Dynamic Inversion Control Law Research Articles

Rotary inverted pendulum control using neuro-adaptive robust generalized dynamic inversion

The objective of this research is to design a robust control system for trajectory tracking of the under-actuated Rotary Inverted Pendulum (RIP). The focus is on achieving semi-global asymptotic stability in the absence of knowledge about the RIP geometric and inertia parameters. The control design commences by formulating differential servo constraint dynamics (VCD) that encapsulates the control objectives for the RIP. The baseline generalized dynamic inversion (GDI) control law is derived by inverting the VCD for the control voltage input using the Moore–Penrose generalized inverse. To enhance robustness against modeling uncertainties and exogenous disturbances, a sliding mode control (SMC) element is integrated within the GDI control system, resulting in the robust GDI (RGDI) control system. Furthermore, an adaptive estimator that is based on Radial Basis Function Neural Networks (RBF-NN) is adopted to eliminate the dependency of the RGDI control system on the RIP mathematical model. The weighting matrices of the RBF-NN are updated with the aid of a Lyapunov control function. The proposed control system offers robust solution and guarantees semi-global asymptotic stability to the unstable equilibria of the RIP dynamics in the absence of a mathematical model. The proposed control system’s performance is evaluated through computer simulations and experimental tests on a real RIP system. Comparative analyses with traditional SMC and linear quadratic control methodologies are conducted to show the effectiveness of the proposed approach.

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.

Gliding Vehicle Controller Based on Neural Network Compensating Dynamic Inversion Error

Aiming at the attitude control problem of the gliding vehicle with uncertainty and strong coupling, a dynamic inversion control method based on RBF neural network compensated inversion error is discussed. Firstly, based on the double time scale separation hypothesis, the controlled aircraft model is divided into a fast and slow state subsystem. Then the dynamic inversion control laws are designed for each of the two subsystems. The weight update rule of the RBF neural network is derived online based on the Lyapunov stability principle to compensate for the inversion error caused by the modeling error and uncertainty. The simulation verifies the effectiveness of the control law. The robustness of the control system after neural network compensation is significantly improved.

Improved Adaptive NDI Flight Control Law Design Based on Real-Time Aerodynamic Identification in Frequency Domain

The traditional aircraft controller design is usually based on the off-line aerodynamic model. Due to the deviation of the off-line aerodynamic model, the flight quality is difficult to meet the requirements when the aircraft is flying in the real atmosphere. To solve this problem, this paper proposes a frequency domain identification-based improved adaptive nonlinear dynamic inversion (NDI) control method (FDI-ANDI). In this paper, an online recursive aerodynamic parameter identification method in the frequency domain is first designed, and then an adaptive dynamic inversion control method based on the online aerodynamic parameter identification results is established. Finally, aiming at the problem of the slow response speed of the NDI controller, an improved adaptive dynamic inversion control law is designed by using the method of series lead correction. Compared with the traditional control method, the adaptive dynamic inversion method based on online aerodynamic identification has stronger robustness and a faster response speed in the face of model uncertainty. The final simulation analysis shows that the method has a better control effect than the traditional control method.

A Dual Aircraft Maneuver Formation Controller for MAV/UAV Based on the Hybrid Intelligent Agent

This paper proposes a hybrid intelligent agent controller (HIAC) for manned aerial vehicles (MAV)/unmanned aerial vehicles (UAV) formation under the leader–follower control strategy. Based on the high-fidelity three-degrees-of-freedom (DOF) dynamic model of UAV, this method decoupled multiple-input-multiple-output (MIMO) systems into multiple single-input-single-output (SISO) systems. Then, it innovatively combined the deep deterministic policy gradient (DDPG) and the double deep Q network (DDQN) to construct a hybrid reinforcement learning-agent model, which was used to generate onboard desired state commands. Finally, we adopted the dynamic inversion control law and the first-order lag filter to improve the actual flight-control process. Under the working conditions of a continuous S-shaped large overload maneuver for the MAV, the simulations verified that the UAV can achieve accurate tracking for the complex trajectory of the MAV. Compared with the traditional linear quadratic regulator (LQR) and DDPG, the HIAC has better control efficiency and precision.

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.

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

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

Underactuated rotary inverted pendulum control using robust generalized dynamic inversion

The article applies the robust generalized dynamic inversion control methodology to the problem of stabilizing upright equilibrium configuration of the under-actuated rotary inverted pendulum system while tracking rotary motion of the actuated arm. The proposed robust generalized dynamic inversion control law comprised equivalent and switching control parts. The equivalent control part works to enforce a virtual constraint dynamics of the controlled state variables by means of Moore–Penrose generalized inversion. The switching control part is of the sliding mode type, and it improves robustness against unmodeled system dynamics, parametric uncertainties, and external disturbances. The robust generalized dynamic inversion control design on the linearized model of the under-actuated rotary inverted pendulum is shown to guarantee semi-global asymptotically stable tracking performance. Numerous computer simulations and experiments are conducted on the Quanser rotary inverted pendulum system, revealing that the proposed algorithm has better convergence and tracking performance than conventional sliding mode and generalized dynamic inversion control strategies when both are applied separately.

Three degrees of freedom rotary double inverted pendulum stabilization by using robust generalized dynamic inversion control: Design and experiments

The aim of this article was to determine control strategy for balance control of rotary double inverted pendulum system, which is highly nonlinear and unstable under-actuated system. The complexities involved in rotary double inverted pendulum dynamics make this system a useful engineering test bed to test and verify newly designed controllers. In this article, a constraint-based control approach titled robust generalized dynamic inversion is designed and implemented for robust stabilization of rotary double inverted pendulum system. The robust generalized dynamic inversion control is designed in two stages; in the first stage, constraint differential equations of the controlled state variables are prescribed, which encompasses the control objectives. To enforce the constraint dynamics, the equivalent control is realized by means of Moore–Penrose generalized inversion. To enhance robustness, the switching (discontinuous) control is introduced in second stage, whose design principle is based on classical sliding mode control theory. Finally, the controllers obtained in two stages are augmented to form the resultant robust generalized dynamic inversion control law. The proposed controller ensures robustness along with improved time domain performance regardless of system nonlinearities, uncertainties, and unwanted disturbances. The stability analysis is presented for guaranteeing semi-global asymptotically stable closed loop performance via Lyapunov stability criteria. Numerical simulation and experimental investigations are carried out along with comparative analysis, to demonstrate the effectiveness of robust generalized dynamic inversion control algorithm over other conventional control methods.

Flexible Aircraft Gust Load Alleviation with Incremental Nonlinear Dynamic Inversion

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

Disturbance observer based reliable H∞ fuzzy attitude tracking control for Mars entry vehicles with actuator failures

This paper introduces a disturbance observer (DO) based reliable H∞ fuzzy attitude tracking control design for Mars entry vehicles with actuator failures. Initially, to reduce the complexity of Takagi–Sugeno (T–S) fuzzy modeling, the two time-scale decomposition technique is used to divide the original nonlinear attitude tracking error model of Mars entry vehicles into a slow subsystem describing the attitude kinematics and a fast subsystem describing the attitude dynamics. The dynamic inversion control (DIC) method is subsequently applied to the slow subsystem to generate the angular velocity command. Then, the T–S fuzzy modeling method is employed to exactly represent the fast subsystem and a disturbance observer (DO) is constructed to estimate the modeled disturbance based on the derived tracking error fuzzy system of angular velocity. By the technique of linear matrix inequalities (LMIs), a DO based reliable H∞ fuzzy controller of attitude tracking is developed to stabilize exponentially the angular velocity tracking error and the modeled-disturbance state estimation error with an H∞ tracking performance both in nominal and actuator failure cases. Furthermore, it is shown that the original nonlinear tracking error system is also exponentially stable and satisfies an H∞ tracking performance both in nominal and actuator failure cases under the proposed fuzzy control law together with the DIC law, provided that the timescale separation between the fast and slow subsystems is valid. Finally, simulation results illustrate the effectiveness of the proposed design method.

Robust Adaptive Nonlinear Dynamic Inversion Control for an Air-breathing Hypersonic Vehicle

This paper presents a robust adaptive nonlinear dynamic inversion control approach for the longitudinal dynamics of an air-breathing hypersonic vehicle. The proposed approach adopts a fast adaptation law using high-gain learning rate, while a low-pass filter is synthesized with the modified adaptive scheme to filter out the high-frequency content of the estimates. This modified high-gain adaptive scheme achieves a good transient process and a nice robust property with respect to parameter uncertainties, without exciting high-frequency oscillations. Based on input-output linearization, the nonlinear hypersonic dynamics are transformed into equivalent linear systems. Therefore, the pole placement technique is applied to design the baseline nonlinear dynamic inversion controller. Finally, the simulation results of the modified adaptive nonlinear dynamic inversion control law demonstrate the proposed control approach provides robust tracking of reference trajectories.

Robust generalized dynamic inversion based control of autonomous underwater vehicles

A novel two-loop structured robust generalized dynamic inversion–based control system is proposed for autonomous underwater vehicles. The outer (position) loop of the generalized dynamic inversion control system utilizes proportional-derivative control of the autonomous underwater vehicle’s inertial position errors from the desired inertial position trajectories, and it provides the reference yaw and pitch attitude angle commands to the inner loop. The inner (attitude) loop utilizes generalized dynamic inversion control of a prescribed asymptotically stable dynamics of the attitude angle errors from their reference values, and it provides the required control surface deflections such that the desired inertial position trajectories of the vehicle are tracked. The dynamic inversion singularity is avoided by augmenting a dynamic scaling factor within the Moore–Penrose generalized inverse in the particular part of the generalized dynamic inversion control law. The involved null control vector in the auxiliary part of the generalized dynamic inversion control law is constructed to be linear in the pitch and yaw angular velocities, and the proportionality gain matrix is designed to guarantee global closed-loop asymptotic stability of the vehicle’s angular velocity dynamics. An additional sliding mode control element is included in the particular part of the generalized dynamic inversion control system, and it works to robustify the closed-loop system against tracking performance deterioration due to generalized inversion scaling, such that semi-global practically stable attitude tracking is guaranteed. A detailed six degrees-of-freedom mathematical model of the Monterey Bay Aquarium Research Institute autonomous underwater vehicle is used to evaluate the control system design, and numerical simulations are conducted to demonstrate closed-loop system performance under various types of autonomous underwater vehicle maneuvers, under both nominal and perturbed autonomous underwater vehicle system’s mathematical model parameters.

Force control of semi‐active valve lag dampers for vibration reduction in helicopters

This study considers the design of a closed-loop force-tracking system for a semi-active damper, designed to be used to reduce in-plane vibrations caused by helicopter rotor blades during steady-state forward flight conditions. The study describes the development of the control law and includes details of (i) how the initial mathematical model of the system is adapted for controller design; (ii) how a non-linear dynamic inversion (NDI) control law is modified into a form suitable for implementation; and (iii) how the free parameters in the NDI controller can be optimised for various different operational modes. The success of the approach is demonstrated through both force-tracking simulations and also more comprehensive tests in which the controller is incorporated into a large-scale vibration simulation of the AgustaWestland 101 helicopter. The results show that the NDI-based controller can provide a satisfactory level of performance and hence greatly assist in the reduction of unwanted vibrations.

Maneuver-Aided Active Satellite Tracking Using Six-DOF Optimal Dynamic Inversion Control

A generalized inter-satellite tracking problem, maneuver-aided active satellite tracking, is addressed here. An active satellite has uncooperative maneuver, which shortens the tracking window and worsens the tracking precision. For tracking an active target satellite, a spacecraft maneuver-aided tracking strategy (SMATS) is proposed. Consisting of a robust tracking algorithm, an osculating-orbit-based coordinate matching scheme, a six-degree-of-freedom (six-DOF) maneuver control law and a transfer function of tracking attitude, the proposed approach can not only achieve precise tracking, but also keep a chaser satellite autonomously staying with the desired position and attitude to guarantee the tracking continuity. Based on sufficient stability conditions derived from system error analysis, a six-DOF optimal dynamic inversion control (ODIC) law is developed. As a precise nonlinear optimal solution, it provides the most adequate control performance with minimum impact to the tracking result. Both formation and hovering keeping of active satellites are simulated to illustrate the efficiency of the proposed SMATS and the advantages of the ODIC law.

Safe Control for Spiral Recovery of Unmanned Aerial Vehicle

With unmanned aerial vehicles (UAVs) widely used in both military and civilian fields, many events affecting their safe flying have emerged. That UAV’s entering into the spiral is such a typical safety issue. To solve this safety problem, a novel recovery control approach is proposed. First, the factors of spiral are analyzed. Then, based on control scheduling of state variables and nonlinear dynamic inversion control laws, the spiral recovery controller is designed to accomplish guidance and control of spiral recovery. Finally, the simulation results have illustrated that the proposed control method can ensure the UAV autonomous recovery from spiral effectively.

Real time adaptive nonlinear model inversion control of a twin rotor MIMO system using neural networks

This paper investigates the development and experimental implementation of an adaptive dynamic nonlinear model inversion control law for a Twin Rotor MIMO System (TRMS) using artificial neural networks. The TRMS is a highly nonlinear aerodynamic test rig with complex cross-coupled dynamics and therefore represents the control challenges of modern air vehicles. A highly nonlinear 1DOF mathematical model of the TRMS is considered in this study and a nonlinear inverse model is developed for the pitch channel of the system. An adaptive neural network element is integrated thereafter with the feedback control system to compensate for model inversion errors. The proposed on-line learning algorithm updates the weights and biases of the neural network using the error between the set-point and the real output. The real-time response of the method shows a satisfactory tracking performance in the presence of inversion errors caused by model uncertainty. The approach is therefore deemed to be suitable to apply real-time to other nonlinear systems with necessary modifications.

Design UCAV Flight Control Law Based on Jamming Observer

In order to study the nonlinear jamming problem in UCAV’s flight control system, a method of using observer to check the system’s jamming was designed, constructed robust dynamic inversion control law based on jamming observer. The simulation results show that the robust dynamic inversion control law based on jamming observer, make UCAV’s flight control system have good stability and robustness, it’s a great convenience analyzing the system stability.

Adaptive non-linear model inversion control of a twin rotor multi-input multi-output system using artificial intelligence

This paper investigates the development of an adaptive dynamic non-linear model inversion control law for a twin rotor multi-input multi-output system (TRMS) utilizing artificial neural networks and genetic algorithms. The TRMS is an aerodynamic test rig representing the control challenges of modern air vehicles. A highly non-linear one degree of freedom mathematical model of the TRMS is considered in this study and a non-linear inverse model is developed for the pitch channel. In the absence of model inversion errors, a genetic algorithm-tuned proportional-derivative (PD) controller is used to enhance the tracking characteristics of the system. An adaptive neural network element is integrated, thereafter, with the feedback control system to compensate for model inversion errors. In order to show the effectiveness of the proposed method in the simulation environment an inversion error has deliberately been provided as an uncertainty in the real situation. Square and sinusoidal reference command signals are used to test the control system performance, and it is noted that an excellent tracking response is exhibited in the presence of inversion errors caused by model uncertainty.

Robustness Analysis of Nonlinear Flight Controllers

The development of robustness analysis tests is presented for quasi-linear-parameter-varying models in the presence of time-varying, parametric uncertainty. The tests are applied for the robustness analysis of nonlinear dynamic inversion control laws giving sufficient conditions for assessing the nonlinear system’s performance in the presence of bounded disturbances and uncertainty. The tests are formulated as linear minimisation problems subject to linear matrix inequality constraints and solved by using a gridding procedure. A detailed example is presented in which two nonlinear dynamic inversion control laws for the short-period dynamics of an aircraft are analysed and compared.