Incremental Nonlinear Dynamic Inversion Control Research Articles

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.

Decoupled incremental nonlinear dynamic inversion control for aircraft autonomous landing with ground-effect

Due to motion coupling and increased model dependence, the use of nonlinear controllers in real-time applications for aircraft is extremely constrained. This explains why proportional, derivative, and integral (PID) controls are frequently used in practice. However, fast changes in the commanded path and the requirement for high accuracy and tracking performance limit use of PID in landing. This paper presents a design of a decoupled incremental nonlinear dynamic inversion (INDI) controller for performing autonomous landing of a fixed-wing aircraft. The investigation is carried out using the ground effect model and is compared without it. A carrot chasing guidance algorithm is implemented for waypoint navigation to generate the command for the proposed controller's outer loop. The navigational state estimate issue has been resolved using the Cubature Kalman Filter (CKF) approach. Two decoupled CKF algorithms named complementary Cubature Kalman Filter (CCKF) and Integrated Cubature Kalman Filter (I-CKF) are proposed to estimate aircraft navigational states comprised of attitudes, navigational position in terms of latitude, longitude altitudes, and North-East-down velocities. The mathematical model for flare and approach trajectory is designed and commanded to follow the same by the proposed INDI controller. The effectiveness of INDI have been evaluated in a simulation environment by landing the aircraft in the same runway position at arbitrary wind conditions. The performance of the proposed INDI controller is juxtaposed with a conventional proportional integrator and derivative (PID) based landing controller. The simulation findings demonstrate that the INDI has a competitive edge over traditional PID approaches due to its robust performance, less dependence on model dynamics, and fast command tracking capability required during the flare phase.

Meta-Learning-Based Incremental Nonlinear Dynamic Inversion Control for Quadrotors with Disturbances

This paper proposes an online meta-learning-based incremental nonlinear dynamic inversion (INDI) control method for quadrotors with disturbances. The quadrotor dynamic model is first transformed into linear form via an INDI control law. Since INDI largely depends on the accuracy of the control matrix, a method composed of meta-learning and adaptive control is proposed to estimate it online. The effectiveness of the proposed control framework is validated through simulation on a quadrotor with 3D wind disturbances.

Full envelope nonlinear flight controller design for a novel electric VTOL (eVTOL) air taxi

AbstractOn-demand urban air transportation gains popularity in recent years with the introduction of the electric VTOL (eVTOL) aircraft concept. There is an emerging interest in short/medium range eVTOL air taxi considering the critical advantages of electric propulsion (i.e. low noise and carbon emission). Using several electric propulsion systems (distributed electric propulsion (DEP)) has further advantages such as improved redundancy. However, flight controller design becomes more challenging due to highly over-actuated and coupled dynamics. This study defines and resolves flight control problems of a novel DEP eVTOL air taxi. The aircraft has a fixed-wing surface to have aerodynamically efficient cruise flight, and uses only tilting electric propulsion units to achieve full envelope flight control via pure thrust vector control. The aircraft does not have conventional control surfaces such as aileron, rudder or elevator. Using pure thrust vector control has some design benefits, but the control problem becomes more challenging due to the over-actuated and highly coupled dynamics (especially in transition flight). A preliminary flight dynamics model is obtained considering the dominant effects at hover and high-speed forward flight. Hover and forward flight models are blended to simulate the transition dynamics. Two central challenges regarding the flight control are significant nonlinearities in aircraft dynamics during the transition and proper allocation of the thrust vector control specifically in limited control authority (actuator saturation). The former challenge is resolved via designing a sensor-based incremental nonlinear dynamic inversion (INDI) controller to have a single/unified controller covering the wide flight envelope. For the latter one, an optimisation-based control allocation (CA) approach is integrated into the INDI controller. CA requires special attention due to the pure thrust vector control’s highly coupled dynamics. The controller shows satisfactory performance and disturbance rejection characteristics. Moreover, the CA plays a vital role in guaranteeing stable flight in case of severe actuator saturation.

Flight Control Law for Stabilizing Transient Response of the Aircraft during Gun Firing

Highly maneuverable fighter aircraft are equipped with various weapons including a gun firing system for successful air-to-air and air-to-ground missions. In the gun firing system, the muzzle is usually positioned at an offset from the centerline of the aircraft to facilitate maintainability and accessibility on the ground, to ensure the pilot’s visibility, and to avoid vibrations. However, this mounting position causes the repulsive force for gun firing to generate a moment around the center of gravity and distorts the aircraft’s attitude, degrading the accuracy of the target point. In this paper, we propose the application of an additional augmentation control method, as a hybrid INDI control, that combines model- and sensor-based incremental nonlinear dynamic inversion (INDI) controls to minimize the maximum overshoot of transient response of the aircraft during gun firing. As a result of the frequency- and time-domain evaluation, the additional augmentation control can effectively reduce the transient response during gun firing. In addition, this control method is more robust against uncertainties, and its structure is simple compared to the conventional open-loop type gun compensation control since it does not require any gain scheduling according to flight conditions.

Adaptive Nonlinear Incremental Flight Control for Systems With Unknown Control Effectiveness

This article exposes that although some sensor-based nonlinear fault-tolerant control frameworks including incremental nonlinear dynamic inversion control can passively resist a wide range of actuator faults and structural damage without requiring an accurate model of the dynamic system, their stability heavily relies on a sufficient condition, which is unfortunately violated if the control direction is unknown. Consequently, it is proved in this article that no matter, which perturbation compensation technique (adaptive, disturbance observer, sliding-mode) is implemented, none of the existing nonlinear incremental control methods can guarantee closed-loop stability. Therefore, this article proposes a Nussbaum function-based adaptive incremental control framework for nonlinear dynamic systems with partially known (control direction is unknown) or even completely unknown control effectiveness. Its effectiveness is proved in the Lyapunov sense and is also verified via numerical simulations of an aircraft attitude tracking problem in the presence of sensing errors, parametric model uncertainties, structural damage, actuator faults, as well as inversed and unknown control effectiveness.

Nonlinear Dynamic Inversion with Actuator Dynamics: An Incremental Control Perspective

In this paper, we derive a sensor-based nonlinear dynamic inversion (NDI) control law for a nonlinear system with first-order linear actuators, and compare it to incremental nonlinear dynamic inversion (INDI), which has gained popularity in recent years. It is shown that, for first-order actuator dynamics, INDI approximates the corresponding NDI control law arbitrarily well under the condition of sufficiently fast actuators. If the actuator bandwidth is low compared to changes in the states, the derived NDI control law has the following advantages compared to INDI: 1) compensation of state derivative terms, 2) well-defined error dynamics, and 3) exact tracking of a reference model, independent of error controller gains in nominal conditions. The comparison of the INDI control law with the well-established control design method NDI adds to the understanding of incremental control. It is additionally shown how to quantify the deficiency of the INDI control law with respect to the exact NDI law for actuators with finite bandwidth. The results are confirmed through simulation results of the roll motion of a fixed-wing aircraft.

Modified adaptive discrete-time incremental nonlinear dynamic inversion control for quad-rotors in the presence of motor faults

Unmanned air vehicles are intrinsically non-linear, unstable, uncertain, and prone to a variety of faults, most commonly the motor faults. The main objective of this paper is to develop a fault-tolerant control algorithm for the quadrotors with the motor faults. Accordingly, a novel adaptive modified incremental nonlinear dynamic inversion (MINDI) control is proposed to stabilize and control the quad-rotor with partial motor faults. The controller consists of a MINDI controller augmented with a discrete-time nonlinear adaptive algorithm. Since the incremental nonlinear dynamic inversion (INDI) algorithm is essentially based on the sensor measurements, it necessitates the angular rates differentiation and therefore amplifies the high-frequency noises produced by the gyroscopes. The application of derivative filters causes unavoidable internal state delays in the INDI structure. Henceforth, the performance of the controller developed for the unstable and uncertain quadrotors degrades considerably. To address this drawback, this paper proposes the MINDI controller which basically derives the angular accelerations from the angular moment estimations. Furthermore, to increase the robustness of the MINDI against motor faults, a discrete-time adaptive controller has been incorporated. The performance of the proposed controllers is verified both through the nonlinear simulations and testbed experiments. The results are compared with a recent efficient algorithm, which had been implemented on a quad-rotor model.

An Adaptive Control Framework for the Autonomous Aerobatic Maneuvers of Fixed-Wing Unmanned Aerial Vehicle

This article proposes an adaptive flight framework that integrates a discrete-time incremental nonlinear dynamic inversion controller and a neural network (NN)-based observer for maneuvering flight. The framework is built on the feedback-inversion scheme in which the adaptive neural network augments a discrete-time disturbance observer in the loop. The effects of the modeling uncertainties and the exogenous perturbations are both taken into consideration and are alleviated by the observer. By utilizing the Lyapunov synthesis method, the updating rule of the NN’s weights is introduced, which guarantees the system’s stability with enhanced tracking performance. The efficiency of the proposed scheme is presented through numerical verification of a 6-DOF fixed-wing fighter performing several aggressive flight maneuvers. Extensive simulation results illustrate that this versatile controller is more practical for aerobatic flights compared with the discontinuous sliding mode (DSM) and the nonlinear dynamic inversion (NDI) methods. Given well-generated maneuver commands, the aircraft can accurately track the aggressive reference in the presence of modeling perturbations such as changes in aerodynamic coefficient, inertial parameters, and wind gusts.

A cascaded nonlinear fault-tolerant control for fixed-wing aircraft with wing asymmetric damage

This paper investigates the flight dynamics of the aircraft with wing asymmetric damage and the fault-tolerant control problem to improve the stability and flight quality of damaged aircraft. A high-fidelity wing asymmetric damaged aircraft nonlinear model is developed, as well as the impact of wing asymmetric damage on the physical and aerodynamic properties of the aircraft is also analyzed. The trim strategies for damaged aircraft are investigated to achieve a rapid estimation of trim states after damage occurs. This paper presents a robust cascaded nonlinear fault-tolerant control framework that integrates the incremental nonlinear dynamic inversion control with improved piecewise-constant-based nonlinear L1 adaptive control for the stability control to enhance the stability and tracking performance of the damaged aircraft. Theoretical analysis proves that the presented fault-control structure is robust to disturbances and can decouple rapidity and robustness while guaranteeing steady-state and transient performance. Finally, the hardware-in-the-loop flight control experiment platform is developed to validate the cascaded nonlinear fault-tolerant controller. In the experiment, the proposed controller is verified under wing asymmetric damage and compared with existing methods. Experimental results show that the proposed fault-tolerant control is able to overcome wing asymmetric damage and significantly improve the tracking performance of the damaged aircraft even with 27.2% of the severe damage to the left-wing.

A hybrid INDI control for ensuring flying qualities in failures of Xcg measurement subsystem

Modern version of fighter aircraft has a wide range of longitudinal center-of-gravity (Xcg) travel due to wide-range fuel tanks layout, various weapons, many payload stations, and so on. The wide Xcg travel degrades flying qualities of a closed-loop control system; moreover, a catastrophic accident can be caused by loss of stability due to the wide Xcg travel in severe cases. For this reason, the inner-loop control law generally employs additional feedback variables such as weight and Xcg position to guarantee the flying qualities and satisfy stability requirements. Nevertheless, this design approach can seriously deteriorate the flight safety and stability of the aircraft in the event of fuel mismanagement and Xcg measurement subsystem failures. Therefore, additional design technique should be considered to ensure the flight safety in response to the situation of the failure conditions. This paper proposes two types of a hybrid Incremental Nonlinear Dynamic Inversion control to guarantee the minimum flight safety for return to base in case of fuel mismanagement and Xcg measurement subsystem failures. The frequency-domain linear analysis and time-domain simulations were performed based on a supersonic trainer mathematical model to evaluate the performances of the proposed control methods. The evaluation results confirm that the proposed control method satisfies the level of the required flying qualities and ensure flight safety even in the event of the subsystem failures for the Xcg measurement.

Arttirimli doğrusal olmayan dinamik çevirmeye dayali bir quadrotor'un hata toleransli kontrolü

The multirotor unmanned aerial vehicles (UAVs) have rapidly attracted interest of the researchers since they play a unique role in a variety of areas including the military, agriculture, rescue, and mining. Actuator fault or failure is inevitable during multi-rotor’s operations, which can endanger humans on the ground in addition to costly damage to the system itself. Therefore, this paper introduces a nonlinear controller algorithm for fault-tolerant control of a quadcopter with partial loss of actuator effectiveness. The introduced controller includes a cascade structure of the fast inner-loop dynamics and slow outer-loop dynamics. In the inner-loop part of the controller, an incremental nonlinear dynamic inversion controller is applied and a modified PID control algorithm is used in the outer-loop of the controller. Simulation results for different fault scenarios demonstrate that the proposed fault-tolerant controller approach can quickly adapt itself to the abrupt change due to the motor faults and tracks the desired inputs satisfactorily.

Autonomous Landing of a Quadrotor on a Moving Platform via Model Predictive Control

Landing on a moving platform is an essential requirement to achieve high-performance autonomous flight with various vehicles, including quadrotors. We propose an efficient and reliable autonomous landing system, based on model predictive control, which can accurately land in the presence of external disturbances. To detect and track the landing marker, a fast two-stage algorithm is introduced in the gimbaled camera, while a model predictive controller with variable sampling time is used to predict and calculate the entire landing trajectory based on the estimated platform information. As the quadrotor approaches the target platform, the sampling time is gradually shortened to feed a re-planning process that perfects the landing trajectory continuously and rapidly, improving the overall accuracy and computing efficiency. At the same time, a cascade incremental nonlinear dynamic inversion control method is adopted to track the planned trajectory and improve robustness against external disturbances. We carried out both simulations and outdoor flight experiments to demonstrate the effectiveness of the proposed landing system. The results show that the quadrotor can land rapidly and accurately even under external disturbance and that the terminal position, speed and attitude satisfy the requirements of a smooth landing mission.

Predictor-based Adaptive Incremental Nonlinear Dynamic Inversion for Fault-Tolerant Flight Control*

The sensor-based Incremental Nonlinear Dynamic Inversion (INDI) control has shown promising robustness in the aerospace research field. This control framework only requires a partial knowledge of plant (control effectiveness) because of its usage of angular accelerations and actuator output measurements. However, there are still un-negligible uncertainties of the control effectiveness model in the flight control system, especially when the aircraft is subjected to structural damage/actuator faults. This paper shows that the conventional INDI control fails to satisfy the sufficient conditions for closed-loop stability in the presence of severe damage. Therefore, this paper also proposes a predictor-based gain adaptive INDI control (named PGA-INDI) which can successfully deal with control effectiveness parametric errors caused by structural damage, actuator faults, and model uncertainties. Various simulations using a public aircraft model have demonstrated the effectiveness of the proposed approach

Incremental Twisting Fault Tolerant Control for Hypersonic Vehicles With Partial Model Knowledge

A passive fault tolerant control scheme is proposed for the full reentry trajectory tracking of a hypersonic vehicle in the presence of modeling uncertainties, external disturbances, and actuator faults. To achieve this goal, the attitude error dynamics with relative degree two is formulated first by ignoring the nonlinearities induced by the translational motions. Then, a multivariable twisting controller is developed as a benchmark to ensure the precise tracking task. Theoretical analysis with the Lyapunov method proves that the attitude tracking error and its first-order derivative can simultaneously converge to the origin exponentially. To depend less on the model knowledge and reduce the system uncertainties, an incremental twisting fault tolerant controller is derived based on the incremental nonlinear dynamic inversion control and the predesigned twisting controller. In this article, it is shown that not only the benefits of both incremental control and twisting control are inherited, but also their side effects are reduced. Notably, the proposed controller is user friendly in that only fixed gains and partial model knowledge are required. Numerical simulations in various cases and comparison studies are conducted to verify the effectiveness of the proposed method.

Robust proportional incremental nonlinear dynamic inversion control of a flying-wing tailsitter

Tailsitter unmanned aerial vehicles are utilized extensively nowadays since they merge advantages of both fixed-wing unmanned aerial vehicles and rotary-wing unmanned aerial vehicles. However, their attitude control suffers from unknown nonlinearities and disturbances due to the wide flight envelope. To solve the problems, a robust attitude controller based on a newly designed flying-wing tailsitter is proposed in this paper. By employing the angular acceleration feedback to compensate unmodeled dynamics, the proportional incremental nonlinear dynamic inversion control law is first developed. The proportional incremental nonlinear dynamic inversion strengthens the conventional nominal gain incremental nonlinear dynamic inversion with a proportional term to reflect the change of the angular acceleration more directly. Therefore, the tailsitter has a quicker response and performs better in suppressing model uncertainties and external disturbances. Since the angular acceleration is difficult to measure in practice, an angular acceleration estimation method is then established to provide accurate signals for the proportional incremental nonlinear dynamic inversion. The signals are derived as complementary results of model prediction method and direct differential method. Theoretical analysis and systematic simulations are conducted to corroborate the effectiveness of the developed estimation method as well as the robustness of the proposed controller.

Incremental Nonlinear Dynamic Inversion for the Apache AH-64 Helicopter Control

Incremental nonlinear dynamic inversion (INDI)-based controller is a promising technique that can be adopted to control dynamic systems with high nonlinearities and extended cross-coupling effects. This paper presents the incremental strategy adopted as a sensor-based controller approach for the Apache AH-64D Longbow helicopter. The strength of the INDI sensor– based approach is that it does not require a detailed vehicle model as it uses only a control effectiveness model and estimates of the vehicle angular accelerations replacing the rest of the model. The weakness is its sensitivity to measurement and actuator delays, demanding additional estimations of model parameters and control effectiveness tuning. Using the Boeing FLYRT Apache model to simulate the vehicle dynamics, the paper has developed three adaptation schemes connecting the INDI sensor–based approach to the Apache partial control authority set as ±20% authority in all axes. The goal was to redesign the existing Apache's flight control systems and demonstrate handling qualities improvements for hover and low-speed flight in normal and degraded visual environment. Implementing the attitude command attitude hold and translational rate command response types in the system through the INDI controller, the paper demonstrates that improvements from Level 2 to Level 1 handling qualities can be achieved when flying the Aeronautical Design Standard-33 (ADS-33E-PRF) hover and pirouette maneuvers in a degraded visual environment.

Model-free control algorithms for micro air vehicles with transitioning flight capabilities

Micro air vehicles with transitioning flight capabilities, or simply hybrid micro air vehicles, combine the beneficial features of fixed-wing configurations, in terms of endurance, with vertical take-off and landing capabilities of rotorcrafts to perform five different flight phases during typical missions, such as vertical takeoff, transitioning flight, forward flight, hovering and vertical landing. This promising micro air vehicle class has a wider flight envelope than conventional micro air vehicles, which implies new challenges for both control community and aerodynamic designers. One of the major challenges of hybrid micro air vehicles is the fast variation of aerodynamic forces and moments during the transition flight phase which is difficult to model accurately. To overcome this problem, we propose a flight control architecture that estimates and counteracts in real-time these fast dynamics with an intelligent feedback controller. The proposed flight controller is designed to stabilize the hybrid micro air vehicle attitude as well as its velocity and position during all flight phases. By using model-free control algorithms, the proposed flight control architecture bypasses the need for a precise hybrid micro air vehicle model that is costly and time consuming to obtain. A comprehensive set of flight simulations covering the entire flight envelope of tailsitter micro air vehicles is presented. Finally, real-world flight tests were conducted to compare the model-free control performance to that of the Incremental Nonlinear Dynamic Inversion controller, which has been applied to a variety of aircraft providing effective flight performances.

Incremental Control and Guidance of Hybrid Aircraft Applied to a Tailsitter Unmanned Air Vehicle

Hybrid unmanned aircraft can significantly increase the potential of micro air vehicles, because they combine hovering capability with a wing for fast and efficient forward flight. However, these vehicles are very difficult to control, because their aerodynamics are hard to model and they are susceptible to wind gusts. This often leads to composite and complex controllers, with different modes for hover, transition, and forward flight. This paper proposes incremental nonlinear dynamic inversion control for the attitude and position control. The result is a single, continuous controller that is able to track the desired acceleration of the vehicle across the flight envelope. The proposed controller is implemented on the Cyclone hybrid unmanned air vehicle. Multiple outdoor experiments are performed, showing that unmodeled forces and moments are effectively compensated by the incremental control structure. Finally, this paper provides a comprehensive procedure for the implementation of the controller on other types of hybrid unmanned air vehicles.

Flexible Aircraft Gust Load Alleviation with Incremental Nonlinear Dynamic Inversion

This paper designs an incremental nonlinear dynamic inversion control law for free-flying flexible aircraft, which can regulate rigid-body motions, alleviate gust loads, reduce the wing root bending moment, and suppress elastic modes. By fully exploring the sensor measurements, the model dependency of the proposed control law can be reduced while maintaining desirable robustness, which simplifies the implementation process and reduces the onboard computational load. The elastic states are observed online from accelerometer measurements, with a Padé approximation to model the pure time delay. Theoretical analyses based on the Lyapunov methods and the nonlinear system perturbation theory show that the proposed control has inherent robustness to model uncertainties, external disturbances, and sudden actuator faults. These merits are demonstrated by time-domain simulations in various spatial turbulence and gust fields, as well as by a Monte Carlo study.