Incremental Nonlinear Dynamic Inversion Research Articles

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.

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%.

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.

Boosted Incremental Nonlinear Dynamic Inversion for Flexible Airplane Gust Load Alleviation

Active gust load alleviation is an important technology for reducing loads on future commercial airplanes so that the structure can be designed to be lighter in order to save fuel. For the intense reduction of gust loads, a highly reactive control system of sensors, control algorithms, and actuators is required, which is not yet available. In this paper, a control algorithm based on incremental nonlinear dynamic inversion is extended so that actuators respond faster. The control algorithm is applied to a future medium-range aircraft with distributed trailing-edge flaps. It is assumed that the vertical acceleration of the center of gravity and the displacement, velocity, and acceleration of the first wing bending mode are available as feedback variables. To allow comparability with other actuator and sensor setups, the authors abstract the actuator dynamics and sensor filter as control system time delay. The feedback gains are adjusted automatically to the control system time delay. In simulation, the authors investigate the influence of the control system time delay on the peak gust loads. They show that gust loads can indeed be intensely reduced with sufficiently small control system time delay in simulation.

Precision Advancements in Aerial Gliding Vehicles: Modeling to FCS Validation

The growing utilization of unmanned aerial vehicles (UAVs) in military operations has necessitated the development of a suitable weaponry for these kind of platforms. One of the trending categories of such armaments is the aerial gliding vehicle (AGV). AGVs have no propulsion system, consequently, a critical need for a robust flight control system (FCS) tailored to this kind of aerial systems is raised. This research focuses on designing a nonlinear model based controller, starting with the construction of a precise model through practical experiments and the establishment of a dedicated testing and flight simulation environment. Recognizing the limitations of traditional nonlinear dynamic inversion (NDI) due to its dependence on the vehicle model, the modified incremental nonlinear dynamic inversion (MI-NDI) is developed to operate in the presence of wind, model mismatches, and external disturbances. In this research, an extensive testing is conducted in a hardware-in-the-loop (HIL) simulation environment which validates the MI-NDI controller’s superior performance, even in challenging conditions. The research outcomes mark a significant advancement in enhancing autopilot precision for advanced aerial weaponry and unmanned vehicles.

Hexa-Propeller Airship for Environmental Surveillance and Monitoring in Amazon Rainforest

This paper proposes a new kind of airship actuator configuration for surveillance and environmental monitoring missions. We present the design and application of a six-propeller electrical airship (Noamini) with independent tilting propellers, allowing improved and flexible maneuverability. The vehicle has different combinations of differential propulsion and can be used in a two-, four- or six-motor configuration. We developed a high-fidelity airship simulator for the Noamini airship, which was used to test and validate a control/guidance approach. Incremental Nonlinear Dynamic Inversion (INDI) is used for the velocity/attitude control to follow a high-level L1 guidance reference in a simulated waypoint-tracking mission with wind and turbulence. The proposed framework will be soon implemented in the onboard control system of the Noamini, an autonomous airship for environmental monitoring and surveillance applications.

Research on cascade control method for turboshaft engine with variable rotor speed

Abstract In order to realize high-quality control for turboshaft engine with variable rotor speed, a cascade control method based on the acceleration estimator of gas turbine speed (N gdot ) through Complementary filtering – incremental nonlinear dynamic inversion (CF-INDI)with Newton’s prediction is proposed. Firstly, an adaptive torsional suppression method based on the Recursive Least Square (RLS) algorithm and combined with the control index of power turbine speed is proposed and designed to solve the torsional instability of control system in turboshaft engine with variable rotor speed. Then, an online N gdot estimated method based on CF-INDI with Newton’s prediction is developed, and the complementary filtering method is applied to compensate for the inaccuracy of the state variable model available at a single working point, and Newton prediction is used to alleviate the problem of lagging acceleration estimate, which is accessible to realize the cascade control for turboshaft engine based on N gdot . The simulation results show that the RLS adaptive torsional filter can effectively suppress the low-order torsional components with frequencies of 1.2 Hz and 2.0 Hz mixing in power turbine speed, and the torsional suppression effect is remarkable. In addition, under different flight conditions, CF-INDI with Newton prediction is faster and more accurate than INDI N gdot estimate, and smoother than central difference method, which proves the feasibility of INDI N gdot estimator. Meanwhile, after the application of CF-INDI with Newton prediction N gdot estimator in cascade control, the anti-interference capacity of power turbine speed is stronger, and the dynamic control effect is superior, which has satisfactory robustness performance.

Dynamic characteristics analysis and robust transition control of tail-sitter VTOL UAVs

The strong nonlinear dynamics of tail-sitter vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs) have consistently constrained their applications. Particularly, the widely-varying flight speed and attitude during the transition flights pose substantial challenges for the controller design. In order to gain a clear understanding of the nonlinear transition flights, the long- and short- period dynamic characteristics of tail-sitter UAVs are investigated for the first time. The results reveal that the short-period mode exhibits either sluggish response or excessive overshoot in different transition stages, primarily due to the widely-varying damping ratio and natural angular frequency. Even worse, the long-period mode can diverge due to positive poles. To address these issues, a systematic controller is proposed. First, the transition trajectory is optimized and the optimal control inputs are employed in a feedforward manner to trim the nominal forces and moments. On this basis, a discrete-time linear quadratic regulation (LQR) controller with a predefined decay rate is developed to position the desired poles, and a novel angular acceleration estimation method is introduced to compensate for unmodeled dynamics. Simulations under different uncertainties indicate that the proposed control method performs better in both transition trajectory tracking and uncertainty suppression, compared to the PID and incremental nonlinear dynamic inversion (INDI) controllers.

Multi-Phase Vertical Take-Off and Landing Trajectory Optimization with Feasible Initial Guesses

The advancement of electric vertical take-off and landing (eVTOL) aircraft has expanded the horizon of urban air mobility. However, the challenge of generating precise vertical take-off and landing (VTOL) trajectories that comply with airworthiness requirements remains. This paper presents an approach for optimizing VTOL trajectories considering six degrees of freedom (6DOF) dynamics and operational constraints. Multi-phase optimal control problems are formulated to address specific constraints in various flight stages. The incremental nonlinear dynamic inversion (INDI) controller is employed to execute the flight mission in each phase. Controlled flight simulations yield dynamically feasible trajectories that serve as initial guesses for generating sub-optimal trajectories within individual phases. A feasible and sub-optimal initial guess for the holistic multi-phase problem is established by concatenating these single-phase trajectories. Focusing on a tilt-wing eVTOL aircraft, this paper computes VTOL trajectories leveraging the proposed initial guess generation procedure. These trajectories account for complex flight dynamics, align with various operation constraints, and minimize electric energy consumption.

Miniaturization and Control of an Unmanned Tiltwing Aircraft

The objective of this paper is to describe the miniaturization and control of an unmanned tiltwing aircraft. For geometric miniaturization and mechanical realization, a lightweight design based on carbon fiber tubes, polystyrene rigid foam and 3D-printed parts is used. The attitude controller is adopted from an existing full-scale unmanned tiltwing aircraft and follows the control strategy of Incremental Nonlinear Dynamic Inversion (INDI). The effects of the miniaturization, including low mass inertia combined with comparatively large aerodynamic surfaces, require a re-evaluation of INDI-based assumptions. Due to the aircraft’s rear-positioned center of gravity, the modeled control ability of the main motors is adapted and explicitly considered in the controller design. The integrity of both, construction and controller, is validated in simulations and flight tests.

External Synchronization of Distributed Redundant Flight Control Computers

<div>This work introduces a practical approach to external synchronization for flight control computers (FCCs) deployed in a decentralized fashion. The internal synchronization among the FCCs in distributed flight control systems needs to be extended for specific applications, necessitating an urgent need for an external synchronization mechanism. For instance, when the air data and attitude reference system (ADAHRS) and the flight control computer (FCC) are not synchronized, a dead time or time offset occurs between the time the ADAHRS transmits data and the time the FCC begins executing its control functions, which can impair flight control system performance or even cause system instability, particularly for the system with incremental control approaches, such as incremental nonlinear dynamic inversion (INDI). Therefore, an external synchronization technique that does not rely on establishing a global view of time that is accurately synchronized with an external reference device has been proposed and implemented for distributed flight control systems. The findings of the implemented system demonstrate that the suggested approach can synchronize the distributed FCCs to an external reference device with high synchronization precision and deal with varying clock drift rates.</div>

Control Design for Soft Transition for Landing Preparation of Light Compound-Wing Unmanned Aerial Vehicles Based on Incremental Nonlinear Dynamic Inversion

This paper proposes a soft switching mode for electric vertical takeoff and landing (eVTOL) compound-wing unmanned aerial vehicles (UAVs) to achieve a smooth transition between modes. The proposed mode pre-compensates the lift loss with the rotary wing during the deceleration stage before UAV landing. The control law adopted in this paper consists of implicit nonlinear dynamic inversion (NDI) and incremental nonlinear dynamic inversion (INDI). The outer loop (attitude angle loop) control law is based on implicit NDI, while the inner loop (attitude angle rate loop) controller is based on INDI. An extended state observer (ESO) is employed to estimate the angular acceleration. This paper innovates by proposing a soft switching strategy that improves the robustness, safety, and smoothness of the transition for the compound-wing UAV, and applying advanced control law to mode transition design. For the future application of eVTOL aircraft in UAM scenarios, this paper evaluates the smoothness of transition and passenger comfort using normal overload as a physical quantity. The Monte Carlo (MC) simulation results demonstrate that the proposed mode can reduce the peak normal overload by about 89%.

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.

Research on integrated aircraft-engine control method of hypersonic vehicle based on dynamic inversion control

In order to reduce the influence of the coupling characteristics between the aircraft and engine of hypersonic vehicle, an integrated aircraft-engine control method of hypersonic vehicle is studied in this paper. Firstly, the control-oriented aircraft-engine integrated mathematical model of the hypersonic vehicle is established. Then, by using the nonlinear dynamic inversion (NDI) and the incremental nonlinear dynamic inversion (INDI), the outer loop control algorithm with slow attitude change and the inner loop control algorithm with fast angular rate change are respectively designed. Moreover, based on the online ontology model including aircraft-engine coupling characteristics of the hypersonic vehicle, the coupling control scheme of flight posture and engine of the hypersonic vehicle is designed in the form of control linkage. Finally, the reference model, error control, online estimation and other modules are introduced into the NDI controller to ensure the flight quality and robustness requirements of the hypersonic vehicle. The simulation results show that the aircraft-engine coupling control scheme based on the NDI achieves the expected control performance.

L1 Adaptive Control Based on Dynamic Inversion for Morphing Aircraft

Morphing aircraft are able to keep optimal performance in diverse flight conditions. However, the change in geometry always leads to challenges in the design of flight controllers. In this paper, a new method for designing a flight controller for variable-sweep morphing aircraft is presented—dynamic inversion combined with L1 adaptive control. Firstly, the dynamics of the vehicle is analyzed and a six degrees of freedom (6DOF) nonlinear dynamics model based on multibody dynamics theory is established. Secondly, nonlinear dynamic inversion (NDI) and incremental nonlinear dynamic inversion (INDI) are then employed to realize decoupling control. Thirdly, linear quadratic regulator (LQR) technique and L1 adaptive control are adopted to design the adaptive controller in order to improve robustness to uncertainties and ensure the control accuracy. Finally, extensive simulation experiments are performed, wherein the demonstrated results indicate that the proposed method overcomes the drawbacks of conventional methods and realizes an improvement in control performance.

Robust Stability and Performance Analysis of Incremental Dynamic-Inversion-Based Flight Control Laws

Incremental nonlinear dynamic inversion (INDI) is a sensor-based control law design strategy that is based on the principles of feedback linearization. Contrary to its nonincremental counterpart (nonlinear dynamic inversion), this design method does not require a complete onboard model of the airframe dynamics and is therefore more robust against regular perturbations arising from aerodynamic variations. Therefore, INDI brings a natural design approach to desirable flying qualities. However, robustness against singular perturbations, which may arise due to transport delays, elastic airframe effects, or other types of badly modeled or unknown dynamics, is a known challenge for INDI-based control laws. Therefore, this paper addresses the question of robust stability and performance for INDI and its linear form (incremental dynamic inversion [IDI]) in the context of mixed regular and singular perturbations. This is done through analytical insights and by performing quantitative robustness assessments based on the structured singular value framework. Additionally, inversion loop augmentation solutions are investigated using robust synthesis techniques to improve the robustness characteristics of basic IDI designs.

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.

Low-level control with actuator dynamics for multirotor UAVs

PurposeA low-level controller is critical to the overall performance of multirotor unmanned aerial vehicles. The purpose of this paper is to propose a nonlinear low-level angular velocity controller for multirotor unmanned aerial vehicles in various operating conditions (e.g. different speed and different mode).Design/methodology/approachTo tackle the above challenge, the authors have designed a nonlinear low-level controller taking the actuator dynamics into account. The authors first build the actuator subsystem by combining the actuator dynamics with the angular velocity dynamics model. Then, a recursive low-level controller is developed by designing a high-gain observer to estimate unmeasurable states. Furthermore, a detailed stability analysis is given with the Lyapunov theory.FindingsSimulation tests and real-world flying experiments are provided to validate the proposed approach. In particular, we illustrate the performance of the proposed controller using violent random command test, attitude mode flight and high-speed flight of up to 18.7 m/s in real world. Compared with the classical method used in PX4 autopilot and the estimation-based incremental nonlinear dynamic inversion method, experimental results show that the proposed method can further reduce the control error.Research limitations/implicationsLow-level control of multirotor UAVs is challenging due to the complex dynamic characteristics of UAVs and the diversity of tasks. Although some progress has been made, the performance of existing methods will deteriorate as operating conditions change due to the disregard for the electromechanical characteristics of the actuator.Originality/valueTo solve the low-level angular velocity control problem in various operating conditions of multirotor UAVs, this paper proposes a nonlinear low-level angular velocity controller which takes the actuator dynamics into account.

Incremental Nonlinear Dynamic Inversion Attitude Control for Helicopter with Actuator Delay and Saturation

In this paper, an incremental nonlinear dynamic inversion (INDI) control scheme is proposed for the attitude tracking of a helicopter with model uncertainties, and actuator delay and saturation constraints. A finite integral compensation based on model reduction is used to compensate the actuator delay, and the proposed scheme can guarantee the semi-globally uniformly ultimately bounded tracking. The overall attitude controller is separated into a rate, an attitude, and a collective pitch controller. The rate and collective pitch controllers combine the proposed method and INDI to enhance the robustness to actuator delay and model uncertainties. Considering the dynamic of physical actuators, pseudo-control hedging (PCH) is introduced both in the rate and attitude controller to improve tracking performance. By using the proposed controller, the helicopter shows good dynamics under the multiple restrictions of the actuators.