Backstepping Control Technique Research Articles

Backstepping and dynamic inversion control techniques for automatic landing of fixed wing unmanned aerial vehicles

The landing control of the unmanned aerial vehicles is a very difficult task having in mind both the external disturbances and their strong nonlinear dynamics with channel interferences. Motivated by this fact, this paper deals with the design of a novel automatic landing system (ALS) for a tailless and fixed blended wing unmanned aerial vehicle (UAV) having mobile centre of mass. By using the backstepping and the dynamic inversion control techniques, a novel auto-landing system is designed and software validated to control the aircraft during all the three landing phases (final approach, glide slope phase, flare) and handle the external disturbances such as the atmospheric turbulences and the errors of the measurement sensors. The dynamics of the aircraft involves the interconnection between the motions in the longitudinal and lateral-directional planes in contrast to other works where the dynamics has been separately linearized before developing of the control laws. The auto-landing system consists of two controllers (for the attitude angles and the forward speed of the UAV), an adaptive observer (for the estimation of the atmospheric turbulences), four reference models (to obtain the desired attitude angles and forward speed). This novel control architecture also uses the desired landing geometry and the operating conditions associated to a default trajectory defined by means of the calculated attitude angles and velocity of the UAV. The first controller (based on the backstepping control technique) provides the deflections of the three control surfaces, while the second one (based on the dynamic inversion technique) provides the throttle command to maintain a constant airspeed. The deviation of the UAV from the runway is cancelled and the desired landing trajectory is followed accurately. The results of the numerical simulations show the fulfilment of all the control objectives, including here the steady and the transient performances of the tracking errors, as well as the robustness relative to the atmospheric turbulences, the errors of the measurement sensors, and the motion of the mass centre.

Trajectory Tracking and Stabilization of Nonholonomic Wheeled Mobile Robot Using Recursive Integral Backstepping Control

In this paper, a generalized nontriangular normal form is presented to facilitate designing a recursive integral backstepping control for the class of underactuated nonholonomic systems, i.e., wheeled mobile robots (WMRs) that perform posture stabilization and trajectory tracking in environments without obstacles. Based on the differential geometry theory, we develop a multiple input multiple output (MINO) generalization of normal form using the input-output feedback linearization technique. Then, the change of variables (diffeomorphism) transform the state-space model of WMR, incorporating both kinematic and dynamic models into nontriangular normal form. As a result, the system dynamics can be represented as internal and external dynamics. The nonlinear internal dynamics of WMR pose serious challenges to design a suitable controller due to its internal dynamics being not minimum phase and non-strict feedback form structure. The proposed backstepping controller is designed in two steps. First, a standard integral backstepping controller is designed to stabilize the robot’s orientation angle. Then, a recursive integral backstepping control technique is applied to achieve asymptotic convergence of position error to zero. Hence, both asymptotic posture stabilization and trajectory tracking are achieved in semi-global regions, except the nonzero initial condition of the orientation angle. The asymptotic stability of the entire closed-loop system is shown using the Lyapunov criteria.

Containment control of non-affine multi-agent systems based on given precision

This paper concentrates on a containment control issue for multi-agent systems in non-affine form with a given accuracy. In comparison with the existing studies on multi-agent systems, precision-based containment control idea is first formulated. With the aid of the proposed strategy, the main merit of this note is that the synchronization errors converge to arbitrary given positive number. Simultaneously, the particular Layapunov functions are constructed by feat of two auxiliary functions. By employing the backstepping and adaptive control technique, the key variables and the actual controller are designed. Unlike the traditional stability analysis, a novel method is used to analyse the convergence of containment errors. In the end, some simulation results demonstrate the correctness for the proposed protocol.

PID tuning approaches for quadrotors unmanned aerial vehicles

In this paper, a comparative study between different PID tunning techniques is presented. The proposed techniques are applied to solve the formation configuration problem for a cooperative team of unmanned vehicles. The formation problem for the cooperative team is divided into two levels of control, one is the backstepping control technique for the stabilization of the team members positions as a higher controller. Simultaneously, PID controller receives the desired position to stabilize the attitude control as a lower controller to track the desired planning trajectories. The main contribution of this paper is the comparison between the different control approaches in tunning the PID gains to stabilize attitude control for the leader quadrotor. Simulation results present the assessment of the proposed PID control technique compared with different PID tuning approaches such as local optimal control, fraction order, Ziegler-Nichols and genetic algorithm. Moreover, disturbance rejection and white noise attenuation criterions are inspected to evaluate the ability of the proposed controllers to preserve the stability of the system.

Performance Investigations of an Improved Backstepping Operational space Position Tracking Control of a Mobile Manipulator

This article implies an improved backstepping control technique for the operational-space position tracking of a kinematically redundant mobile manipulator. The mobile manipulator thought-out for the analysis has a vehicle base with four mecanum wheels and a serial manipulator arm with three rotary actuated joints. The recommended motion controller provides a safeguard against the system dynamic variations owing to the parameter uncertainties, unmodelled system dynamics and unknown exterior disturbances. The Lyapunov’s direct method assists in designing and authenticating the system’s closed-loop stability and tracking ability of the suggested control strategy. The feasibility, effectiveness and robustness of the recommended controller are demonstrated and investigated numerically with the help of computer based simulations. The mathematical model used for the computer-based simulations is derived based on a real-time mobile manipulator and the derived model is further verified with an inbuilt gazebo model in a robot operating system (ROS) environment. In addition, the proposed scheme is verified on an in-house fabricated mobile manipulator system. Further, the recommended controller performance is correlated with the conventional backstepping control design in both computer-based simulations and in real-time experiments.

Robust model reference adaptive backstepping sliding-mode control for quadrotor attitude with disturbance observer

Purpose 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. Design/methodology/approach 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. Findings 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. Practical implications 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. Originality/value 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.

Decentralised adaptive tracking control for the interconnected nonlinear systems with asymmetric full state dynamic constraints

This paper studies the decentralised adaptive tracking control problem for the interconnected nonlinear systems with asymmetric full state dynamic constraints and input quantisation using dynamic event triggering mechanism. The broad learning system (BLS) is firstly utilised to identify the unstructured uncertainties, and a BLS-based nonlinear observer is established to estimate the unmeasurable states. Then, a unified barrier function (UBF) is constructed to address the asymmetric full state dynamic constraints. Next, both of command-filtered backstepping control technique and dynamic event triggering mechanism are adopted to design the control scheme in the asymmetric full state dynamic constraints case. The proposed control scheme could guarantee that all signals of the closed-loop systems are semi-globally ultimately uniformly bounded (SGUUB), the tracking errors converge to the bounded compact set and the full states dynamic constraints are not violated. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.

Indirect power control of DFIG based on wind turbine operating in MPPT using backstepping approach

This paper describes a MPPT control of the stator powers of a DFIG operating within a wind energy system using the backstepping control technique. The objective of this work consists of providing a robust control to the rotor-side converter allowing the stator active power to be regulated at the maximum power extracted from the wind turbine, as well as maintaining the stator reactive power at zero to maintain the power factor at unity, under various conditions. We have used the Matlab/Simulink platform to model the wind system based on a 7.5 kW DFIG and to implement the MPPT control algorithm in a first step, then we have implemented the field-oriented control and the backstepping controller in a second step. The simulation results obtained were very satisfactory with a fast transient response and neglected power ripples. They furthermore confirmed the high robustness of the approach used in dealing with the variation of the internal parameters of the machine.

Adjustable impact-time-control guidance law against non-maneuvering target under limited field of view

This article proposes an impact-time-control guidance law that can keep a non-maneuvering moving target in the seeker’s field of view (FOV). For a moving target, the missile calculates a predicted intercept point (PIP), designates the PIP as a new virtual stationary target, and flies to the PIP at the desired impact time. The main contribution of the article is that the guidance law is designed to always lock onto the moving target by adjusting the guidance gain. The guidance law for the purpose is based on the backstepping control technique and designed to regulate the defined impact time error. In this procedure, the desired look angle, which is a virtual control, is designed not to violate the FOV limit, and the actual look angle of the missile is kept within the FOV by tracking the desired look angle. To validate the performance of the guidance law, numerical simulation is conducted with different impact times. The result shows that the proposed guidance law intercepts the moving target at the desired impact time maintaining the target lock-on condition.

Study of Nonlinear Control Techniques

In this expository paper, the studies related to nonlinear control theory has been done by referring to most of the papers ever written on nonlinear control. In recent years, control techniques which are mainly based on nonlinear process models have received much research attention and miscellaneous amount of research have been carried out in this field. The paper reviews NL control techniques such as feedback linearization (FL), sliding mode control (SMC) and backstepping control technique. Pros and cons related to these techniques have also been discussed and a recently proposed technique i.e., backstepping sliding mode is also taken into consideration. Robustness of the designed controller is the important issue while designing the controller to stabilize NL-system. This paper also presents the basic idea of nonlinearities which could be present in NL-systems along with introductory description of lyapunov stability issues. An informatory comparison chart is figured out projecting various issues along with the area of application of nonlinear control techniques.

Nonlinear Control of Hydrostatic Thrust Bearing Using Multivariable Optimization

This research work is focused on the nonlinear modeling and control of a hydrostatic thrust bearing. In the proposed work, a mathematical model is formulated for a hydrostatic thrust bearing system that includes the effects of uncertainties, unmodelled dynamics, and nonlinearities. Depending on the type of inputs, the mathematical model is divided into three subsystems. Each subsystem has the same output, i.e., fluid film thickness with different types of input, i.e., viscosity, supply pressure, and recess pressure. An extended state observer is proposed to estimate the unavailable states. A backstepping control technique is presented to achieve the desired tracking performance and stabilize the closed-loop dynamics. The proposed control technique is based on the Lyapunov stability theorem. Moreover, particle swarm optimization is used to search for the best tuning parameters for the backstepping controller and extended state observer. The effectiveness of the proposed method is verified using numerical simulations.

Electrical control strategy for an ocean energy conversion system

Globally abundant wave energy for power generation attracts ever increasing attention. Because of non-linear dynamics and potential uncertainties in ocean energy conversion systems, generation productivity needs to be increased by applying robust control algorithms. This paper focuses on control strategies for a small ocean energy conversion system based on a direct driven permanent magnet synchronous generator (PMSG). It evaluates the performance of two kinds of control strategies, i.e., traditional field-oriented control (FOC) and robust adaptive control. The proposed adaptive control successfully achieves maximum velocity and stable power production, with reduced speed tracking error and system response time. The adaptive control also guarantees global system stability and its superiority over FOC by using a non-linear back-stepping control technique offering a better optimization solution. The robustness of the ocean energy conversion system is further enhanced by investigating the Lyapunov method and the use of a DC-DC boost converter. To overcome system complexity, turbine-generator based power take-off (PTO) is considered. A Matlab/Simulink study verifies the advantages of a non-linear control strategy for an Oscillating Water Column (OWC) based power generation system.

Robust adaptive backstepping INTSM control for robotic manipulators based on ELM

This paper investigates a novel control algorithm to deal with trajectory tracking control problems of robotic manipulators based on adaptive backstepping integral nonsingular terminal sliding mode control (BINTSMC). The proposed approach is developed based on an integration between the integral nonsingular terminal sliding mode control (INTSMC) and stability analysis procedure of backstepping control technique. In addition, the extreme learning machine (ELM) learning algorithm is introduced to approximate lumped uncertain component of the dynamics model. The approximated lumped uncertain terms are transmitted to rebuild the dynamics and provide a compensation feedback for control systems. Moreover, the robust term is utilized to counteract the approximation residual error, wherein the nonconstant ELM approximation error is analyzed. The superior performance of the BINTSMC is validated by comparing conventional NTSMC in the simulations.

Adaptive backstepping robust tracking control for stabilizing lateral dynamics of electric vehicles with uncertain parameters and external disturbances

This paper presents a composite adaptive backstepping robust tracking controller which aims to improve the lateral dynamics stability for an electric vehicle (EV) while considering the uncertain parameters and external disturbances. First, a nonlinear three degree-of-freedom vehicle model is built up to describe the lateral and roll dynamics behaviors of this EV. Then, the projection adaptive control law is developed by combining adaptive backstepping and dynamic surface control techniques, which is expected to make the sideslip angle and the yaw rate approaching the ideal ones as closely as possible. The sufficient conditions for designing such a controller are also derived in the framework of Lyapunov theory to guarantee its asymptotical stability, thus the desirable controller design is devised. Finally, a comparative CarSim–Simulink joint simulation is carried out to verify the effectiveness of the proposed controller under single-lane-change and J-turn maneuvers.

Observer-Based Adaptive Event-Triggered Control for Nonstrict-Feedback Nonlinear Systems With Output Constraint and Actuator Failures

An observer-based adaptive dynamic surface control (DSC) strategy is proposed for nonlinear nonstrict-feedback systems with time-varying disturbance, event-triggered mechanism, and actuator failures in this paper. Fuzzy logic systems are implemented to construct an observer to estimate the unmeasured states. The DSC method is exploited to solve the issue of “explosion of complexity” with the backstepping control technique. The constructed event-triggered mechanism can avoid the waste of communication resources. The barrier Lyapunov functions are utilized to address the problem of output constraint. It is demonstrated that the reference signals can be well tracked by the system output and all closed-loop signals remain semi-globally uniformly ultimately bounded. Two examples illustrate the effectiveness of the constructed controller.

Fault-Tolerant Formation Tracking Control for Heterogeneous Multiagent Systems with Directed Topology

In this paper, the adaptive fault-tolerant formation tracking control problem for a set of heterogeneous unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) systems with actuator loss of effectiveness faults is investigated. The cooperative fault-tolerant formation control strategy for UAV and UGV collaborative systems is classified into the altitude consensus control scheme for follower UAVs and the position cooperative formation control scheme for all followers. The altitude consensus control algorithm is designed by utilizing backstepping control technique to drive all UAVs to a desired predefined height. Then, based on synchronization formation error information, the position cooperative formation control algorithm is proposed for all followers to reach the expected position and perform the desired formation configuration. The adaptive fault estimation term is adopted in the designed fault-tolerant formation control algorithm to compensate for the actuator loss of effectiveness fault. Finally, a simulation example is proposed to reveal the validity of the designed cooperative formation tracking control scheme.

A combined backstepping and adaptive fuzzy PID approach for trajectory tracking of autonomous mobile robots

A combined backstepping and adaptive fuzzy PID approach for a nonholonomic autonomous mobile robot to follow the desired path is proposed in this paper. Two adaptive fuzzy PID controllers are adopted at the dynamic control level for velocity tracking and steering control of the robot. The fuzzy PID controller consists of a PID controller which is designed by a trial-and-error approach, optimized using the cross-entropy method, and a fuzzy controller based on relational models with two inputs and three outputs. Adaptive adjustment of the PID controllers is implemented by means of the fuzzy controllers. The pose deviations of the robot when trajectory tracking will be eliminated by the backstepping control technique at the kinematic level using a kinematic model. The simulation validation results demonstrate that the proposed control system can offer good performances for the robot in terms of small distance error, rapid response, high stability, and trajectory tracking more accuracy.

Adaptive Fuzzy Cooperative Control for Nonlinear Multiagent Systems with Unknown Control Coefficient and Actuator Fault

In this paper, an adaptive fuzzy containment condtrol is considered for nonlinear multiagent systems, in which it contains the unknown control coefficient and actuator fault. The uncertain nonlinear function has been approximated by fuzzy logic system (FLS). The unknown control coefficient and the remaining control rate of actuator fault can be solved by introducing a Nussbaum function. In order to avoid the repeated differentiations of the virtual controllers, first-order filters are added to the traditional backstepping control method. By designing the maximum norm of ideal adaptive parameters, only one adaptive parameter needs to be adjusted online for each agent itself. An adaptive fuzzy containment controller is constructed through the backstepping control technique and compensating signals. It is demonstrated that all the signals in nonlinear multiagent systems are bounded by designing adaptive fuzzy containment controller, and all followers can converge to the convex hull built by the leaders. The simulation studies can further confirm the effectiveness of the proposed control method in this paper.

Adaptive fuzzy containment control for nonlinear multi-agent systems with input delay

This paper focuses on a problem of adaptive fuzzy containment control for nonlinear multi-agent systems with input delay. Through the Pade approximation and intermediate variable, the positive constant delays of nonlinear systems inputs are transferred to the coefficients of the next dynamic equation. The phenomenon of “complexity explosion” in traditional backstepping control technique is avoided by introducing first-order filters, in which a new variable replaces the derivative of the virtual controller. In addition, fuzzy logic systems (FLSs) are used to approximate the unknown nonlinear functions of nonlinear multi-agent systems. No matter what the order of the nonlinear multi-agent systems is, only two adaptive laws need to be designed in the adaptive fuzzy containment controller design process for each follower. Using the proposed control method, all followers can converge to the convex hull established by the leaders, and the closed-loop system is stable. The simulation results can further illustrate the effectiveness of the proposed control method.

Adaptive constraint control for nonlinear multi-agent systems with undirected graphs

<abstract><p>This paper investigates the problem of adaptive distributed consensus control for stochastic multi-agent systems (MASs) with full state constraints. By utilizing adaptive backstepping control technique and barrier Lyapunov function (BLF), an adaptive distributed consensus constraint control method is proposed. The developed control method can ensure that all signals of the controlled system are semi-globally uniformly ultimately bounded (SGUUB) in probability, and outputs of the follower agents keep consensus with the output of leader. In addition, system states are not transgressed their constrained sets. Finally, simulation results are provided to illustrate the feasibility of the developed control algorithm and theorem.</p></abstract>