Multivariable sliding mode backstepping controller design for quadrotor UAV based on disturbance observer

In this paper, a nonlinear adaptive speed controller for permanent magnet linear synchronous motors based on a newly developed adaptive recursive Backstepping control approach for a permanent magnet synchronous motor drive is discussed and analyzed. The Backstepping technique provides a systematic method to address this type of problem. It combines the notion of Lyapunov function and a controller procedure recursively. The adaptive Backstepping control approach is utilized to obtain the robustness for mismatched parameter uncertainties. The overall stability of the system is shown using Lyapunov stability theorem. The simulation results clearly show that the proposed scheme can track the speed reference.

Quadrotor unmanned aerial vehicles (UAVs) operating in agricultural fields for aerial photography are susceptible to external disturbances. The disturbances result in trajectory deviation and irregular image overlapping that considerably degrade image quality. Disturbance observers (DOs) are commonly researched for counteracting these effects but may have delays and limitations in handling diverse and high-frequency disturbances. To this end, this work proposes a continuous high-order sliding mode-assisted DO (HSMDO) with limited time convergence characteristics for the estimation of disturbances in systems. The observer consists of a classical nonlinear DO (NDO) and a sliding mode-assisted system (SMAS). The NDO is used to estimate disturbances preliminarily. The SMAS is utilised to assist the NDO in estimating the high-frequency component of disturbances and ensure that the entire DO is finite-time convergent. Finally, the tracking controller is designed on the basis of the HSMDO, which enables UAVs to track the prescribed trajectories under disturbances stably. Simulation results show that the proposed HSMDO can accurately estimate various types of disturbances. Moreover, the tracking controller based on the HSMDO can improve the antidisturbance performance of systems and ensure the trajectory tracking accuracy of UAVs.

A quadrotor unmanned aerial vehicle (UAV) must achieve desired flight missions despite internal uncertainties and external disturbances. This paper proposes an adaptive trajectory tracking control method that attenuates unknown uncertainties and disturbances. Although the quadrotor is underactuated, a fully actuated controller is designed using backstepping control. To avoid repeated derivatives of control inputs, a dynamic surface method introduces a filter and auxiliary controller. Lyapunov criteria guide adaptive laws for tuning controller gain and filters. A low-power observer is integrated for state estimation. Additionally, a disturbance observer is developed and combined with the control scheme to handle unknown disturbances. Simulations on a DJI F450 quadrotor demonstrate that the proposed control algorithm offers strong trajectory-tracking performance and system stability under multiple uncertainties and external disturbances during flight.

The control performance of quadrotor unmanned aerial vehicles (UAVs) in complex environments can be affected by external disturbances and other factors. In this paper, an adaptive neural network backstepping controller based on the barrier Lyapunov function (BLF) is designed for a quadrotor UAV with internal uncertainties, input–output constraints and external disturbances. Radial basis function neural networks are used to approximate the uncertainties in the dynamic model of the UAV, while the minimum parameter learning method is combined to accelerate the adjustment speed of neural network weights. A robust term is designed to balance the total system disturbance and improve the anti-interference performance. The BLF is used to handle the output constraint so that the constrained parameters cannot break the predefined constraints. An auxiliary system is introduced to solve input saturation and avoid the dependence of tracking error on the input amplitude in the method of approximating input saturation using the smoothing function. The stability of the control system is demonstrated by the Lyapunov method. The simulation results show that the proposed method has high tracking accuracy compared with the backstepping dynamic surface control method, and the input and output are in the predefined range.

A type‐2 fuzzy logic‐based adaptive backstepping control (T2F‐ABSC) approach is presented for a DC/DC Buck converter. Lyapunov‐based backstepping control (BSC), which can guarantee convergence along with asymptotic stability of the system. Also, the black‐box technique is applied for the proposed system, which does not require an accurate mathematical model resulting in a lower computational burden, easy implementation, and lower dependency on the states of the model. On the other hand, for wider ranges of disturbances, including parametric variations, load uncertainty, supply voltage variation, and noise, this approach shows an unsuitable practical application based on its fixed gain values; therefore, the control parameters need to be optimized again to provide ideal operations. Type‐2 fuzzy structure is adopted here to optimize the gains of the ABSM in challenging conditions. Type‐2 fuzzy (T2F) has higher efficiency and faster dynamics with more adaptability to the system. To enhance the performance of the T2F, antlion optimization (ALO) has been used in this structure. ALO is a modern nature‐inspired algorithm, and it has some advantages over other optimizing algorithms. Furthermore, it has ability to find optimal answers in a shorter time, more accurately in contrast to the other optimization algorithms and is used to tune the membership function parameters of the (T2F) under the diverse search spaces. To depict the strength of the designed work, fuzzy‐PID and backstepping schemes proposed to carry out an analysis with this work.

This paper addresses the problem of fixed-time consensus tracking for a class of nonlinear multiagent systems (MASs) with disturbances. We establish a novel fixed-time consensus tracking protocol with adaptive disturbance rejection capabilities, leveraging adaptive selective disturbance elimination (ASDE) technology. This protocol consists of a distributed fixed-time observer (DFTO), a fixed-time disturbance observer (FTDO), and an adaptive selective disturbance elimination backstepping controller (ASDE) with adaptive lumped disturbance compensation abilities. The DFTO estimates the leader’s output using the communication network topology of each follower, while the FTDO rapidly observes the lumped disturbances and their derivatives. By adding disturbance indicator terms and disturbance observation attenuation terms to the control law, the beneficial and harmful effects of disturbance are distinguished. Under favorable disturbance conditions, lumped disturbances can be used to accelerate tracking speed. If disturbances are harmful, they are adaptively compensated to improve tracking accuracy. Furthermore, the fixed-time stability of each part of the protocol is analyzed using Lyapunov theory. Simulation results show that, under different initial states and command inputs, the proposed method achieves faster convergence and smaller tracking errors compared to the adaptive conditional disturbance negaton backstepping controller (ACDN), conditional disturbance negation backstepping controller (CDN), and non-smooth backstepping controller (NBCDC), verifying the effectiveness of the proposed method. The research outcomes serve as a reference for future multiagent adaptive anti-disturbance cooperative control technology.

To solve the control problem for a class of uncertain pure feedback nonlinear systems subjected to external disturbances and multiple constraints, an adaptive robust control methodology is proposed based on a disturbance observer. To handle unknown nonlinearity and external unknown disturbances, a nonlinear disturbance observer is constructed based on a radial basis function neural network, which uses a Butterworth low-pass filter to remove the algebraic loop problem. Then, to guarantee that the system can stably track the desired trajectory under the state constraints, input saturation, and prescribed tracking performance constraints, we developed a novel barrier Lyapunov function and a backstepping controller that combines an auxiliary bounded function, a Nussbaum function, and a first-order sliding-mode differentiator. Subsequently, the stability of the closed-loop system is rigorously proved by Lyapunov analysis. Finally, simulations are conducted to demonstrate the effectiveness of the proposed approach.

In this article, a fuzzy-approximation-based adaptive backstepping control method for dual-arm of a humanoid robot was proposed. The purpose of this control system is to provide coordinated movement assistance to enable the humanoid robot’s human-like forearm to grab objects coordinately (or track any continuous desired trajectory), even in the presence of environmental disturbances and parametric uncertainties. We analyze the proposed adaptive backstepping by mathematical modeling and actually measure the robot dual-arm motion information of a number of case when they simulate the trajectory to verify the model. We design the adaptive fuzzy-approximation control strategy and combining the synthesis of the robust design, backstepping control, and Lyapunov function method, the proposed adaptive fuzzy backstepping control does not need to know the humanoid robot’s arms model precisely. In the control system proposed here, once the desired trajectories of the robot’s dual-arm positions are given, the adaptive fuzzy system was closed to any unknown functions and to the derivative of the virtual control law of the humanoid robot system. In this case, a robust design scheme was utilized to compensate for any approximation errors. With the proposed trajectory tracking, not only able to generate the coordinate motions for a humanoid robot’s two arms, but it can also control the arms to move to the desired positions. The proposed closed-loop system under the adaptive fuzzy backstepping control design was effective and that asymptotic stability was successfully achieved. The adaptive fuzzy-approximation backstepping control strategy should be more complete and intelligent and more actual test should be conducted to further evaluate the effect of the proposed trajectory tracking. The instability of dual-arm of humanoid robot system is systematically analyzed and a backstepping control strategy based on the adaptive fuzzy-approximation to improve the continuity of trajectory tracking of the robot’s arms is proposed.

Auxiliary-system-based composite adaptive optimal backstepping control for uncertain nonlinear guidance systems with input constraints

This paper proposes a novel command-filtered backstepping control method integrated with nonlinear disturbance observers (NDO-CFBS) to improve early-stage rehabilitation training for patients with lower-limb dysfunction across multiple postures, including sitting, lying, and standing. A backstepping control strategy is first developed for the human–robot system, considering the characteristics of passive rehabilitation training. Nonlinear disturbance observers (NDOs) are designed to compensate for model uncertainties and external disturbances. A command filter is then introduced to efficiently compute the derivatives of the virtual control variables within the backstepping framework, leading to the formulation of the NDO-CFBS method. Finally, simulation results of trajectory tracking performance are presented for the multi-posture lower limb rehabilitation robot, demonstrating the effectiveness of the proposed control strategy.

A Lypunov‐based Adaptive Backstepping Control (ABSC) approach is designed for a power Buck converter. This strategy is an advanced version of the Backstepping method utilising Lyapunov stability function to reach a higher stability and a better disturbance rejection behaviour in the practical applications. In addition, to reduce the computational burden and increase ease of implantation, Black‐box technique is considered assuming no accurate mathematical model for the system. Nonetheless, in real‐time environments, disturbances with wider ranges including: supply voltage variation, parametric variation, and noise can negatively impact the operation of this method. To compensate for this problem, the gains of the controller should be tuned again for better adaptability with the working condition. Therefore, to satisfy this need and enhance the controller's performance, a metaheuristic algorithm is applied in the control scheme called Grey Wolf Optimisation (GWO) algorithm. GWO is a well‐behaved nature‐inspired algorithm with faster decision‐making dynamics along with more accuracy over different optimisation algorithms. To better elaborate the merits of this approach, conventional BSM and PSO‐based PID schemes are also designed and tested in different situations.

The displacement tracking performance of the electro-hydraulic servo actuator is critical for hydraulic active suspension control. To tackle the problem of slow time-varying parameters in the existing actuator dynamics model, a nonlinear adaptive back-stepping control (ABC) approach is adopted. Simultaneously, the parameters of the nonlinear ABC are difficult to configure, resulting in a poor control effect. An enhanced particle swarm optimization (PSO) approach integrating crazy particles (CP) and time-varying acceleration coefficients (TVAC) is suggested to optimize the controller settings. Furthermore, in order to obtain satisfactory dynamic characteristics of the transition process, the absolute value of the error time integral performance index is used as the minimum performance index function of parameter selection, and the square term of the control input is added to the performance index function to prevent excessive controller energy. Finally, it can be observed from the simulation results of the highest value emax of the displacement tracking error, the average value eμ of error, and the standard deviation eσ of error that the performance of the ABC parameters optimized by PSO+CP+ATVC is superior to the manually given ABC parameters. Therefore, this control method significantly improves the stability and speed of the control system. It provides a new research idea for the parameter optimization of controllers.

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.

This paper presents a novel algorithm for the design and analysis of an adaptive backstepping controller (ABC) for a microgyroscope. Firstly, Lagrange–Maxwell electromechanical equations are established to derive the dynamic model of a z-axis microgyroscope. Secondly, a nonlinear controller as a backstepping design approach is introduced and deployed in order to drive the trajectory tracking errors to converge to zero with asymptotic stability. Meanwhile, an adaptive estimator is developed and implemented with the backstepping controller to update the value of the parameter estimates in the Lyapunov framework in real-time. In addition, the unknown system parameters including the angular velocity may be estimated online if the persistent excitation (PE) requirement is met. A robust compensator is incorporated in the adaptive backstepping algorithm to suppress the parameter variations and external disturbances. Finally, simulation studies are conducted to prove the validity of the proposed ABC scheme with guaranteed asymptotic stability and excellent tracking performance, as well as consistent parameter estimates in the presence of model uncertainties and disturbances.

A robust Sugeno type adaptive fuzzy neural network (RSAFNN) backstepping control for a two-axis motion control system is proposed in this paper. The adopted two-axis motion control system is composed of two permanent magnet linear synchronous motors (PMLSMs). The single-axis motion dynamics with the introduction of a lumped uncertainty, which includes parameter variations, external disturbances, cross coupled interference between the two PMLSMs and fiction force, is derived first. Then, a backstepping control approach is proposed to compensate the lumped uncertainty occurred in the two-axis motion control system. Moreover, to improve the control performance in the tracking of the reference contours, a RSAFNN backstepping control is proposed where a Sugeno type adaptive fuzzy neural networks (SAFNN) is employed to estimate the lumped uncertainty directly. Furthermore, the proposed control algorithms are implemented in a TMS320C32 DSP-based control computer.