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This paper aims to describe the 2D meshless local boundary integral equation (LBIE) method for solving the Navier–Stokes equations.

The velocity–vorticity formulation is selected to eliminate the pressure gradient of the equations. The local integral representations of flow kinematics and transport kinetics are derived. The integral equations are discretized using the local RBF interpolation of velocities and vorticities, while the unknown fluxes are kept as independent variables. The resulting volume integrals are computed using the general radial transformation algorithm.

The efficiency and accuracy of the method are illustrated with several examples chosen from reference problems in computational fluid dynamics.

The meshless LBIE method is applied to the 2D Navier–Stokes equations. No derivatives of interpolation functions are used in the formulation, rendering the present method a robust numerical scheme for the solution of fluid flow problems.

The hydrodynamic and thermal characteristics of the turbulent boundary layer developed on a porous wall with heat transfer and various angles of transpiration are analyzed numerically with the proper boundary conditions. The wall functions of the viscous and turbulent sub‐layers for velocity and temperature are modified to allow for the effect of the angle of injection and suction through the porous wall. The finite difference method based on a control volume approach is used for solving the time averaged Navier‐Stokes equations for incompressible flow in conjunction with the standard k‐ε turbulence model equations. A non‐uniform staggered grid arrangement is used. The parameters studied include the suction and injection velocity (V_w) and the angle (α) of the injection and suction. The present numerical results of the normal injection and suction are compared with a known experimental data and a good agreement is obtained. The numerical results also indicate that the characteristics of the turbulent boundary layer such as local friction coefficient and thermal boundary layer thickness are substantially influenced by the velocity and the angle of transpiration.

In the present study, the characteristics of the turbulent boundary layer developing on a porous wall with various angles of injection and suction are analyzed numerically with the proper boundary conditions. The finite difference method based on a control volume approach is used for solving the time averaged Navier‐Stokes equations for incompressible flow in conjunction with the standard k‐ε turbulence model equations. The wall functions of the viscous and turbulent sub‐layers are modified to allow for the effect of the angle of injection and suction through the porous wall. A non‐uniform staggered grid arrangement is used. The parameters studied include the velocity (V_w) and the angle (α) of the injection and suction. The present numerical results of the normal injection and suction are compared with the known experimental data and a good agreement is obtained. The numerical results also indicate that the characteristics of the turbulent boundary layer such as local friction coefficient, boundary layer thickness and shape factor are substantially influenced by the velocity and the angle of injection and suction.

This study aims to realize the constant force grinding of automobile wheel hub.

A force control strategy of backstepping + proportion integration differentiation (PID) is proposed. The grinding end effector is installed on the flange of the robot. The robot controls the position and posture of the grinding end actuator and the grinding end actuator controls the grinding force output. First, the modeling and analysis of the grinding end effector are carried out, and then the backstepping + PID method is adopted to control the grinding end effector to track the expected grinding force. Finally, the feasibility of the proposed method is verified by simulation and experiment.

The simulation and experimental results show that the backstepping + PID strategy can track the expected force quickly, and improve the dynamic response performance of the system and the quality of grinding and polishing of automobile wheel hub.

The mathematical model is based on the pneumatic system and ideal gas, and ignores the influence of friction in the working process of the cylinder, so the mathematical model proposed in this study has certain limitations. A new control strategy is proposed, which is not only used to control the grinding force of automobile wheels, but also promotes the development of industrial control.

The automatic constant force grinding of automobile wheel hub is realized, and the manpower is liberated.

First, the modeling and analysis of the grinding end effector are carried out, and then the backstepping + PID method is adopted to control the grinding end effector to track the expected grinding force. The nonlinear model of the system is controlled by backstepping method, and in the process, the linear system composed of errors is obtained, and then the linear system is controlled by PID to realize the combination of backstepping and PID control.

This paper aims to present a control method to realize the constant force grinding of automobile wheel hub.

A constant force control strategy combined by extended state observer (ESO) and backstepping control is proposed. ESO is used to estimate the total disturbance to improve the anti-interference and stability of the system and Backstepping control is used to improve the response speed of the system.

The simulation and grinding experimental results show that, compared with the proportional integral differential control and active disturbance rejection control, the designed controller can improve the dynamic response performance and anti-interference ability of the system and can quickly track the expected force and improve the grinding quality of the hub surface.

The main contribution of this paper lies in the proposed of a new constant force control strategy, which significantly improved the stability and precision of grinding force.

This 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.

To 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.

An 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.

Few 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.

Considering the response lag and viscous slip oscillation of the system caused by cylinder piston friction during automatic polishing of aero-engine blades by a robotic pneumatic end-effector, the purpose of this study is to propose a constant force control method with adaptive friction compensation.

First, the mathematical model of the pneumatic end-effector is established based on the continuous LuGre model, and the static parameters of the LuGre model are identified to verify the necessity of friction compensation. Second, aiming at the problems of difficult identification of dynamic parameters and unmeasurable internal states in the LuGre model, the parameter adaptive law and friction state observer are designed to estimate these parameters online. Finally, an adaptive friction compensation backstepping controller is designed to improve the response speed and polishing force control accuracy of the system.

Simulation and experimental results show that, compared with proportion integration differentiation, extended state observer-based active disturbance rejection controller and integral sliding mode controller, the proposed method can quickly and effectively suppress the polishing force fluctuation caused by nonlinear friction and significantly improve the blade quality.

The pneumatic force control method combining backstepping control with the friction adaptive compensation based on LuGre friction model is studied, which effectively suppresses the fluctuation of normal polishing force.

This paper aims to investigate the problem of finite-time consensus tracking control without unwinding for formation flying spacecraft in the presence of external disturbances.

Two distributed finite-time controllers are developed using the backstepping sliding mode. The first robust controller can compensate for external disturbances with known bounds, and the second one can compensate for external disturbances with unknown bounds.

Because the controllers are designed on the basis of rotation matrix, which represents the set of attitudes both globally and uniquely, the system can overcome the drawback of unwinding, which results in extra fuel consumption. Through introducing a novel virtual angular velocity, exchange of control signals between neighboring spacecraft becomes unnecessary, and it is able to reduce the communication burden.

The two robust controllers can deal with unwinding that may result in fuel consumption by traveling a long distance before returning to a desired attitude when the closed-loop system is close to the desired attitude equilibrium.

Two finite-time controllers without unwinding are proposed for formation flying spacecraft by using backstepping sliding mode. Furthermore, exchange of control signals between neighboring spacecraft is unnecessary.

Quadrotor micro aerial vehicle (MAV) is nonlinear and under actuated plant, and it is difficult to obtain an accurate mathematical model for quadrotor MAV due to uncertainties. The purpose of this paper is to propose one robust control strategy for quadrotor MAV to accommodate system uncertainties, variations, and external disturbances.

The robust control strategy is composed of two self‐organizing interval type‐II fuzzy neural networks (SOIT‐IIFNNs) and one PD controller: the PD controller is adopted to control the attitude and position; one of the SOIT‐IIFNNs is designed to learn the inverse model of quadrotor MAV online; the other SOIT‐IIFNNs is the copy of the former one to compensate for model errors, system uncertainties and external disturbances, both structure and parameters of SOIT‐IIFNNs are tuned online at the same time, and then the stability of the resulting quadrotor MAV closed‐loop control system is proved using Lyapunov stability theory.

The validity of the proposed control method has been verified through real‐time experiments. The experimental results show that the performance of SOIT‐IIFNNs is significantly improved compared with Backstepping‐based controller.

This approach has been used in quadrotor MAV, the controller works well, and it could guarantee quadrotor MAV control system with good performances under uncertainties, variations, and external disturbances.

The proposed SOIT‐IIFNNs controller is interesting for the design of an intelligent control scheme. The main contributions of this paper are: the overall closed‐loop control system is globally stable, demonstrated by Lyapunov stable theory; the tracking error can be asymptotically attenuated to a desired small level around zero by appropriate chosen parameters and learning rates; and the quadrotor MAV control system based on SOIT‐IIFNNs controller can achieve favorable tracking performance.

The purpose of this research paper is to design a disturbance observer-based control based on the robust model reference adaptive backstepping sliding-mode control for attitude quadrotor model subject to uncertainties and disturbances.

To estimate and reject the disturbance, a disturbance observer is designed for the exogenous disturbances with perturbation while a control criterion is developed for the tracking of desired output. To achieve the control performance, backstepping and sliding-mode control techniques are patched together to obtain robust chattering-free controller. Furthermore, a model reference adaptive control criterion is also combined with the design of robust control for the estimation and rejection of uncertainties and unmodeled dynamics of the attitude quadrotor.

The findings of this research work includes the design of a disturbance observer-based control for uncertain attitude quadrotor system with the ability of achieving tracking control objective in the presence of nonlinear exogenous disturbance with and without perturbation.

In practice, the quadrotor flight is opposed by different kinds of the disturbances. In addition, being an underactuated system, it is difficult to obtain an accurate mathematical model of quadrotor for the control design. Thus, a quadrotor model with uncertainties and disturbances is inevitable. Hence, it is necessary to design a control system with the ability to achieve the control objectives in the presence of uncertainties and disturbances.

Designing the control methods for quadrotor control without uncertainties and disturbances is a common practice. However, investigating the uncertain quadrotor plant in the presence of nonlinear disturbances is rarely taken into consideration for the control design. Hence, this paper presents a control algorithm to address the issues of the uncertainties and disturbances as well as investigate a control algorithm to achieve tracking performance.