Nonlinear Dynamic Inversion Research Articles

Fault-Tolerant Control for Aircraft with Structural Damage Using Sparse Online Gaussian Process Regression

This paper presents the design of data-driven fault-tolerant control using sparse online Gaussian process regression (SOGPR) to stabilize an aircraft with left-wing damage. The structural damage causes changes in mass, moment of inertia, center of gravity, and aerodynamic coefficients. These parameter variations deteriorate the performance of model-based nonlinear control methods. Hence, Gaussian process-based nonlinear dynamic inversion (GP-NDI) is proposed to compensate for uncertainties in situations of structural damage. Unlike parametric adaptive control approaches, Gaussian process regression is a non-parametric method that does not need prior information about uncertainties. And the proposed method implements SOGPR to reduce computational time and memory by incrementally updating the mean and variance. To compensate for the error in the estimated uncertainty, a robust control input is designed. In addition, a weighted delete score is used to improve the transient response. Numerical simulation results are compared with model reference adaptive control (MRAC) and nonlinear disturbance observer (NDO) to analyze a stabilizing and tracking performance in a structural damage situation.

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.

Coupled funnel control for supersonic tailless aerial vehicle on penetrating counter air

Supersonic Tailless Aerial Vehicles (STAVs) will become an essential force in Penetrating Counter Air (PCA), but STAVs do not have the traditional horizontal and vertical tails, making pitch and yaw control difficult. The attack angle and the sideslip angle need to be limited to ensure that the engine inlet and the aerodynamic rudder at the rear of the vehicle can work properly, which is the so-called security constraints. In addition, the tracking error of the aerodynamic angle needs to be limited to achieve effective attitude control or high-accuracy tracking of trajectories, which is the so-called performance constraints. To this end, an attitude control method that meets the needs of PCA has been devised, based on constraint definition, coupled constraints handling, and control law design. Firstly, mathematical descriptions of the security constraints, performance constraints, and control constraints are given. Secondly, two treatment methods, coupled command filter and coupled funnel control are proposed for the aerodynamic angle coupled constraint problem. Finally, based on Nonlinear Dynamic Inverse (NDI) design, the coupled funnel controller is designed and validated by simulation for two typical mission scenarios, high-altitude penetration and low-altitude surprise defence. The proposed control method not only satisfies the security and performance constraints of STAV attitude control but also is highly robust.

A flexible mixed-optimization with H∞ control for coupled twin rotor MIMO system based on the method of inequality (MOI)- An experimental study.

This article introduces a cutting-edge H∞ model-based control method for uncertain Multi Input Multi Output (MIMO) systems, specifically focusing on UAVs, through a flexible mixed-optimization framework using the Method of Inequality (MOI). The proposed approach adaptively addresses crucial challenges such as unmodeled dynamics, noise interference, and parameter variations. Central to the design is a two-step controller development process. The first step involves Nonlinear Dynamic Inversion (NDI) and system decoupling for simplification, while the second step integrates H∞ control with MOI for optimal response tuning. This strategy is distinguished by its adaptability and focus on balancing robust stability and performance, effectively managing the intricate cross-coupling dynamics in UAV systems. The effectiveness of the proposed approach is validated through simulations conducted in MATLAB/Simulink environment. Results demonstrated the efficiency of the proposed robust control approach as evidenced by reduced steady-state error, diminished overshoot, and faster system response times, thus significantly outperforming traditional control methods.

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.

Experimental Nonlinear and Incremental Control Stabilization of a Tail-Sitter UAV with Hardware-in-the-Loop Validation

Tail-sitters aim to combine the advantages of fixed-wing aircraft and rotorcraft but require a robust and fast stabilization strategy to perform vertical maneuvers and transitions to and from aerodynamic flight. The research conducted in this work explores different nonlinear control solutions for the problem of stabilizing a tail-sitter when hovering. For this purpose, the first controller is an existing strategy for tail-sitter control obtained from the literature, the second is an application of Nonlinear Dynamic Inversion (NDI), and the last one is its incremental version, INDI. These controllers were implemented and tuned in a simulation in order to stabilize a model of the tail-sitter, complemented by estimation methods that allow the feedback of the necessary variables. These estimators and controllers were then implemented in a microcontroller and validated in a Hardware-in-the-Loop (HITL) scenario with simple maneuvers in vertical flight. Lastly, the developed control solutions were used to stabilize the aircraft in experimental flight while being monitored by a motion capture system. The experimental results allow the validation of the model of the X-Vert and provide a comparison of the performance of the different control solutions, where the INDI presents itself as a robust control strategy with accurate tracking capabilities and less actuator demand.

Event-Based Guidance and Incremental Control with Application to Fixed-wing Unmanned Aerial Vehicle Perched Landing Maneuvers

Considering the nonlinearity and unknown dynamics of fixed-wing unmanned aerial vehicles in perched landing maneuvers, an event-based online guidance and incremental control scheme is proposed. The guidance trajectory for perched landing must be dynamically feasible therefore an event-based trapezoidal collocation point optimization method is proposed. Introduction of the triggering mechanism for the rational use of computing resources to improve PL accuracy. Furthermore, a filter-based incremental nonlinear dynamic inverse (F-INDI) control with state transformation is proposed to achieve robust trajectory tracking under high angle of attack (AOA). The F-INDI uses low-pass filters to obtain incremental dynamics of the system, which simplifies the design process. The state transformation strategy is to convert the flight-path angle, AOA and velocity into two composite dynamics, which avoids the sign reversal problem of control gain under high AOA. The stability analysis shows that the original states can be controlled only by controlling the composite state. Simulation results show that the proposed scheme achieves high perched landing accuracy and a reliable trajectory tracking control.

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.

Tau Theory-Based Flare Control in Autonomous Helicopter Autorotation

A novel trajectory generation and control architecture for fully autonomous autorotative flare that combines rapid path generation with model-based control is proposed. The trajectory generation component uses optical Tau theory to compute flare trajectories for both longitudinal and vertical speed. These flare trajectories are tracked using a nonlinear dynamic inversion (NDI) control law. One convenient feature of NDI is that it inverts the plant model in its feedback linearization loop, which eliminates the need for gain scheduling. However, the plant model used for feedback linearization still needs to be scheduled with the flight condition. This key aspect is leveraged to derive a control law that is scheduled with linearized models of the rotorcraft flight dynamics obtained in steady-state autorotation, while relying on a single set of gains. Computer simulations are used to demonstrate that the NDI control law is able to successfully execute autorotative flare in the UH-60 aircraft. Autonomous flare trajectories are compared to piloted simulation data to assess similarities and discrepancies between piloted and automatic control approaches. Trade studies examine which combinations of downrange distances and altitudes at flare initiation result in successful autorotative landings.

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.

Curved-Line Path-Following Control of Fixed-Wing Unmanned Aerial Vehicles Using a Robust Disturbance-Estimator-Based Predictive Control Approach

In this research, the design of a robust curved-line path-following control system for fixed-wing unmanned aerial vehicles (FWUAVs) affected by uncertainties on the latitude plane is studied. This is undertaken to enhance closed-loop system robustness under unknown uncertainties and derive the control surface deflection angle directly used to control FWUAVs, which has rarely been studied in previous works. The system is formed through the mass center position control (MCPC) and yaw angle control (YAC) subsystems. In the MCPC, the desired yaw angle, which is treated as the reference signal for the YAC subsystem, is calculated analytically using path-following errors, current flow angles, and the yaw angle. In the YAC, a disturbance estimator is designed to estimate uncertainties such as nonlinearities, couplings, time variations, model parameter perturbations, and unmodeled dynamics. Predictive functional controllers are designed to target nominal systems in the absence of uncertainties, such that the estimations of the uncertainties can be incorporated through feedback for closed-loop system robustness enhancement. The simulation results show that higher path-following precision and stronger robustness for the FWUAVs based on the proposed approach can be achieved using only rough model parameters compared with the conventional nonlinear dynamic inversion, which requires detailed model information.

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.

Nonlinear Control Allocation Using a Piecewise Multilinear Representation

Nonlinear control allocation is an important part of modern nonlinear dynamic inversion based flight control systems which require a highly accurate model of aircraft aerodynamics. Generally, an accurately implemented onboard model determines how well the system nonlinearities can be canceled. Thus, a more accurate model results in better cancellation, leading to higher performance of the controller. In this paper, a control system is presented that combines nonlinear dynamic inversion with a piecewise multilinear representation based control allocation. The piecewise multilinear representation is developed through a generalization of the Kronecker product for block matrices, combined with the canonical piecewise linear representation of nonlinear functions. Analytical expressions for the Jacobian of the piecewise multilinear model are also presented. The proposed formulation gives an equivalent analytical representation of piecewise multilinear aerodynamic data and thus is capable of accurately modeling nonlinear aerodynamics over the entire flight envelope of an aircraft. The resulting nonlinear controller is applied to control a tailless flying wing aircraft with ten independently operating control surfaces. The simulation results for two innovative control surface configurations indicate that an accurate control allocation performance can be achieved, leading to better tracking performance compared with the control allocation methods based on multivariate polynomials and splines.

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.