast maneuvering, the attitude trajectory is optimized to maximize the system’s stability by establishing a new indicator function, while satisfying multiple physical constraints. Furthermore, the novel adaptive multivariable command filtering backstepping fault-tolerant controller is proposed for the coupled spacecraft, to achieve the finite-time attitude tracking to the optimized trajectory, despite the measurement errors and actuator faults. The merits lie in the modified auxiliary signals and virtual commands design, which can compensate the filter errors, caused by the applied filters to deal with the “explosion of terms” of conventional backstepping control, in finite time with better control performance. The numerical simulations are performed to verify the effectiveness of the proposed method.

Backstepping Control Merged with Disturbances Observer for Quadrotor with Rotating Arms

Controlling nonlinear systems is an important and serious task, especially in the presence of external disturbances and uncertain parameters. The main aim of this paper is to design a robust controller that ensures good trajectory tracking of a new quadrotor with rotating arms subjected to external disturbances. Before proceeding to the quadrotor control, it is necessary to first develop a dynamic model of the studied system that takes into account the variation of: the Center of Gravity (CoG), the inertia, and the allocation matrix. Then, based on the finite time Lyapunov stability theory, the theoretical basis of backstepping control integrated with disturbance observer is explained. The observer estimates online the external disturbances and compensates them in the internal loop that contains the attitude and the position backstepping controllers. Numerical simulations are performed to illustrate the efficiency of the proposed control technique, where the controller’s parameters are tuned using a Genetic Algorithm (GA). Finally, qualitative and quantitative comparison of the suggested controller with the conventional backstepping controller is carried out. Overall, the findings show that the proposed control technique outperforms in terms of accuracy and robustness.

Robust Backstepping Control Combined with Fractional-Order Tracking Differentiator and Fractional-Order Nonlinear Disturbance Observer for Unknown Quadrotor UAV Systems

In this paper, we studied a fractional-order robust backstepping control (BSC) combined with a fractional-order tracking differentiator and a fractional-order nonlinear disturbance observer for a quadrotor unmanned aerial vehicle (UAV) system. A fractional-order filtered error and a fractional-order tracking differentiator were utilized in a conventional BSC system to improve the positioning control performance of a highly coupled nonlinear quadrotor UAV system and bypass the differentiation issue of the virtual control and compensation of the transformation error in the conventional BSC design. A new fractional-order disturbance observer with the sine hyperbolic function was then proposed to enhance the estimation performance of the uncertain quadrotor UAV. Sequential comparative simulations were conducted, demonstrating that the proposed positioning controller and observer utilizing fractional-order calculus outperformed those of the conventional controller and observer systems.

Adaptive Finite-Time Command Filtered Controller Design for Nonlinear Systems With Output Constraints and Input Nonlinearities.

This work addresses a finite-time tracking control issue for a class of nonlinear systems with asymmetric time-varying output constraints and input nonlinearities. To guarantee the finite-time convergence of tracking errors, a novel finite-time command filtered backstepping approach is presented by using the command filtered backstepping technique, finite-time theory, and barrier Lyapunov functions. The newly proposed method can not only reduce the complexity of computation of the conventional backstepping control and compensate filtered errors caused by dynamic surface control but also can ensure that the output variables are restricted in compact bounding sets. Moreover, the proposed controller is applied to robot manipulator systems, which guarantees the practical boundedness of all the signals in the closed-loop system. Finally, the effectiveness and practicability of the developed control strategy are validated by a simulation example.

Real‐time implementation of adaptive neural backstepping controller for battery‐less solar‐powered PMDC motor

A low-cost battery-less solar-powered PMDC motor using an adaptive backstepping Chebyshev neural network controller to track the desired speed for any change in irradiance and load torque is proposed in this paper. The neural network is used for approximating the variable load torque because of its approximation property. The computational burden of the control law is reduced because of the orthogonal property of Chebyshev polynomials. The asymptotically stable system is obtained by tuning the weights of neurons in accordance with the Lyapunov stability analysis. From the Lyapunov control function of backstepping control design procedure, the control law is obtained by an innovative way of elucidating the cubic equation, in place of resolving the derivative of the control law in the control function. This approach eliminates the constraints caused by the non-strict feedback system for the backstepping control approach and also this reduces ripples in the duty cycle which makes its appropriateness in real-time. To ensure its robustness in tracking the desired speed at a faster time and minimum overshoot, simulations are done for an extensive range of variations in irradiance and load torque, and the obtained results are assessed by comparing it with the PID controller and conventional backstepping controller. Because of the use of neural network the robustness of the proposed controller is ensured with enhanced transient and steady state responses. A prototype is developed in the laboratory and the obtained results are assessed by comparing it with the backstepping controller and PID controller.

Enhanced backstepping control for an unconventional quadrotor under external disturbances

AbstractRobust control of non-linear systems is a challenging task, notably in the presence of external disturbances and uncertain parameters. The main focus of this paper is to solve the trajectory tracking problem of an unconventional quadrotor with rotating arms (also known as a foldable drone), while overcoming some of the challenges associated with this type of vehicle. Therefore, in a first step, the model of this vehicle is presented, taking into account the change of the inertia, the centre of gravity, and the control matrix. The theoretical foundations of backstepping control, based on the finite time Lyapunov stability theory and enhanced by a Super-Twisting algorithm, are then discussed. Numerical simulations are performed to demonstrate the efficiency of the suggested control approach. Finally, a qualitative and quantitative comparative study of the proposed controller with the conventional backstepping controller is performed. Overall, the obtained results show that the proposed control strategy outperforms in terms of accuracy and resilience.

A Nonlinear Adaptive Backstepping Controller for Stabilizing the DC Bus Voltage of an Islanded Hybrid Microgrid

A bidirectional interlinking converter (BIC) interconnects the ac and dc buses of a hybrid microgrid (HMG). Under certain operating conditions, the BIC may appear as constant power load to the dc bus causing low-frequency oscillations in it. This instability is observed during the power flow from dc to ac buses and is attributed to an interaction between the input and output impedances seen at the point of interface. In this article, an active damping scheme based on an adaptive backstepping controller (ABC) is proposed for the BIC of an islanded HMG to address the voltage instability in the dc bus. The proposed scheme can be easily integrated with a conventional backstepping controller and an attractive feature is its ability to disengage itself from the ac voltage controller of the BIC as soon as voltage oscillations in the dc bus die out. Thus, the active damper does not deteriorate the ac voltage quality at steady state. The proposed method uses fewer current sensors as compared with a recently reported active damping technique based on predictive control. Typical of a backstepping controller, large signal stability is ensured while deriving the control and adaptation laws. Experimental validation is included.

A generalized proportional integral observer–based robust tracking design approach for quadrotor unmanned aerial vehicle

This article mainly studies the trajectory tracking control for quadrotor unmanned aerial vehicle with unknown time-varying disturbances including parametric uncertainties, model errors, and external disturbances such as wind effects. Conventional backstepping control schemes usually cannot guarantee the performance when it faces the time-varying disturbances. Improved schemes, such as integral backstepping, can only compensate the disturbances in a relatively slow way. By introducing disturbance observer technology into the design of controller, a composite generalized proportional integral observer–based robust control design method is developed. First, by utilizing the generalized proportional integral observer, the lumped time-varying disturbances of unmanned aerial vehicle are estimated. Secondly, combining the value of disturbance estimation and feedforward controller by using backstepping control technology together, a composite controller has been developed, which can be called as backstepping control + generalized proportional integral observer. The proposed control method has a better capability of disturbance rejection and is easy to implement. Simulation and experimental results illustrate the good robustness and tracking performance of the proposed scheme.

Optimal Design and Command Filtered Backstepping Control of Exoskeleton With Series Elastic Actuator

Abstract The lower limb exoskeleton can improve mobility and safety during rehabilitation for human. However, most current exoskeleton systems are not capable of providing variable joint stiffness in response to changing external demands. In this paper, a knee exoskeleton based on the series elastic actuator (SEA) is designed for safe human-computer interaction. The structural dimensions of the exoskeleton actuation mechanism were optimized based on gait biomechanics to ensure stability and compactness. While maintaining the mechanism range of motion (ROM), this optimization ensures that less peak force is required during the gait cycle. However, the insertion of series elastic actuators inevitably brings new challenges for high precision control of the exoskeleton, such as the problems of modeling errors, compliance, friction, and external disturbances in the exoskeleton joint. To achieve high precision control of the exoskeleton, an extended disturbance observer (EDO) based command filtered backstepping control (CFBC) of the knee exoskeleton is developed. The effective observation of friction, external disturbances, and modeling errors in the system is obtained by the EDO. Compared with conventional backstepping control, the CFBC can not only solve the “explosion of complexity” problem through a command filter but also reduce filter errors by an error compensation mechanism. Based on the Lyapunov stability, all signals in the closed-loop system are semiglobal uniformly ultimately bounded. Finally, comparison simulation results demonstrate the effectiveness of the proposed control approach.

Command filtering‐based adaptive neural network control for uncertain switched nonlinear systems using event‐triggered communication

AbstractIn this article, a command filtering‐based adaptive event‐triggered neural network control scheme is proposed for a class of uncertain switched nonlinear systems with unknown control coefficient and input saturation. First, radial basis function neural networks are used as function approximators to estimate unknown nonlinear functions. Then, an event‐triggering mechanism based on the tracking error is introduced to avoid the over‐consumption of communication resources. Furthermore, command filters are employed to solve the problem of complexity explosion that exists in conventional backstepping control design, and the error compensation signals are designed to reduce the errors caused by the filters. Considering that the unknown control gain and input saturation exist in many practical applications, a Nussbaum‐type function is thus introduced into the controller design to address these challenging issues. Finally, stability of the closed‐loop system is strictly proven under a standard Lyapunov stability analysis framework. The effectiveness of the proposed control scheme is illustrated by a simulation example.

Adaptive fuzzy finite-time backstepping control of fractional-order nonlinear systems with actuator faults via command-filtering and sliding mode technique

In the paper, a class of unknown fractional-order nonlinear systems suffering from actuator faults are investigated. Meanwhile, an adaptive finite-time sliding mode control (SMC) approach based on approximation principle of fuzzy logic system (FLS) and backstepping layout is proposed. It is well known that the standard backstepping control has inherent computational complexity. Therefore, a type of fractional-order command filter (CF) is introduced to overcome such a shortcoming, that is, by means of fractional-order CF, the virtual input signal and its fractional derivative can be estimated properly as anticipated. Fractional-order sliding mode surfaces are constructed to diminish the filtering errors such that more better performance is guaranteed. Besides, compared to the conventional backstepping control, the CF-based fuzzy backstepping SMC approach presented in the paper not only shows the superior robustness, but also facilitates to accomplish the desired tracking control objective in finite time. The finite-time stability analysis is established on the basis of fractional-order Lyapunov method. Finally, the effectiveness of the proposed methodology is identified by numerical simulations.

Adaptive backstepping control of linear induction motors using artificial neural network for load estimation

Linear induction motors (LIMs) make performing a direct linear motion possible without any mechanical rotary to linear motion transforming parts. <span lang="EN-US">Obtaining a precise mathematical model of such type of motors presents a difficulty due to time varying parameters and external load disturbance. This paper proposes an adaptive backstepping controller structure based on lyapunov stability for controlling a LIM position. Which can guarantee the annulment of position tracking error, despite of parameter uncertainties. Parameter update laws are extracted to estimate mover mass, friction coefficient and load force disturbance, which are assumed to be constant parameters; as a result, compensating their undesirable effect on control design. Then, load disturbance estimate is replaced with an artificial neural network (ANN) to reduce the estimation error. The numerical validation has shown better performance compared to the conventional backstepping controller, and proved the robustness of the proposed adaptive controller design against parameter changes.</span>

Fuzzy Based Backstepping Control Design for Stabilizing an Underactuated Quadrotor Craft under Unmodelled Dynamic Factors

Since the quadrotor unmanned aerial vehicle (UAV) is one of the systems that has four (4) control inputs and six (6) degree of freedom (DOF) which makes it as an underactuated system. Such underactuated mechatronic systems are very difficult to stabilize but at the same time these systems are power efficient and cost-effective because of a lower number of actuators. Later, if someone tries to stabilize this underactuated quadrotor UAV under the impact of unmodelled dynamic factors, it will lead to huge instability, low convergence rate, chattering effect, trajectory deviation and may also encounter some of the serious transient and steady state issues as well. This paper presents one of the adaptive-robust control algorithms, called the fuzzy based backstepping control (FBSC) design, to address the quadrotor’s helical trajectory tracking issue under an influence of unmodelled dynamic factors and external disturbances. This manuscript proposes the synthesis of the proposed FBSC design using MATLAB and Simulink software whereas these results are correlated with the conventional backstepping control (BSC) algorithm to show the effectiveness of the proposed algorithm by computing the integral absolute error values with and without disturbances.

Robust Super-Twisting Sliding Mode Backstepping Control Blended with Tracking Differentiator and Nonlinear Disturbance Observer for an Unknown UAV System

In this study, we examined the robust super-twisting sliding mode backstepping control (SBSC) method, which employed a tracking differentiator and nonlinear disturbance observer for a hexacopter unmanned aerial vehicle (UAV) system. To realize robust tracking control performance for a highly coupled nonlinear hexacopter UAV system, a super-twisting sliding mode control method was combined with designing stabilizing controls of backstepping control (BSC) applied to the UAV system. Furthermore, the differentiation issue of the virtual control and compensation of transformation error in the conventional BSC design were bypassed via a new continuous tracking differentiator structure. Additionally, a new disturbance observer based on the proposed tracking differentiator was considered to estimate uncertainties of the hexacopter UAV. Comparative simulation results demonstrated that the proposed tracking-differentiator-based SBSC scheme (PTSBSC) blended with the tracking differentiator and nonlinear disturbance observer exhibits improved performance when compared to that of conventional BSC and disturbance observer systems.

Backstepping-based Super-Twisting Sliding Mode Control for a Quadrotor Manipulator with Tiltable Rotors

Designing a robust controller is very important in the control of outdoor unmanned aerial vehicles. This paper presents the design procedures and implementation of super-twisting sliding mode controller, which is a robust nonlinear controller. The robust controller is applied to an over-actuated quadrotor manipulator with four tiltable rotors. A serial manipulator with two links is mounted on the bottom of the quadrotor. The quadrotor possesses the property of decoupling its position and orientation. The main contribute of this paper is that a super-twisting sliding mode controller in vector form is designed and applied to the control of an over-actuated quadrotor manipulator. Another contribution of this paper is that the stability of the closed-loop system is proved by utilizing the Lyapunov stability theory. It is confirmed that the performance of the super-twisting sliding mode controller is superior to that of the conventional backstepping controller in terms of convergence rate and accuracy by simulations.

Command-Filtered Backstepping Control for a Class of Chaotic Systems

The problem of command-filtered backstepping control for a class of chaotic systems was studied in this paper. At each step of the backstepping design, a command filtering backstepping method is introduced to use a new virtual control signal, in which the derivative of the virtual control was approximated by using the output of filter. Then, the asymptotic stability conditions for synchronization errors are obtained by using the Lyapunov stability criterion and this control method. The design technique has the advantages of the conventional command-filtered backstepping control. An example shows the proposed method was feasible.

THE MOTION TRAJECTORY-BASED FINITE-TIME CONTROL FOR THE MARINE SURFACE VEHICLE

This brief is devoted to the predesigned motion trajectory-based finite time dynamic positioning (DP) control for a marine surface vehicle (MSV) with unknown external disturbances. Firstly, a preset motion trajectory is presented through establishing the relationship function among position tracking errors and heading tracking error, facilitating the MSV to arrive in the equilibrium point along the pre-designed trajectory. Furthermore, a novel nonsingular and fast terminal sliding mode control (NTSMC) approach is investigated, which ensures faster convergence rate and better stability performance of the close-loop system than the conventional backstepping control approach. What’s more, by incorporating the adaptive technique with the NTSMC approach, an adaptive nonsingular and fast terminal sliding mode control (ANTSMC) strategy is addressed. Compared to the NTSMC approach, it strengthens robustness to disturbances and guarantees system states to converge to a closer neighborhood of the equilibrium point. Finally, simulation results illustrate the remarkable effectiveness of proposed control schemes.

Finite‐time adaptive fuzzy control for a class of output constrained nonlinear systems with dead‐zone

SummaryThe article investigates the finite‐time adaptive fuzzy control for a class of nonlinear systems with output constraint and input dead‐zone. First, by skillfully combining the barrier Lyapunov function, backstepping design method, and finite‐time control theory, a novel adaptive state‐feedback tracking controller is constructed, and the output constraint of the nonlinear system is not violated. Second, the fuzzy logic system is used to approximate unknown function in the nonlinear system. Third, the finite‐time command filter is introduced to avoid the problem of “complexity explosion” caused by repeated differentiations of the virtual control signal in conventional backstepping control schemes. Meanwhile, a new saturation function is added in the compensating signal for filter error to improve control accuracy. Finally, based on Lyapunov stability analysis, all the signals of the closed‐loop are proved to be semi‐globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood region of the origin in a finite time. A simulation example is presented to demonstrate the effectiveness for the proposed control scheme.