Nonlinear Dynamic Inversion Control Research Articles

Research on incremental nonlinear dynamic inverse control method for turboshaft engine based on Jacobi matrix

In order to enhance the anti-interference ability of the speed to external load and achieve the rapid response control for turboshaft engine of next-generation helicopters, an incremental nonlinear dynamic inverse (INDI) control method for turboshaft engine based on Jacobi matrix is proposed. First, the control law of turboshaft engine based on state variable model (SVM) is obtained according to the mathematical derivation of INDI. Then, based on adopting Jacobi matrix and sequential quadratic programming (SQP) algorithm, the SVM is online obtained, so as to express the steady and dynamic characteristics of turboshaft engines under different flight conditions precisely. Finally, several numerical simulations are conducted to validate the control effect of INDI control method. The results demonstrate that compared with cascade PID controller, INDI control method based on single SVM can significantly decrease the overshoot and sag of power turbine speed by more than 50% under constant flight conditions. Under variable flight conditions, INDI control method based on Jacobi matrix can effectively decrease the overshoot and sag of power turbine speed by more than 30% compared with INDI control method based on single SVM, which has more significant control effect and superior robustness, and realizes the fast response control of turboshaft engines.

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.

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.

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.

Design of Thrust Vectoring Vertical/Short Takeoff and Landing Aircraft Stability Augmentation Controller Based on L1 Adaptive Control Law

Aiming at the conversion process of thrust vectoring vertical/short takeoff and landing (V/STOL) aircraft with a symmetrical structure in the transition stage of takeoff and landing, there is a problem with the coupling and redundancy of the control quantities. To solve this problem, a corresponding inner loop stabilization controller and control distribution strategy are designed. In this paper, a dynamic system model and a dynamic model are established. Based on the outer loop adopting the conventional nonlinear dynamic inverse control, an L1 adaptive controller is designed based on the model as the inner loop stabilization control to compensate the mismatch and uncertainty in the system. The key feature of the L1 adaptive control architecture is ensuring robustness in the presence of fast adaptation, so as to achieve a unified performance boundary in transient and steady-state operations, thus eliminating the need for adaptive rate gain scheduling. The control performance and robustness of the controller are verified by inner loop simulation and the shooting Monte Carlo approach. The simulation results show that the controller can still track the reference input well and has good robustness when there is a large parameter perturbation.

Robust Trajectory-Tracking for a Bi-Copter Drone Using INDI: A Gain Tuning Multi-Objective Approach

This paper presents an optimized robust trajectory control system for an autonomous tiltrotor bi-copter based on an incremental nonlinear dynamic inversion (INDI) strategy combined with a set of PID/PD controllers. The methodology includes a lower level, fast attitude control action using an incremental nonlinear dynamic inversion (INDI) strategy, which is driven by a higher level, slow trajectory control action that uses nonlinear dynamic inversion (NDI). The nonlinear dynamic model of the drone is derived, and the basis of the motion and the design of the attitude and position stabilizing controllers are discussed. To develop and test the suggested controller, a circle-shaped flight profile is simulated. The linear control providing inputs to the NDI and INDI controllers is tuned via a novel multi-objective optimization auto-tuning method using the non-dominated sorting genetic algorithm II (NSGA-II). The tracking and disturbance rejection optimization is achieved via the use of the integral of time multiplied by the absolute error (ITAE) and the integral of the square of the error (ISE) objective functions, which are optimized concurrently. The simulation results reveal that the proposed control design outperforms the traditional dynamic inversion controller design and demonstrate that the developed INDI + PID/PD controller possesses exceptional accuracy and performance, enabling the tiltrotor bi-copter to track the given trajectory. Furthermore, the paper shows that the proposed controller produces 40% lower overshoot and settling time as measured with respect to previous backstepping controllers reported in the literature. The robustness of the controller is validated through diverse tests where the aircraft is subjected to external (wind gust) disturbances.

L1 Adaptive Structure-Based Nonlinear Dynamic Inversion Control for Aircraft with Center of Gravity Variations

L1 Adaptive Structure-Based Nonlinear Dynamic Inversion Control for Aircraft with Center of Gravity Variations

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.

Dynamic modeling and robust nonlinear control of a laboratory gas turbine engine

In this paper, a physics-based mathematical model of a mini SR-30 gas turbine engine (GTE) is presented using a state variable modeling method. This model is developed by utilizing approximated maps of the engine components and generic governing equations that describe the engine's behavior. The mathematical model captures both the steady-state and transient behavior of the engine. Using the developed model, a modern control system design approach is proposed to satisfy the stability and performance of the GTE. The objective of this control design is to adjust the required fuel flow rate to the combustion chamber such that the shaft speed of the engine tracks its command signal as closely as possible. The proposed robust nonlinear fuel flow controller is developed based on the nonlinear dynamic inversion (NDI) technique, augmented with a dual extended Kalman filter (DEKF) estimation design. DEKF-based state and parameter estimation are used here to ensure robustness against model inaccuracies due to not accurately known component maps, as well as process and measurement noises. To validate the developed mathematical model, the realistic data extracted from the SR-30 GTE are utilized. The simulation results of the proposed control design approach indicate that it is effective in achieving satisfactory performance of the engine. Also, the proposed NDI controller is compared with the well-established proportional-integral-derivative (PID) controller to illustrate its superiority.

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.

Neuro-adaptive augmented distributed nonlinear dynamic inversion for consensus of nonlinear agents with unknown external disturbance

This paper presents a novel neuro-adaptive augmented distributed nonlinear dynamic inversion (N-DNDI) controller for consensus of nonlinear multi-agent systems in the presence of unknown external disturbance. N-DNDI is a blending of neural network and distributed nonlinear dynamic inversion (DNDI), a new consensus control technique that inherits the features of Nonlinear Dynamic Inversion (NDI) and is capable of handling the unknown external disturbance. The implementation of NDI based consensus control along with neural networks is unique in the context of multi-agent consensus. The mathematical details provided in this paper show the solid theoretical base, and simulation results prove the effectiveness of the proposed scheme.

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

Signal reconstruction and disturbance observer-based fault-tolerant control for civil aircrafts

PurposeThis paper aims to focus on the sensor fault-tolerant control (FTC) for civil aircraft under exterior disturbance.Design/methodology/approachFirst, a three-step cubature Kalman filter (TSCKF) is designed to detect and isolate the sensor fault and to reconstruct the sensor signal. Meanwhile, a nonlinear disturbance observer (NDO) is designed for disturbance estimation. The NDO and the TSCKF are combined together and an NDO-TSCKF is proposed to solve the problem of sensor faults and bounded disturbances simultaneously. Furthermore, an FTC scheme is designed based on the nonlinear dynamic inversion (NDI) and the NDO-TSCKF.FindingsThe method is verified by a Cessna 172 aircraft model under bias gyro fault and constant angular rate disturbance. The proposed NDO-TSCKF has the ability of signal reconstruction and disturbance estimation. The proposed FTC scheme is also able to solve the sensor fault and disturbance simultaneously.Research limitations/implicationsNDO-TSCKF is the novel algorithm used in sensor signal reconstruction for aircraft. Then, disturbance observer-based FTC can improve the flight control system performances when the system with faults.Practical implicationsThe NDO-TSCKF-based FTC scheme can be used to solve the sensor fault and exterior disturbance in flight control. For example, the bias gyro fault with constant angular rate disturbance of a civil aircraft is studied.Social implicationsSignal reconstruction for critical sensor faults and disturbance observer-based FTC for civil aircraft are useful in modern civil aircraft design and development.Originality/valueThis is the research paper studies on the signal reconstruction and FTC scheme for civil aircraft. The proposed NDO-TSCKF is better than the current reconstruction filter because the failed sensor signal can be reconstructed under disturbances. This control scheme has a better fault-tolerant capability for sensor faults and bounded disturbances than using regular NDI control.

Robust dynamic inversion control of flight control system based on L1 adaptive structure

Nonlinear Dynamic Inversion(NDI) control has excellent rapidity and decoupling ability, unfortunately it lacks the essential robustness to disturbance. From the perspective of enhancing the robustness, an adaptive NDI method based on L1 adaptive structure is proposed. The L1 adaptive structure is introduced into the NDI control to enhance its robustness, which also guarantees the stability and expected dynamic performance of the system suffering from the disturbance influence. Secondly, the flight control law of the advanced aircraft is designed based on the present method to improve the robustness and fault tolerance of the flight control system. Finally, the effectiveness of the flight control law based on the present approach is verified under the fault disturbance. The results showed that the flight control law based on L1 adaptive NDI has excellent dynamic performance and strong robustness to parameter uncertainties and disturbances.

Incremental fault-tolerant control for a hybrid quad-plane UAV subjected to a complete rotor loss

Quad-plane is a popular type of electric vertical and takeoff/landing (eVTOL) vehicle that hybridizes a quadrotor and a fixed-wing airplane. However, the mechanical simplicity of a quad-plane also makes it vulnerable to rotor failures. When a complete rotor fails, it becomes physically impossible to stop the quad-plane from fast yaw spinning, which further induces considerable abnormal aerodynamic forces and moments on the wing. In this paper, a novel incremental adaptive sliding mode control (I-ASMC) is proposed to address these challenges. First, by exploiting sensor measurements, it simultaneously reduces the control model dependency and the minimum possible sliding mode control/observer gains. Second, finite-time convergence is guaranteed in the Lyapunov sense. Third, the control gains are automatically adapted to their minimum possible values without prior-knowledge on the uncertainty bounds. The proposed I-ASMC method is verified on a high fidelity simulation platform with computational fluid dynamic (CFD) aerodynamic models. Simulation results demonstrate that I-ASMC can drive a quad-plane with a complete loss of a single rotor to follow a trajectory. Its robustness to aerodynamic model uncertainties and rotor faults is also better than the linear quadratic regulator (LQR) and the incremental nonlinear dynamic inversion (INDI) control. In conclusion, the reduced model dependency, implementation simplicity, and improved robustness make the proposed I-ASMC promising for enhancing quad-plane safety in real life.

Nonlinear Incremental Control for Flexible Aircraft Trajectory Tracking and Load Alleviation

This paper proposes a nonlinear control architecture for flexible aircraft simultaneous trajectory tracking and load alleviation. By exploiting the control redundancy, the gust and maneuver loads are alleviated without degrading the rigid-body command tracking performance. The proposed control architecture contains four cascaded loops: position control, flight path control, attitude control, and optimal multi-objective wing control. Because the position kinematics are not influenced by model uncertainties, the nonlinear dynamic inversion control is applied. On the contrary, the flight path dynamics are perturbed by both model uncertainties and atmospheric disturbances; thus the incremental sliding mode control is adopted. Lyapunov-based analyses show that this method can simultaneously reduce the model dependency and the minimum possible gains of conventional sliding mode control methods. Moreover, the attitude dynamics are in the strict-feedback form; thus the incremental backstepping sliding mode control is implemented. Furthermore, a novel load reference generator is designed to distinguish the necessary loads for performing maneuvers from the excessive loads. The load references are realized by the inner-loop optimal wing controller, whereas the excessive loads are naturalized by flaps without influencing the outer-loop tracking performance. The merits of the proposed control architecture are verified by trajectory tracking tasks in spatial von Kármán turbulence fields.