Dynamic Inversion Research Articles

Combining seismic signal dynamic inversion and numerical modeling improves landslide process reconstruction

Abstract. Landslides present a significant hazard for humans, but continuous landslide monitoring is not yet possible due to their unpredictability. In recent years, numerical simulation and seismic inversion methods have been used to provide valuable data for understanding the entire process of landslide movement. However, each method has shortcomings. Dynamic inversion based on long-period seismic signals gives the force–time history of a landslide using an empirical Green's function but lacks detailed flowing characteristics for the hazards. Numerical simulation can simulate the entire movement process, but results are strongly influenced by the choice of modeling parameters. Therefore, developing a method for combining those two techniques has become a focus for research in recent years. In this study, we develop such a protocol based on analysis of the 2018 Baige landslide in China. Seismic signal inversion results are used to constrain and optimize the numerical simulation. We apply the procedure to the Baige event and, combined with a field geological survey, show it provides a comprehensive and accurate method for dynamic process reconstruction. We found that the Baige landslide was triggered by detachment of the weathered layer, with severe top fault segmentation. The landslide process comprised four stages: initiation, main slip, blocking, and deposition. Multi-method mutual verification effectively reduces the inherent drawbacks of each method, and multi-method joint analysis improves the rationality and reliability of the results. The approach outlined in this study could help us to better understand the landslide dynamic process.

Consensus Tracking of Nonlinear Agents Using Distributed Nonlinear Dynamic Inversion with Switching Leader-Follower Connection

In this paper, a consensus tracking protocol for nonlinear agents is presented, which is based on the Nonlinear Dynamic Inversion (NDI) technique. Implementation of such a technique is new in the context of the consensus tracking problem. The tracking capability of nonlinear dynamic inversion (NDI) is exploited for a leader-follower multi-agent scenario. We have provided all the mathematical details to establish its theoretical foundation. Additionally, a convergence study is provided to show the efficiency of the proposed controller. The performance of the proposed controller is evaluated in the presence of both (a) random switching topology among the agents and (b) random switching of leader-follower connections, which is realistic and not reported in the literature. The follower agents track various trajectories generated by a dynamic leader, which describes the tracking capability of the proposed controller. The results obtained from the simulation study show how efficiently this controller can handle the switching topology and switching leader-follower connections.

Incremental nonlinear dynamic inversion based path‐following control for a hybrid quad‐plane unmanned aerial vehicle

AbstractHybrid quad‐plane unmanned aerial vehicles (UAVs), which combine the advantages of multicopters and fixed‐wing UAVs, are gaining increasing attention. However, quad‐planes are characterized by complex structures, high nonlinearity, strong coupling, and three flight regimes (hover, transition, and fixed‐wing flight), which bring great challenges to the research of their control laws. This article aims to design control laws for a quad‐plane in fixed‐wing and hover flight regimes based on a robust nonlinear control method, incremental nonlinear dynamic inversion (INDI), so that the quad‐plane can follow a given path autonomously. Firstly, a mathematical model of the quad‐plane is established on the basis of kinematics and dynamics. Subsequently, cascade control structures are proposed and divided into inner and outer loops. A control law is designed for each control loop based on INDI. To improve the performance of the designed control law, reference models are added to the inner loops to shape the input commands and provide feedforward inputs. Finally, simulation results corroborate the performance and robustness of the proposed control law. Compared with the control law designed by active disturbance rejection control and proportional‐integral‐derivative control methods, the INDI‐based control law is more robust.

Parallel Dynamic Sparse Approximate Inverse Preconditioning Algorithm on GPU

The dynamic sparse approximate inverse (SPAI) preconditioner has proven to be effective in accelerating the convergence of iterative methods for large linear systems. Recently, accelerating it on graphics processing unit (GPU) has attracted considerable attention due to the fact that the cost of constructing the preconditioner is high. However, the existing parallel dynamic SPAI preconditioning algorithms on GPU are usually ineffective because of the out-of-memory error for large matrices. This motivates us to investigate how to accelerate the construction of dynamic SPAI preconditioners on GPU. In this article, we propose an efficient dynamic SPAI preconditioning algorithm on GPU, called GDSPAI. For our proposed GDSPAI, there are the following novelties: (1) a well-known dynamic SPAI preconditioning algorithm is substantially modified to address the main challenges of parallelization on GPU, (2) a parallel framework of constructing the dynamic SPAI preconditioner on GPU is presented on the basis of the modified dynamic SPAI preconditioning algorithm; and (3) each component of the preconditioner is computed in parallel inside a group of threads. Experimental results show that the proposed GDSPAI is effective for large matrices, and outperforms the popular preconditioning algorithms in three public libraries, as well as a recent parallel static SPAI preconditioning algorithm.

Vision-Based Nonlinear Incremental Control for a Morphing Wing With Mechanical Imperfections

Morphing structures have acquired much attention in the aerospace community because they enable an aircraft to actively adapt its shape during flight, leading to fewer emissions and fuel consumption. Researchers have designed, manufactured, and tested a morphing wing named SmartX-Alpha, which can actively alleviate loads while achieving the optimal lift distribution. However, the widely existing mechanical imperfections can degrade the performance of the morphing wing and even lead to instabilities. To tackle these issues, this article proposes a vision-based adaptive control approach to actively compensate for mechanical imperfections. In this approach, an incremental model is constructed online to identify the system dynamics using servo commands and vision measurements, and then, nonlinear dynamic inversion control is applied based on the identified model. This data-driven control approach with visual feedback has been validated by real-world experiments on the SmartX-Alpha. The results demonstrate that the vision-based system combined with the proposed control methodology can actively compensate for mechanical imperfections with minimal adjustments to the actual system design. Compared to a controller that only uses a feedforward input-output mapping, this proposed approach improves the system performance and decreases the tracking errors by more than 62% despite disturbances. The results collectively demonstrate the effectiveness of the proposed control system, which sets a foundation for realizing morphing in next-generation 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.

A Comparative Study of Nonlinear MPC and Differential-Flatness-Based Control for Quadrotor Agile Flight

Accurate trajectory-tracking control for quadrotors is essential for safe navigation in cluttered environments. However, this is challenging in agile flights due to nonlinear dynamics, complex aerodynamic effects, and actuation constraints. In this article, we empirically compare two state-of-the-art control frameworks: the nonlinear-model-predictive controller (NMPC) and the differential-flatness-based controller (DFBC), by tracking a wide variety of agile trajectories at speeds up to 20 m/s (i.e., 72 km/h). The comparisons are performed in both simulation and real-world environments to systematically evaluate both methods from the aspect of tracking accuracy, robustness, and computational efficiency. We show the superiority of the NMPC in tracking dynamically infeasible trajectories, at the cost of higher computation time and risk of numerical convergence issues. For both methods, we also quantitatively study the effect of adding an inner loop controller using the incremental nonlinear dynamic inversion method, and the effect of adding an aerodynamic drag model. Our real-world experiments, performed in one of the world’s largest motion capture systems, demonstrate more than 78% tracking error reduction of both NMPC and DFBC, indicating the necessity of using an inner loop controller and aerodynamic drag model for agile trajectory tracking.

Active control of human-induced vibrations on lightweight structures via electrodynamic actuator dynamics inversion

The active vibration absorber represents an effective means to mitigate excessive vibrations in low-damping structures. Nevertheless, the dynamics of the actuators employed in such systems may negatively affect their performance and stability restricting their operational frequency range. This article presents an application of dynamics inversion techniques to the force control of electrodynamic proof-mass actuators employed as active vibration absorbers in lightweight pedestrian structures. The dynamics inversion approach is applied to enhance the classical direct velocity feedback scheme. Additionally, a novel method relying on dynamics inversion is presented: the Broadband Force Cancellation Algorithm. This procedure consists in estimating, in real-time, the equivalent force acting on the system to later apply it back to the structure with the opposed sign. The effectiveness of the proposed methods is assessed via numerical simulations carried over a realistic model of an existing lightweight footbridge and an electrodynamic proof-mass actuator. Two load cases are analyzed: a fixed swept-sine force and a walking load. Both cases account for the actuator-structure interaction. The human-structure interaction is considered in the latter scenario due to its importance when dealing with lightweight pedestrian structures. Simulation results demonstrate that the dynamics inversion techniques effectively cancel out actuator dynamics leading to an excellent tracking of the reference force output by the suggested or other vibration control algorithm. The proposed schemes are proved promising since they substantially outperform the widespread direct velocity feedback approach. In particular, the Broadband Force Cancellation Algorithm minimizes the action of the external forces within their estimation frequency range, thus being especially suited to tackle broadband excitations, important in lively pedestrian structures, whereas the velocity feedback methodology performs best at the structural resonant frequencies.

Broadband Dynamic Rupture Modeling With Fractal Fault Roughness, Frictional Heterogeneity, Viscoelasticity and Topography: The 2016 Mw 6.2 Amatrice, Italy Earthquake

AbstractAdvances in physics‐based earthquake simulations, utilizing high‐performance computing, have been exploited to better understand the generation and characteristics of the high‐frequency seismic wavefield. However, direct comparison to ground motion observations of a specific earthquake is challenging. We here propose a new approach to simulate data‐fused broadband ground motion synthetics using 3D dynamic rupture modeling of the 2016 Mw 6.2 Amatrice, Italy earthquake. We augment a smooth, best‐fitting model from Bayesian dynamic rupture source inversion of strong‐motion data (<1 Hz) with fractal fault roughness, frictional heterogeneities, viscoelastic attenuation, and topography. The required consistency to match long periods allows us to quantify the role of small‐scale dynamic source heterogeneities, such as the 3D roughness drag, from observational broadband seismic waveforms. We demonstrate that 3D data‐constrained fully dynamic rupture synthetics show good agreement with various observed ground‐motion metrics up to ∼5 Hz and are an important avenue toward non‐ergodic, physics‐based seismic hazard assessment.

Robustification of stabilizing controllers for ODE-PDE-ODE systems: A filtering approach

In this paper, we present a filtering technique that robustifies stabilizing controllers for systems composed of heterodirectional linear first-order hyperbolic Partial Differential Equations (PDEs) interconnected with Ordinary Differential Equations (ODEs) through their boundaries. The actuation is either available through one of the ODE or at the boundary of the PDE. The proposed framework covers a broad general class of interconnected systems. Assuming that a stabilizing controller is available, we derive simple sufficient conditions under which appropriate low-pass filters can be combined with the control law to robustify the closed-loop system. Our approach is based on a rewriting of the distributed dynamics as a delay-differential algebraic equation and an analysis in the Laplace domain. The proposed technique will simplify the design of stabilizing controllers for the class of systems under consideration (which can now be done only on a case-by-case basis due to the complexity and generality of the underlying interconnections) since it dissociates the stabilization problem from the robustness aspects. Indeed, it becomes possible to use convenient (but non-robust) techniques for the stabilization of such systems (as the cancellation of the boundary coupling terms or the inversion of the ODE dynamics), knowing that the resulting control law can be made robust (to delays and uncertainties) using the proposed filtering methodology.

Atmospheric Density Response to a Severe Magnetic Storm Detected by the 520 km Altitude Spherical Satellite

The polar-orbiting spherical experimental satellite of China for atmospheric density detection with an altitude of ~520 km was successfully launched on 14 October 2021. Based on the dynamic inversion method for atmospheric density and the precise orbit determination data obtained by its GNSS, we inverted the orbital atmospheric density during the severe geomagnetic storm in early November 2021. In this paper, we compared the atmospheric density data obtained by the spherical satellite with the simulations of the MSISE00 and the DTM, evaluated their error distribution, and analyzed the response of the atmospheric density during the severe geomagnetic storm in the dawn–dusk orbit of 520 km altitude. The properties and the physical processes for the atmospheric density of the time evolutions in different latitudes and the global distributions during the severe geomagnetic storm were obtained. We found that the substantial disturbance enhancement and recovery of the atmospheric density of the dawn–dusk orbit have a close correlation with the geomagnetic indexes Kp and Dst. The elevation extends from the poles to the equator, and the relative variation in two hemispheres demonstrates a bimodal nearly symmetric growth structure. The maximum relative variation of the two hemispheres both occurred in the middle latitude, and, for this case, the enhancement of atmospheric density in the mid-latitude region accounted for a larger proportion. The asymmetry between the northern and southern hemispheres is demonstrated by the fact that the absolute value and absolute change in the southern hemisphere in summer are larger than those in the northern hemisphere, and the bimodal structure of the relative variation is inclined to the northern hemisphere.

Incremental control system design and flight tests of a micro-coaxial rotor UAV

This paper applies the incremental nonlinear dynamic inversion (INDI) method to the control system design of coaxial rotor UAVs. The aerodynamic uncertainties and anti-disturbances problems are solved in the control system design. The designed controller gives the UAV excellent flight performance and control robustness. The incremental gain method (IGM) is adopted for the delay problem of the state derivatives. This method has the advantages of less calculation load and simple parameter adjustment, which provides excellent convenience for applying INDI controllers to coaxial rotor UAVs. The principle of IGM is further investigated by the discrete-time stability analysis methods, and the parameter selection strategy of the IGM is provided. The advantages of the controller design method are verified by comparative flight tests. The experimental results show that the average trajectory tracking error of INDI is only 58.3% of that of NDI under the same wind speed. When the angular acceleration delay is less than 0.06 s, IGM can easily keep the system stable. In addition, INDI has better robustness under obvious model errors and strong input disturbances.

Fast inner-loop control of air-breathing hypersonic vehicles

This paper investigates the inner-loop attitude and velocity control problem for air-breathing hypersonic vehicles subject to practically constrained actuators. Traditional nonlinear dynamic inverse (NDI) is enhanced by an intelligent control allocation (ICA) to realise the low-complexity attitude decoupling. The ICA addresses various characteristics of aerodynamic control surfaces while providing an efficient detecting mechanism for allocation errors. Within the ICA-NDI frame, a finite-time disturbance observer-based terminal sliding mode (FTDO-based TSM) attitude controller regulates Euler angles in the fast manner. This attitude controller employs an improved integral sliding surface containing necessary information from both ICA detection and FTDO estimation, which, therefore, is capable of accommodating constrained control surfaces and rejecting mismatched disturbances. Meanwhile, an adaptive governor adjusts the velocity reference according to the current saturation level of the scramjet fuel-to-air equivalency ratio. The governor is further integrated to a baseline adaptive velocity controller to synthetically handle scramjet input saturations and uncertain factors.

Automated 3-D Electromagnetic Manipulation of Microrobot With a Path Planner and a Cascaded Controller

Manipulating microrobots to move in a 3-D space is a basic requirement for their in vivo medical applications. In this study, the automatic manipulation of a microrobot in a liquid 3-D space via an electromagnetic coil system is investigated. A path planner is designed to search an optimal path in a 3-D space with obstacles automatically, and a cascaded control algorithm is developed to control the microrobot’s movement along the planned path. The path is generated by combining the A-star and minimum jerk methods. The collision of the generated path with the obstacles is prevented and the hysteresis caused by the current change is minimized by reducing the jerk of the movement with a passable path from the starting point to the endpoint. In the cascaded control algorithm, the incremental nonlinear dynamic inversion (INDI) method and a proportional control are used as the inner and outer loops to guide the microrobot’s movement along the desired trajectory with an appropriate velocity while eliminating the influence of system uncertainty and external disturbances. Simulation and experiments are performed to verify the effectiveness of the proposed control strategy.

Application of the Improved Incremental Nonlinear Dynamic Inversion in Fixed-Wing UAV Flight Tests

Incremental nonlinear dynamic inversion shows good robustness and low dependence on the model information. In this study, incremental nonlinear dynamic inversion is improved and utilized to solve the six-degrees-of-freedom waypoint tracking problem of fixed-wing unmanned aerial vehicles (UAVs). This research is focused on studying the acquisition of the state derivatives and the processing method of the derivative time delay. A nondelay differentiator design method and an incremental gain method that responds to time delay are developed in this study. Additionally, a universal waypoint navigation method based on incremental nonlinear dynamic inversion is put forward to enable the aircraft to successfully reach its waypoint from any spatial position and under any motion states. Finally, the proposed improvements of the incremental nonlinear dynamic inversion are verified through flight tests.

Hybrid Adaptive Dynamic Inverse Compensation for Hypersonic Vehicles with Inertia Uncertainty and Disturbance

This paper studies an intelligent hybrid compensation scheme for the uncertain parameter and disturbance of hypersonic flight vehicles (HFV). For the longitudinal model of HFV with modeling errors, a nominal nonlinear dynamic inverse (NDI) controller ensures that the system output can accurately track the reference command. In the presence of rotational inertia uncertainty, a multi-learning law adaptive NDI controller is proposed to directly compensate for its impact on tracking performance, making the system robust to the uncertainty and reducing high maneuvering attitude angles and velocities vibration. Then, an improved adaptive NDI controller with a sliding mode disturbance observer is designed to actively compensate for the elastic mode disturbance, and continuously ensure the system’s anti-disturbance flight quality. Ultimately, this active–passive hybrid control scheme compensates for both high maneuvering inertia uncertainty and global disturbance. The Lyapunov functions prove the system’s stability, and the semi-physical simulation platform verifies the effectiveness of the method.

Adaptive flight control system for flight safety improvement in reentry and other high-velocity vehicles

An adaptive controller and a nonlinear rate limiter are presented in order to improve the flight safety of manually controlled reentry vehicles and supersonic transport (SST) aircraft. The adaptive controller is based on the principle of dynamic inversion. The calculation of the controller parameters corresponding to the aerodynamic coefficients of the vehicle was carried out by a proposed online identification procedure. The effectiveness of the adaptive controller was tested through a set of experiments performed using a ground-based simulator. The obtained results were used to estimate the probability of an accident due to pilot error for the basic Space Shuttle flight control system and for its improved version with the adaptive controller. It was found that using the adaptive controller causes high required rates of elevon deflection. Because of the actuator's rate limiting, this is a source of pilot-induced oscillations. To counteract these oscillations in the pilot-vehicle closed loop system, an adaptive nonlinear rate limiter is introduced. The effectiveness of using the adaptive prefilter for improving the flight safety and flying qualities of the Space Shuttle reentry vehicle and an SST was demonstrated in experiments involving a ground-based simulator.

Control Design for a Marine Hydrokinetic Cycloturbine Vehicle

Abstract Marine Hydrokinetic (MHK) cycloturbines generate sustainable power by exploiting tidal currents. By powering the turbines and using pitching foils for control, a vehicle comprised of MHK cycloturbines also has the ability to station keep and maneuver. The vehicle consists of four counter-rotating cycloturbines, with hydrofoils oriented perpendicular to the flow in a paddlewheel configuration. Lift and drag generated from these foils sum together to produce thrust. An experimentally tuned simulation model that solves the six-degrees-of-freedom rigid body equations of motion for the MHK vehicle subject to hydrodynamic, hydrostatic, and propulsive forces is used to aid the design of vehicle controllers. Global feedback controllers are initially designed by applying classical control methods to an approximate linear model of the system dynamics. A higher performing nonlinear controller is designed using the nonlinear dynamic inversion (NDI) method. NDI accounts for the nonlinearities of the MHK system and therefore is suitable for a wide range of operating conditions. The response of the classical and NDI controllers to speed, depth, roll, pitch, and yaw commands are evaluated and compared in simulation. The classical controller outperforms the NDI controller for small amplitude maneuvers, although the degradation with NDI is minor. However, in the nonlinear operating regime the NDI controller outperforms the classical controller and the classical controller exhibits instability.

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.