Nonlinear Dynamic Inversion Research Articles

Neural-Network-Based Incremental Backstepping Sliding Mode Control for Flying-Wing Aircraft

The nonlinear trajectory tracking control problem is studied for a flying-wing aircraft. Starting from a nonlinear dynamics model of the flying-wing aircraft, the trajectory tracking control is decomposed into multiple loops of position control, flight path control, and attitude control. An incremental backstepping sliding mode control is proposed to implement attitude control, while an incremental nonlinear dynamic inversion and a nonlinear dynamic inversion design are used to deal with the nonlinear system model for the flight path and position control, respectively. In addition, a radial basis function neural-network-based extended state disturbance observer is proposed to deal with model uncertainties, gust disturbances, and unknown faults of the aircraft. The closed-loop control system is proved to be stable using Lyapunov theory. The performance of the proposed disturbance-observer-based incremental backstepping sliding mode control is demonstrated in simulation through a set of three-dimensional tracking scenarios. Compared with both backstepping control and backstepping sliding mode control, tracking performance measured by settling time, tracking error, and overshoot are improved by the proposed design when realistic trajectory tracking missions are executed.

Full Envelope Control of Over-Actuated Fixed-Wing Vectored Thrust eVTOL

A novel full-envelope controller for an over-actuated fixed-wing vectored thrust eVTOL aircraft is presented. It proposes a generic control architecture, which is applicable to piloted, semi-automatic, and fully automated flight, consisting of an aircraft-level controller (high-level controller) and a control allocation scheme. The aircraft-level controller consists of a main inner loop classical nonlinear dynamic inversion controller and an outer loop proportional–integral linear controller. The inner loop nonlinear dynamic inversion controller is a velocity controller that cancels the nonlinear bare airframe dynamics, while the outer loop proportional–integral linear controller is an attitude and navigation position controller. Together, they are used for hover/low-speed control and forward flight. The control allocation scheme uses a novel architecture, which transfers the nonlinearity in the vectored thrust effector model formulation to the computation of the actuator limits by converting the effector model from polar to rectangular form, thus allowing the use of classical control allocation linear optimisation technique. The linear optimisation technique is an active set linear quadratic programming constrained optimisation algorithm with a weighted least squares formulation. The control allocation allocates the overall control demand (virtual controls) to individual redundant effectors while performing control error minimisation, control channel prioritisation and control effort minimisation. Simulation results show the transition from hover to cruise, climb and descent, and coordinated turn clearly demonstrate that the controller can handle actuator saturation (position or rate).

Incremental Nonlinear Dynamics Inversion Control with Nonlinear Disturbance Observer Augmentation for Flight Dynamics

A flight controller formulation based on incremental nonlinear dynamics inversion (INDI) control with nonlinear disturbance observer (NDO) is proposed. INDI control is a nonlinear controller based on incremental dynamics. Aimed to attain robustness for nonlinear dynamics inversion (NDI)-based controller, incremental dynamics are derived using the first-order Talyor series expansion to nonlinear systems. The incremental dynamics-based controller requires information on state derivative terms to strengthen the robustness property of the nonlinear controller. The proposed controller utilizes the first-order low-pass filter to obtain the state derivative estimate to implement incremental dynamics into the system. Because the incremental form creates uncertainty term which is an aftermath of the Taylor series expansion, the proposed controller adopts the NDO to eliminate this effect. The controller is applied to the generic transport model which was developed by NASA for simulation purposes. The proposed NDO-based INDI control underwent simulations, together with an INDI controller without disturbance observer, and showed that the developed method results in better performances, providing important advantages where it compensates the uncertainties, removes the steady-state error, and shows less oscillating longitudinal body rate response than the baseline controller, desirable for aerodynamics applications with faster system response.

Modeling and Transition Flight Control of Distributed Propulsion–Wing VTOL UAV with Induced Wing Configuration

The integration of propulsion and wing in distributed propulsion–wing UAVs (DPW UAVs) introduces significant propulsion-aerodynamic coupling, complicating dynamic modeling and flight control. This complexity is heightened by using induced wing surfaces for vertical takeoff and landing, requiring controllers to adapt to configuration changes and disturbances during transition flight. This paper develops a propulsion-aerodynamic coupling model for a medium-sized DPW UAV with induced wings (DPW-IW), enabling real-time aerodynamic performance calculations. Furthermore, a unified flight-control framework is proposed to avoid controller scheduling and switching during flight mode transitions. The proposed control framework employs the time-scale separation principle, divided into an outer loop and an inner loop. The outer loop uses a fuzzy controller to adjust allocation parameters, while the inner loop applies incremental nonlinear dynamic inversion (INDI) and control allocation (INCA) methods, providing robustness to nonlinear changes during flight transitions. Finally, simulations under various conditions demonstrate the controller’s effectiveness in ensuring smooth and robust transitions.

Linear Disturbance Observer-Enhanced Continuous-Time Predictive Control for Straight-Line Path-Following Control of Small Unmanned Aerial Vehicles

This paper studies the straight-line path-following problem on the lateral plane for fixed-wing unmanned aerial vehicles (FWUAVs) which are susceptible to uncertainties. Firstly, based on the natural frame’s location on the prescribed reference paths, the command yaw angle (which is the basis for yaw angle control system design) is solved analytically by combining it with the errors of path following, attack angle, sideslip angle, attitude angles, and geometric parameters of the prescribed reference paths. Secondly, by considering complicated dynamic characteristics, a linear extended state observer is designed to estimate uncertainties such as nonlinearities, couplings, and unmodeled dynamics whose estimated values are incorporated into the continuous-time predictive controllers for feedback compensation. Finally, numerical simulations are conducted to demonstrate the advantages of the proposed method, including reduced tracking errors and enhanced robustness in the closed-loop system, as compared to the conventional nonlinear dynamic inversion and sliding mode control approaches.

Cascaded Incremental Nonlinear Dynamic Inversion Trajectory Following for a Stratospheric Airship in Wind

This paper presents a guidance and control system for controlling the trajectory of a stratospheric unmanned airship using a cascaded Incremental Nonlinear Dynamic Inversion (INDI) method. The control system uses a two-loop cascaded INDI controller with virtual efforts and moments formulation to control both the airship attitude and velocity, while providing perturbation rejection properties. An active-set solver allocates the virtual controls to the airship propellers and aerodynamic surfaces while respecting the actuator bounds and rates saturation. The guidance system uses a Nonlinear Dynamic Inversion controller, where the position error dynamics formulation explicitly considers the lateral velocity of the airship, which enables it to counteract the wind influence. Simulation results demonstrate that the reference trajectory is precisely followed, even in the presence of unknown wind perturbations and both aerodynamic coefficients and mass and inertia parametric uncertainties through Monte-Carlo simulations.

Optical flow-based control for micro air vehicles: an efficient data-driven incremental nonlinear dynamic inversion approach

Optical flow-based control for micro air vehicles: an efficient data-driven incremental nonlinear dynamic inversion approach

Cascaded robust fixed-time terminal sliding mode control for uncertain cartpole systems with incremental nonlinear dynamic inversion

This paper proposes a cascaded fixed-time terminal sliding mode controller (TSMC) for uncertain underactuated cartpole dynamics using incremental nonlinear dynamic inversion (INDI). Leveraging partial linearization and prioritizing pole dynamics for internal tracking, the proposed controller achieves efficient stabilization of the cart upon convergence of the pole. Stability analysis is carried out using Lyapunov stability theorem, proving that the proposed controller stabilizes the state variables to an arbitrarily small neighborhood of the equilibrium in fixed-time, along with the suboptimality (steady-state error), existence and uniqueness of the solutions. The INDI is also integrated into TSMC to further improve the robustness while suppressing the conservativeness of conventional TSMC. The stability of INDI is rigorously proved using sampling-based Lyapunov function under sampling-based control realm. The simulation results illustrate the superiority of the proposed method with comparison and ablation studies.

Nonlinear dynamic inversion based full envelope robust flight control for coaxial compound helicopter

The flight control system of coaxial compound helicopters (CCHs) is a complex multi-variable system characterized by redundant control effectors, strong nonlinear characteristics, and multiple flight modes. This paper presents a unified robust control framework tailored for CCH full-envelope flight, utilizing nonlinear dynamic inversion and extended state observer techniques. The framework is specifically designed to tackle issues arising from a multi-mode nature, parametric uncertainties, and external disturbances. Within the unified framework, the study addresses inherent complexities such as nonlinearities and cross-coupling effects in CCH by leveraging nonlinear dynamic inversion to formulate flight control laws for both inner and outer-loops. To mitigate model uncertainties and external disturbances, the extended state observer is employed to estimate lumped disturbance effectively. Control allocation for both inner and outer-loops is devised to adapt to changes in control effector authorities and flight modes. Furthermore, an exponential control allocation strategy is proposed for the outer-loop to ensure a smooth pitch angle during transition flight. The effectiveness of the proposed control laws and control allocation strategies in achieving precise attitude tracking, transition flight and mission task elements (MTEs), even in the presence of notable model uncertainties and external disturbances, is demonstrated through numerical simulations.

An asymmetrically variable wingtip anhedral angles morphing aircraft based on incremental sliding mode control: Improving lateral maneuver capability

This paper presents the design of an asymmetrically variable wingtip anhedral angles morphing aircraft, inspired by biomimetic mechanisms, to enhance lateral maneuver capability. Firstly, we establish a lateral dynamic model considering additional forces and moments resulting during the morphing process, and convert it into a Multiple Input Multiple Output (MIMO) virtual control system by importing virtual inputs. Secondly, a classical dynamics inversion controller is designed for the outer-loop system. A new Global Fast Terminal Incremental Sliding Mode Controller (NDO-GFTISMC) is proposed for the inner-loop system, in which an adaptive law is implemented to weaken control surface chattering, and a Nonlinear Disturbance Observer (NDO) is integrated to compensate for unknown disturbances. The whole control system is proven semi-globally uniformly ultimately bounded based on the multi-Lyapunov function method. Furthermore, we consider tracking errors and self-characteristics of actuators, a quadratic programming-based dynamic control allocation law is designed, which allocates virtual control inputs to the asymmetrically deformed wingtip and rudder. Actuator dynamic models are incorporated to ensure physical realizability of designed allocation law. Finally, comparative experimental results validate the effectiveness of the designed control system and control allocation law. The NDO-GFTISMC features faster convergence, stronger robustness, and 81.25% and 75.0% reduction in maximum state tracking error under uncertainty compared to the Incremental Nonlinear Dynamic Inversion Controller based on NDO (NDO-INDI) and Incremental Sliding Mode Controller based on NDO (NDO-ISMC), respectively. The design of the morphing aircraft significantly enhances lateral maneuver capability, maintaining a substantial control margin during lateral maneuvering, reducing the burden of the rudder surface, and effectively solving the actuator saturation problem of traditional aircraft during lateral maneuvering.

Commonalities between robust hybrid incremental nonlinear dynamic inversion and proportional-integral-derivative flight control law design

Incremental Nonlinear Dynamic Inversion (INDI) has received substantial interest in the recent years as a nonlinear flight control law design methodology that features inherent robustness against bare airframe aerodynamic variations. However, systematic studies into the robust design benefits of INDI-based control over the classical divide-and-conquer philosophy have been scarce. To bridge this gap, this paper compares the setup of hybrid INDI with a standard industry benchmark that is based on two-degree-of-freedom gain-scheduled proportional-integral-derivative control. This is done on an architectural basis and in terms of achievable robust stability and performance levels with respect to a common set of design requirements. To this end, a non-smooth, multi-objective H∞-synthesis algorithm is used that incorporates mixed parametric and dynamic uncertainties in the design objective and constraints. It is shown that close similarities exist between hybrid INDI design and gain-scheduled PID control, which leads to virtually equivalent robustness and performance outcomes in both linear time-invariant and linear time-varying contexts. It is therefore concluded that the main benefit of the hybrid INDI does not lie in improved robustness properties per se, but in the opportunity to perform modular robust design in an implicit model-following context. Specifically, this implies that the areas of flying qualities, robustness, and nonlinear implementation are directly visible and accessible in the control law structure.

Aerodynamic Feedforward-Feedback Architecture for Tailsitter Control in Hybrid Flight Regimes

This paper presents a guidance-control design methodology for the autonomous maneuvering of tailsitter transitioning unmanned aerial systems (t-UASs) in hybrid flight regimes (i.e., the dynamics between VTOL and fixed-wing regimes). The tailsitter guidance-control architecture consists of a trajectory planner, an outer-loop position controller, an inner-loop attitude controller, and a control allocator. The trajectory planner uses a simplified tailsitter model, with aerodynamic and wake effect considerations, to generate a set of transition trajectories with associated aerodynamic force estimates based on an optimization metric specified by a human operator (minimum time transition). The outer-loop controller then uses the aerodynamic force estimate computed by the trajectory planner as a feedforward signal alongside feedback linearization of the outer-loop dynamics for 6DOF position control. The inner-loop attitude controller is a standard nonlinear dynamic inversion control law that generates the desired pitch, roll, and yaw moments, which are then converted to the appropriate rotor speeds by the control allocator. Analytical conditions for robust stability are derived for the outer-loop position controller to guarantee performance in the presence of uncertainty in the feedforward aerodynamic force compensation. Finally, both tracking performance and stability of the control architecture are evaluated on a high-fidelity flight dynamics simulation of a quadrotor biplane tailsitter for flight missions that demand high maneuverability in transition between flight modes.

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.

Particularities of Rotorcraft in Dealing with Advanced Controllers

Advanced nonlinear controllers are a desirable solution to rotorcraft flight control as they can solve the system high nonlinear dynamic behavior. However, conventional nonlinear controllers such as Nonlinear Dynamic Inversion (NDI) controller heavily rely on the availability of accurate model knowledge and this can be problematic for rotorcraft. Therefore, incremental control theory can solve the modelling errors sensitivity by relying on the information obtained from the sensors instead. The paper applied the Incremental Nonlinear Dynamic Inversion (INDI) controller to rotorcraft case. It will be demonstrated that, for rotorcraft, the incremental nonlinear controllers depend on the delays introduced in the controller by the rotor dynamics. To correct this behaviour, residualization and synchronization methods need to be applied accordingly in order to remove the effects of rotor flapping (disctilt) dynamics from the controller. These particularities of rotorcraft in dealing with advanced controllers shows that incremental nonlinear controllers can have relatively small stability robustness margin and careful controller design is needed in order to account properly for rotorcraft time delays and unmodelled dynamics.

Robust-augmentation nonlinear dynamic inversion control of over-actuated coaxial high-speed helicopter in transition mode

As the elevator and rudder can be used actively for control, in addition to the rotors, Coaxial High-speed Helicopters (CHHs) have the problems of control redundancy and changing control authority in the transition mode. This paper presents a robust-augmentation transitioning flight control design for a CHH under the adverse conditions of parametric uncertainties and external disturbances. First, based on control characteristic analysis, an Adaptive Filtered Nonlinear Dynamic Inversion (AFNDI) controller is proposed for the angular rate to handle the effect of unknown unstructured uncertainties and external turbulence. Theoretical analysis proves that the presented angular rate controller can guarantee steady-state and transient performance. Furthermore, the attitude angle and velocity controllers are also added. Then, an Incremental-based Nonlinear Prioritizing Control Allocation (INPCA) method is designed to take into account control surface transition and changing control authority, which efficiently distributes the required moments between coaxial rotors and aero-surfaces, and avoids the control reversal problem of the yaw channel. In the proposed control architecture, the low-pass filter is introduced to alleviate the adverse influence of time delay and measurement noise. Finally, the effectiveness of the proposed controller is demonstrated through nonlinear numerical simulations, and is compared with existing methods. Simulation results show that the proposed control law can improve both capabilities of disturbance rejection and fast response, and works satisfactorily for the CHH transitioning control characteristic.

Aggressive flight control of quadrotors using incremental nonlinear dynamic inversion with a high-fidelity thrust unit model

The application of quadrotors has been expanded into aggressive tasks such as military confrontation and aerobatics shows, making it crucial to enhance flight maneuverability to adapt to rapid and large-scale command changes. Unlike hovering or low-speed modes, aggressive flight exacerbates quadrotor model uncertainty, making it challenging for controllers to balance response speed and robustness. This paper proposes an INDI control method that integrates a high-fidelity thrust model unit to address this practical need. First, based on the pole distribution theory and the application of INDI on quadrotors, it is concluded that the dynamic response of quadrotor flight is impacted by the accuracy of the thrust model. Second, consider the airflow velocity and angles, the high-fidelity modeling approach, and the aerodynamic forces and torque expression validated through wind tunnel experiments are provided. Then the flight controller for the quadrotor is designed with the established high-fidelity thrust unit model. Finally, aggressive trajectory-tracking flight tests are set to evaluate the improvement of our work. The results demonstrate that our proposed method indeed enhances the response speed and tracking accuracy, as well as the flight stability of the quadrotor.

Parameter Tuning Approach for Incremental Nonlinear Dynamic Inversion-Based Flight Controllers

Incremental nonlinear dynamic inversion (INDI) is a widely used approach to controlling UAVs with highly nonlinear dynamics. One key element of INDI-based controllers is the control allocation realizing pseudo controls using available actuators. However, the tracking of commanded pseudo controls is not the only objective considered during control allocation. Since the approach only works locally due to linearization and the solution is often ambiguous, additional aspects like control efforts or penalizing the deviation of certain states must be considered. Conducting the control allocation by solving a quadratic program this results in a considerable number of weighting parameters, which must be tuned during control design. Currently, this is conducted manually and is therefore time consuming. An automated approach for tuning these parameters is therefore highly beneficial. Thus, this paper presents and evaluates a model-based approach automatically tuning the control allocation parameters of a tiltrotor VTOL using an optimization algorithm. This optimization algorithm searches for optimal parameters minimizing a cost functional that reflects the design target. This cost functional is calculated based on a test mission for the VTOL which is conducted within a simulation environment. The test mission represents the common operating range of the VTOL. The simulation environment consists of an aircraft model as well as a model of the INDI-based controller which is dependent on the control allocation parameters. On this basis, model-based optimization is conducted and the optimal parameters are identified. Finally, successful real-world tests on a 4-degrees-of-freedom testbench using the identified parameters are presented. Since the control allocation parameters can significantly influence the aircraft’s stability, the 4-DOF testbench for the aircraft is required for rapid validation of the parameters at a minimum amount of risk.

Output feedback control for hypersonic flight vehicles via distributed high-gain observer

During the hypersonic flight process of rigid hypersonic flight vehicles (HFVs), the flight-path angle and angle of attack are usually small and sensitive to flight condition variation, the accurate measurements are difficult, subsequently the formulation of states observers is an urgent issue. A distributed high-gain observer is proposed to reconstruct the admissible system state dynamics based on limited measured output. First, a distributed observer is proposed for the cascade strict-feedback system to ensure the global convergence of the state estimation errors between the estimated state in each local observer and system states, for the prescribed system initial values. Second, the distributed high-gain observer-based nonlinear control is investigated on the longitudinal dynamics of HFVs with partial measurable states. The rigid body system dynamic is divided into the altitude subsystem and the velocity subsystem. In the altitude subsystem, the proposed distributed high-gain observer is formulated to exact estimate the flight-path angle and angle of attack, and then the back-stepping design is proposed for constructing the controllers. The nonlinear dynamic inversion controller is introduced to accomplish the velocity tracking. Finally, simulation examples are served to verify that the proposed output feedback control possesses the superior properties of high tracking performance, fast convergence of state estimation error and easy-implementation.

Robust Adaptive Control Based on Incremental Nonlinear Dynamic Inversion for a Quadrotor in Presence of Partial Actuator Fault

This paper presents a novel nonlinear robust adaptive trajectory tracking control architecture for stabilizing and controlling a quadrotor in the presence of actuator partial faults. The proposed control strategy utilizes an Incremental Nonlinear Dynamic Inversion (INDI) algorithm as the baseline controller in the inner loop and augments a nonlinear model reference adaptive controller in the outer loop to ensure robustness against unmodeled faults. Additionally, a modified PID controller is introduced in the most outer-loop to track the desired path. The effects of actuator faults are modeled by considering sudden variations in motor thrust and torques. To enhance the control algorithm's robustness, a projection operator is employed in the robust adaptive structure. Comparative performance evaluations with a previous successful algorithm implemented on a quadrotor model demonstrate that the proposed controller achieves full controllability of the faulty quadrotor in pitch, roll, and yaw channels in the presence of actuator partial faults up to 50%.

Finite-Time Attitude Control of Quadrotor Unmanned Aerial Vehicle with Disturbance and Actuator Saturation

This paper introduces a nonlinear dynamic inversion control algorithm designed to address unknown disturbances and actuator saturation issues in unmanned aerial vehicle (UAV) attitude control. The algorithm is based on a combination of finite-time disturbance observer and anti-saturation auxiliary system, which ensures the rapid convergence of attitude tracking error. Firstly, based on the Newton–Euler equations, this paper establishes a model of the attitude system for quadrotor UAVs, and this paper eliminates the small-angle flight assumption. Secondly, considering the actuator saturation problem, an anti-saturation auxiliary control system is designed to shorten the time when the control volume is in the saturation interval and achieve finite-time convergence of the attitude error. And then, to improve the robustness of the controller, this paper proposes a disturbance observer based on the finite-time stability theory, which achieves a continuous smooth output of the observation results by introducing a hyperbolic tangent function in the observer, so that the observation error can be converged to zero in a finite time. Finally, it is demonstrated by Simulink simulation that the attitude error and the observation error converge quickly to zero.