Incremental Backstepping Research Articles

Command-filtered incremental backstepping attitude control of spacecraft with predefined-time stability

This paper investigates the predefined-time attitude tracking control problem within the theoretical framework of incremental dynamic inversion. The utilization of the Taylor series facilitates the transformation of the attitude control system into a discrete-time plant, with the control input expressed in an incremental form. Additionally, a novel predefined-time stable dynamics system is presented and incorporated into the disturbance observer designing process, serving the purpose of estimating lumped disturbance. It is also employed in a command filter design to approximate the derivatives of the virtual control law within a predefined time. Consequently, an incremental backstepping attitude tracking control scheme is further developed, integrating the proposed predefined-time disturbance observer to ensure the system's robustness and the predefined-time filter to address challenges related to “term explosion” and singularity problem. Rigorous Lyapunov analysis affirms that the attitude control system, when using the incremental backstepping controller, remains predefined-time stable. The effectiveness of the proposed control scheme is subsequently validated through numerical simulations.

Incremental Nonlinear Dynamics Inversion and Incremental Backstepping: Experimental Attitude Control of a Tail-Sitter UAV

Incremental control strategies such as Incremental Nonlinear Dynamics Inversion (INDI) and Incremental Backstepping (IBKS) provide undeniable advantages for controlling Uncrewed Aerial Vehicles (UAVs) due to their reduced model dependency and accurate tracking capacities, which is of particular relevance for tail-sitters as these perform complex, hard to model manoeuvres when transitioning to and from aerodynamic flight. In this research article, a quaternion-based form of IBKS is originally deduced and applied to the stabilization of a tail-sitter in vertical flight, which is then implemented in a flight controller and validated in a Hardware-in-the-Loop simulation, which is also made for the INDI controller. Experimental validation with indoor flight tests of both INDI and IBKS controllers follows, evaluating their performance in stabilizing the tail-sitter prototype in vertical flight. Lastly, the tracking results obtained from the experimental trials are analysed, allowing an objective comparison to be drawn between these controllers, evaluating their respective advantages and limitations. From the successfully conducted flight tests, it was found that both incremental solutions are suited to control a tail-sitter in vertical flight, providing accurate tracking capabilities with smooth actuation, and only requiring the actuation model. Furthermore, it was found that the IBKS is significantly more computationally demanding than the INDI, although having a global proof of stability that is of interest in aircraft control.

Adaptive finite-time incremental backstepping fault-tolerant control for flying-wing aircraft with state constraints

This paper proposes an incremental nonlinear fault-tolerant control scheme for flying-wing aircraft subject to state constraints under model uncertainties, external disturbances, and actuator faults. Firstly, the aircraft attitude dynamics system with state constraints is transformed into a free-constrained system by a nonlinear state-dependent function (NSDF), which simplifies the controller design in a direct and concise way. Based on the NSDF, a novel finite-time incremental backstepping (FT-IBS) method is proposed to achieve rapid attitude tracking and reduce the reliance on model knowledge, simultaneously. In this method, a command filter is designed to address the issues of complexity explosion and singularity, and particular stability compensators ensures the closed-loop system to achieve finite-time stability. Then, to overcome the lumped disturbances composed of uncertainties and faults, a new adaptive multivariable finite-time disturbance observer (AMFTDO) is designed for rapid estimation and compensation, and its adaptive strategy ensure high-precision tracking performance under complex time-varying lumped disturbances. Finally, comparative simulation results confirm that the proposed control scheme can achieve faster convergence, higher tracking accuracy, and stronger robustness.

Incremental backstepping for the stratospheric airship control driven by tracking differentiator

This article proposes a control methodology, referred to as the Nonlinear Disturbance Observer-based Incremental Backstepping (NIBS) approach, for the stratospheric airship with model uncertainty and time delay. In particular, a novel tracking differentiator based on the inverse hyperbolic sine function is designed and utilized in a nonlinear disturbance observer to estimate disturbance and sensor noise. The incremental backstepping control theory is further improved, and combined with the proposed nonlinear disturbance observer to overcome the issues of “term explosion” and signal transmission delay, ensuring the system’s robustness. Moreover, the Lyapunov theory is employed to investigate the stability of the NIBS approach. The simulation results validate that the NIBS control strategy can accurately regulate the speed and angular velocity of the stratospheric airship, while effectively mitigating the effects of sensor noise and time delay.

Discrete-Time Incremental Backstepping Control with Extended Kalman Filter for UAVs

In this study, a discrete-time incremental backstepping (DTIBS) controller with an extended Kalman filter (EKF) is proposed for unmanned aerial vehicles (UAVs) with unknown actuator dynamics. The Taylor series and an approximate discrete method are employed, transforming the second-order continuous-time nonlinear system into a discrete-time nonlinear plant with an incremental input form. The incremental control laws are designed using the incremental nonlinear dynamic inversion (INDI) method and the time-delay control (TDC) method. The TDC is introduced to design the control law, eliminating the need for prior knowledge of the control effectiveness matrix involving some unknown aerodynamic coefficients. In addition, the airflow angle and body rotation rate are selected as key system states, and the EKF is used to design a state estimator to estimate the local state of the small unmanned aerial vehicle closed-loop flight control system under strong noise conditions. The effectiveness of the DTIBS control method with EKF is verified through numerical simulation. The results show that the proposed method can effectively estimate the state under the typical noise characteristics of low-cost sensors, and the closed-loop control systems has good tracking performance and can quickly and effectively track sudden commands.

Observer based incremental backstepping terminal sliding-mode control with learning rate for a multi-vectored propeller airship

The problem of finite-time trajectory tracking control for a multivectored propeller airship with model parameter uncertainties and unknown disturbances is addressed in the paper. In order to obtain a fast transient response and finite time convergence without singularity, an incremental backstepping nonsingular terminal sliding mode controller is designed to track desired trajectory within finite time. To overcome the limitation of backstepping terminal sliding-mode control design being dependant on prior knowledge, a nonlinear disturbance-observer is designed to estimate the external observable disturbances. Meanwhile, to reduce system chattering when the tracking error reaches the sliding mode surface, an adaptive learning rate design is proposed for the terminal sliding mode controller such that the tracking error approaches the sliding mode surface at a low speed and so the system chattering is restrained. The closed-loop trajectory tracking control system is proved to be stable and finite time convergence by using Lyapunov theory. The results are compared with traditional backstepping sliding mode control and different learning rate based control design, and they demonstrate the averaged tracking error in altitude and pitch motion is reduced more than 30% by using the disturbance-observer based incremental backstepping terminal sliding mode controller for the multivectored propeller airship to execute a realistic trajectory tracking mission, even in the presence of aerodynamic coefficient uncertainties, unknown disturbances.

Reconfiguration control allocation of actuator faults for tailless aircraft with low aspect ratio

The triaxial attitude control of the tailless aircraft depends heavily on the effectiveness of the actuators. Still, the actuators have redundancy characteristics, cross-coupling of rudder effect, and so on. Therefore, the reconfigurable control allocation of the tailless aircraft under typical actuator faults is deeply studied in this paper. The effectiveness and rationality of the incremental control allocation method based on quadratic programming are thoroughly verified for application to maximize the residual control ability of the aircraft, ensure that the aircraft can still complete the flight mission typically, and guarantee flight safety. According to the research principle of surface failures from slight to severe, three typical rudder surface faults are designed successively: Efficiency loss of single actuator, single actuator stuckness, and double actuators combined stuckness. On this basis, the mechanism of reconfiguration allocation after actuator failures is studied, and the residual control ability of the actuator after loss is fully explored. What’s more, the range of allowable reduction of efficiency of each actuator and the acceptable stuck angle range of each actuator are explored, and the most severe failure in the combination of double actuators stuck is obtained. The attitude controller is designed with incremental backstepping (IBKS). The reconstruction allocation adopts a quadratic programming allocation method based on an effective set solver, which can be seamlessly connected with the IBKS method to improve the control accuracy and disturbance immunity effectively.

Sparse online Gaussian process adaptation for incremental backstepping flight control

Presence of uncertainties caused by unforeseen malfunctions in actuation or measurement systems or changes in aircraft behaviour could lead to aircraft loss-of-control during flight. This paper considers sparse online Gaussian Processes (GP) adaptive augmentation for Incremental Backstepping (IBKS) flight control. IBKS uses angular accelerations and control deflections to reduce the dependency on the aircraft model. However, it requires knowledge of the relationship between inner and outer loops and control effectiveness. Proposed indirect adaptation significantly reduces model dependency. Global uniform ultimate boundness is proved for the resultant GP adaptive IBKS. Conducted research shows that if the input-affine property is violated, e.g., in severe conditions with a combination of multiple failures, the IBKS can lose stability. Meanwhile, the proposed sparse GP-based estimator provides fast online identification and the resultant controller demonstrates improved stability and tracking performance.

Guidance and control for autonomous emergency landing of the rotorcraft using the incremental backstepping controller in 3-dimensional terrain environments

This paper treats the approach to safe emergency landing for an autonomous rotorcraft in 3-dimensional terrain environments. The autorotation flight that the rotorcraft flies without the power supply is dangerous and needs the high-skilled control ability of the pilot. Ordinary, this flight is divided into three phases: Entry, Steady-Descent, and Flare phase. The emergency landing trajectory is generated by imitating each phase. The Trajectory optimization method using the high-fidelity math model is applied to the entry and flare phase to consider the complex dynamics of the rotorcraft. To generate a steady-descent phase trajectory without obstacle collisions, one of the path planning methods, the improved Rapidly-exploring Random Tree algorithm is used. The Incremental Backstepping controller is adopted as the trajectory tracking controller. Simulation is conducted in the One Engine Inoperative condition. Through the simulation, it is shown that the method proposed in this paper guarantees the safe landing of the rotorcraft in an emergency like engine failure.

Incremental Backstepping Sliding-Mode Trajectory Control for Tailless Aircraft with Stability Enhancer

This paper presents an incremental backstepping sliding-mode (IBS) controller for trajectory control of a tailless aircraft with unknown disturbances and model uncertainties. The proposed controller is based on a nonlinear dynamic model of the tailless aircraft. A stability enhancer (SE) that limits both the rate and amplitude of the virtual control input is proposed. The stability enhancer consists of two layers. When the virtual control input approaches the edge, the first layer SE would be activated to modify the trajectory tracking error; when the virtual control input exceeds the edge, the second layer SE would reduce the control gains to make sure the virtual control input drops within the edge as soon as possible. With the help of SE, the incremental control method could be extended to outer-loop control without considering the dynamics of the inner-loop system. In addition, an adaptive estimator for state derivatives is proposed, together with IBS, allowing the controller to show excellent robustness. Finally, two simulations are presented. The first simulation shows that the system is insensitive to external disturbances and model uncertainties, and the effectiveness of SE is proved in the second simulation.

Slip Constrained Torque Controller Using Incremental Backstepping with Integral Barrier Lyapunov Function*

This paper develops a speed controller for a rear-drive electric vehicle. A Barrier Incremental Backstepping strategy is proposed for tracking the desired speed, aiming to increase the robustness of the controller and avoid loss of traction due to excessive longitudinal slip. The solution is evaluated in simulation for different scenarios, showing satisfactory results in constraining the tire slip.

Adaptive incremental sliding mode control for a robot manipulator

An adaptive incremental sliding mode control (AISMC) scheme for a robot manipulator is presented in this paper. Firstly, an incremental backstepping (IBS) controller is designed using time-delay estimation (TDE) to reduce dependence on the mathematical model. After substituting IBS controller into the nonlinear system, a linear system w.r.t. tracking errors is obtained while TDE error is the disturbance. Then, the AISMC scheme, including a nominal controller and an SMC, is developed for the resulted linear system to improve control performance. According to the equivalent control method, the SMC in the AISMC scheme is to handle TDE error. To receive optimal control performance at the sliding manifold, an LQR controller is selected as the nominal controller. The SMC is designed based on positive semi-definite barrier function (PSDBF) since it prevents switching gains from being over/under-estimated, and two practical problems are addressed in this paper: A new PSDBF is designed and conservative (large) setting bounds affecting tracking precision and/or system stability are avoided; An improved PSDBF based SMC is developed where the PSDBF and an adaptive parameter are used simultaneously to regulate switching gains, and the system is still stable when sliding variable occasionally exceeds the predefined vicinity. Moreover, finite-time convergence property of the sliding variable is strictly analyzed. Finally, real-time experiments are conducted to verify the effectiveness of the proposed control method.

Robustness of Incremental Backstepping Flight Controllers: The Boeing 747 Case Study

Incremental control strategies have been proposed recently to reduce the dependence on the aircraft model. However, the technique still requires modeling the actuator effectiveness, which depends on inertial and aerodynamic parameters. Therefore, it is of the utmost importance to analyze the robustness of the strategy regarding these parameters. This work focuses on evaluating the robustness of an incremental backstepping strategy applied for automatic control of a Boeing 747 (B747). A sensitivity analysis is carried out to quantify the impact of inertial parameters and flight condition in the input effectiveness, whose results are used to define scheduling strategies for the incremental controller. A robustness analysis is then performed using a B747 simulator applying different maneuvers in several flight conditions. The flight performance is evaluated according to the military standard MIL-DTL-9490E. Results show that the proposed controller is robust to mismatches in the input effectiveness model, evidencing that even without using a scheduling strategy the controller is able to perform within the requirements specified in the standard.

Trajectory-Tracking Controller Design of Rotorcraft Using an Adaptive Incremental-Backstepping Approach

This paper treats a robust adaptive trajectory-tracking control design for a rotorcraft using a high-fidelity math model subject to model uncertainties. In order to control the nonlinear rotorcraft model which shows strong inter-axis coupling and high nonlinearity, incremental backstepping approach with state-dependent control effectiveness matrix is utilized. Since the incremental backstepping control suffers from performance degradation in the presence of control matrix uncertainties due to change of flight conditions, control system robustness is improved by combining the least squares parameter estimator to estimate time varying uncertainties contained in the control effectiveness matrix. Also, by selecting a suitable gain set by investigating the error dynamics, a uniform trajectory-tracking performance over operational flight envelope of the rotorcraft is ensured without resorting to the conventional gain scheduling method. To evaluate the proposed controller, comparative results between IBSC and Adaptive IBSC are provided in this paper with sequential maneuvers from the ADS-33E-PRF. The proposed method shows improved tracking performance under variations in control effective matrix in the flight simulation. Robust and stable parameter estimation is also guaranteed due to the implementation of the DF-RLS algorithm for the least squares estimator.

Nonlinear Incremental Control for Flexible Aircraft Trajectory Tracking and Load Alleviation

This paper proposes a nonlinear control architecture for flexible aircraft simultaneous trajectory tracking and load alleviation. By exploiting the control redundancy, the gust and maneuver loads are alleviated without degrading the rigid-body command tracking performance. The proposed control architecture contains four cascaded loops: position control, flight path control, attitude control, and optimal multi-objective wing control. Because the position kinematics are not influenced by model uncertainties, the nonlinear dynamic inversion control is applied. On the contrary, the flight path dynamics are perturbed by both model uncertainties and atmospheric disturbances; thus the incremental sliding mode control is adopted. Lyapunov-based analyses show that this method can simultaneously reduce the model dependency and the minimum possible gains of conventional sliding mode control methods. Moreover, the attitude dynamics are in the strict-feedback form; thus the incremental backstepping sliding mode control is implemented. Furthermore, a novel load reference generator is designed to distinguish the necessary loads for performing maneuvers from the excessive loads. The load references are realized by the inner-loop optimal wing controller, whereas the excessive loads are naturalized by flaps without influencing the outer-loop tracking performance. The merits of the proposed control architecture are verified by trajectory tracking tasks in spatial von Kármán turbulence fields.

Observer-based incremental backstepping sliding-mode fault-tolerant control for blended-wing-body aircrafts

This paper presents an adaptive incremental nonlinear backstepping sliding-mode (INBSM) controller, for fault tolerant tracking control of a blended wing body (BWB) aircraft with unknown disturbances and actuator faults. The INBSM controller is based on a nonlinear dynamics model of the BWB aircraft. In addition, a radial basis function neural network disturbance observer (RBF-NNDO) is proposed to enhance the disturbance attenuation ability. A fault estimator is suggested to improve actuator fault tolerant control level. The closed-loop control system of the BWB aircraft is proved to be globally asymptotically stable using Lyapunov theory. Simulations of the combined NNDO-INBSM controller are presented and compared with both the INBSM design and an adaptive fuzzy controller. The results demonstrate an improved capability of the NNDO-INBSM control for the BWB aircraft to execute realistic attitude tracking missions, even in the presence of center of gravity movement, unknown disturbances, model uncertainties and actuator faults.

Integration of path planning, trajectory generation and trajectory tracking control for aircraft mission autonomy

Integrating multiple features for autonomous flight of aircraft requires extensive research over wide categories, high-level of know-how, and experiences. To contribute to these issues, this paper treats the realizable integration techniques of the path planning, trajectory generation, and trajectory-tracking control for the mission autonomy of the aircraft. A collision-free path over the three-dimensional digital terrain is efficiently generated using the P-RRT* algorithm and optimized using the line-of-sight path optimizer proposed in this paper. After additional waypoints are inserted into the planned straight-line path segments, a flyable trajectory for the position and heading angle can be built using the spline trajectory generator with reference to the prescribed velocity distribution. Finally, the incremental backstepping-control design has been adopted to provide accurate trajectory-tracking control. The paper addresses in detail the underlying rationales of the present selection of each technique from the realizability point of view. The integrated designs are validated through simulation studies for a series of autonomous mission scenarios of the rotorcraft. The results show that the P-RRT* algorithm combined with the line-of-sight path optimizer can provide a fast and efficient solution for path planning. Also, the extremely accurate trajectory-tracking performance has been achieved by applying the incremental backstepping control to the flyable trajectory obtained using the spline trajectory generator.

Adaptive Trajectory Tracking Control for Rotorcraft Using Incremental Backstepping Sliding Mode Control Strategy

This paper investigates the adaptive incremental backstepping sliding mode control for the rotorcraft trajectory-tracking control problem to enhance the robustness to the matched uncertainty in the model. First, the incremental dynamics is used for the control design to exclude the adverse effect of the mismatched model uncertainties on the trajectory-tracking performance. Secondly, the sliding-mode control strategy is adopted in the second design stage of the backstepping controller, and the effect of switching gains on the controller robustness is thoroughly studied using the rotorcraft model with different levels of the matched uncertainties. To clarify the robustness enhancement using the adaptive selection of switching gains, this paper chooses three different control structures consisting of the traditional backstepping control and two backstepping sliding mode controls with the fixed or adaptively adjusted switching gains. These control designs are applied to the trajectory-tracking control for the helical-turn maneuver of the Bo-105 helicopter to compare their relative robustness to the matched uncertainties. The results prove that adaptive incremental backstepping sliding mode control shows much higher robustness than other two designs, and the controller even with the fixed switching gains can be used to improve the robustness of the pure backstepping control design. Therefore, the present adaptive incremental backstepping sliding mode control is effectively applicable with the rotorcraft model which typically contains many different sources of both matched and mismatched uncertainties.

Understandings of incremental backstepping controller considering measurement delay with model uncertainty

In this paper, closed loop characteristics with an incremental backstepping (IBKS) controller are investigated with consideration of measurement delays and model uncertainties. To judge absolute stability of the system, a systematic analysis framework is proposed which examines the existence of unstable poles from a derived characteristic equation with high nonlinearity due to the considered measurement delays. One of the key findings from the analysis results is that the system is stable only when a specific relationship between the measurement delays is satisfied and this stability condition is affected by the model uncertainty. Critical understandings about individual and integrated effects of the measurement delays and the model uncertainties to the system are suggested through a comparative study. Verification and validation of the obtained properties from the framework are performed through simulations.

Flying qualities evaluation based nonlinear flight control law design method for aircraft

This paper is focused on the parameter tuning problem for the design of nonlinear flight controllers. Taking into account the preferences and requirements of the pilot, a novel flying qualities evaluation framework and a tuning method are proposed for the design of nonlinear flight controllers. Considering that the existing flying qualities criteria are not applicable to evaluating the closed-loop aircraft system, a novel evaluation framework consisting of three modules namely ideal reference model, controller and aircraft model, is proposed. Based on this evaluation framework, an overall evaluation model is established, the flying qualities based rating scores for this model will reflect the level of the controller performance. Subsequently, a schematic evaluation method, consisting of three sub-procedures namely linearization, low-order equivalent fitting and flying qualities criteria based rating, is proposed for the controller design. To validate the evaluation framework and the method, a nonlinear F/A-18 aircraft model and the incremental backstepping control law are chosen to build a demonstration example. Theoretical analysis and the simulation results reveal that the proposed evaluation framework and schematic method are effective for the design of nonlinear flight control laws.