J.A. Mulder

Nonlinear Flight Control Design Using Constrained Adaptive Backstepping

The design of an adaptive backstepping flight control law for the F-16/MATV (multi-axis thrust vectoring) aircraft is discussed. The control law tracks reference trajectories with the angle of attack a, the stability-axes roll rate p s , and the total velocity V T . Furthermore, the sideslip angle β has to be kept at zero. B-spline neural networks are used inside the parameter update laws of the backstepping control law to approximate the uncertain aerodynamic forces and moments. Command filters are used to implement the constraints on the control surfaces and the virtual control states. The stability of the parameter estimation process during periods of saturation is guaranteed by using a modified tracking error definition, in which the effect of the saturation has been filtered out. The controller and its performance are evaluated on a nonlinear, six-degrees-of-freedom dynamic model of an F-16/MATV aircraft in a number of simulation scenarios.

Real Time Damaged Aircraft Model Identification for Reconfiguring Flight Control

This paper presents a study on the real time identification process of a damaged aircraft model. This is part of a Delft University research project which investigates the possibilities of adaptive control methods for recovering damaged aircraft operating in failure conditions. With help of a Boeing 747 simulation model supplied by the Dutch Aerospace Laboratory, including realistic failure modes with additive as well as parametric failures, it is possible to analyse the considered method’s capabilities to identify these types of damage. The types of failures included in the simulation model describe also asymmetric damage, resulting in a situation where it is impossible to base the damaged aircraft model upon the concept of decoupled longitudinal and lateral motions. The considered identification method in this study is the so-called two step method, which has been continuously under development at Delft University of Technology over the last 20 years. The two consecutive steps of this method, which are its important cornerstones, are presented: Aircraft State Estimation (ASE) and Aerodynamic Model Identification (AMI). Also two important validation tests of this method are illustrated. Furthermore, modified stepwise regression (MSWR) is introduced as a model structure development tool. Thereafter, as an application, some preliminary identification results are shown for damaged aircraft models. Future work will include further investigations on the capabilities and eventual modifications on the current status of these methods, as well as the implementation of this resulting real time damaged aircraft model in an adaptive control strategy.

Robust Model Predictive Control of a Feedback Linearized System for a Lifting-body Re-entry Vehicle

Model Predictive Control (MPC) has the advantage of including constraints into the optimization. By combining MPC with Feedback Linearization (FBL) it is possible to use linear, discrete time MPC algorithms with nonlinear models. This way the constraints on the control systems, thrusters and aerodynamic surface deflections, and on the attitude of the vehicle can be integrated into the controller synthesis. The main disadvantage of this type of controller is the lack of robustness when uncertainties enter the system. This paper therefore improves the nominal FBL-MPC controller by replacing the Quadratic Programming algorithm with a minmax MPC technique involving Linear Matrix Inequalities. Uncertainties on the nonlinear aerodynamic coecients are used as a source of disturbances. By mapping these uncertainties to a linear state space model as used by the MPC controller, a polytopic set of uncertainty models is created that can be used by the min-max algorithm to minimize the performance cost over the worst case model from the uncertainty set. This approach will be illustrated using a model of the X-38 re-entry vehicle flying along a predefined trajectory with active input and state constraints. The results show that the robustness is improved significantly when compared to the nominal controller with the same uncertainties.

Constrained Adaptive Backstepping Flight Control: Application to a Nonlinear F-16/MATV Model

A constrained adaptive backstepping approach is used to design a flight control law for the nonlinear model of an F-16/MATV fighter aircraft. The objectives of the control law are to track command trajectories with the total velocity VT, the angle of attackand the stability-axes roll rate ps. Furthermore, regulation of the sideslip angleis provided. On-line parameter update laws that make use of B-spline neural networks are used to approximate the aerodynamic force and moment coefficients. Using the neural networks inside the adaptive backstepping framework ensures a stable weight updating process. The parameter update laws are able to compensate for any uncertainties or changes in the aerodynamics. The control law makes use of command filters to implement any physical or operating constraints on the control variables and states. The effect of these constraints on the input and states is estimated and used by the update laws to ensure a stable parameter estimation process even when these limitations are in effect. Simulation examples are presented to evaluate the control law on the nonlinear model of an F-16 fighter aircraft with Multi-Axis Thrust Vectoring (MATV) model. Initial simulations verify that the adaptive control law performs well on the undamaged aircraft model, the B-spline networks are able to estimate the dependency of the aerodynamic data on the aircraft variables. Longitudinal maneuvers with some symmetric structural damage and actuator damage scenarios are also simulated, where the adaptive control law has to deal with large sudden changes in the dynamics of the F-16/MATV model. The results of these simulations show that the constrained adaptive backstepping control law is able to provide accurate tracking, even after these sudden failures have occurred.

Flight control of atmospheric re-entry vehicle with non-linear dynamic inversion

This paper concerns the design of an attitude control system for a six-degree-of-freedom atmospheric re-entry vehicle. The dynamics of the vehicle’s rotation is described with the full set of equations of motion. The control objectives are to obtain tight reference-tracking of the total-angle-of-attack, as well as to keep the vehicle spinning around the body x-axis at the desired speed. The control system is constructed by using the nonlinear dynamic inversion technique in combination with the classical PID control. Three sets of thrusters are mounted on the vehicle to provide the necessary control moments. This technique provides satisfactory results, which are tested by using nonlinear six-degree-of-freedom simulations.

Continuous Adaptive Critic Flight Control aided with Approximated Plant Dynamics

A relatively new approach to adaptive flight control is the use of reinforcement learning methods. Controllers that apply reinforcement learning methods learn by interaction with the environment and their ability to adapt themselves online makes them especially useful in adaptive and reconfigurable flight control systems. This paper is focused on a group of reinforcement learning methods, called Adaptive Critic Designs(ACD), that are characterized by their subdivision of tasks and components (actor/critic). One specific ACD that has previously been implemented in a helicopter flight control system is Action Dependent Heuristic Dynamic Programming(ADHDP). The exchange of information between the actor and the critic component in ADHDP controllers is by means of a direct connection of the actor output to the critic input, although the actor output is not a necessary input for the critic to accurately estimate the optimal value function. An alternative approach to this information exchange is implemented where the actor network is disconnected from the critic and the update of the actor network is realized by using a neural network that approximates the dynamics of the plant that is controlled. The approximated plant dynamics network is then updated online to adapt to changes in the plant dynamics. This alternative controller is called the action independent Heuristic Dynamic Programming (HDP) controller using approximated plant dynamics. The goal of this paper is to gain insight into the theoretical and practical differences between the ADHDP and the HDP controller, when applied in an online environment with changing plant dynamics. To investigate the practical differences the ADHDP and HDP controllers are implemented for a model of the General Dynamics F-16 and the characteristics of the controllers are investigated and compared to each other by conducting two types of experiments. First the controllers are trained offline to control the baseline F-16 model, next the dynamics of the F-16 model are changed online and the controllers will have to adapt to the new plant dynamics. The results from the offline experiments show that the HDP controller with the approximated plant dynamics has a higher success ratio for learning to control the baseline F-16 model. Both the baseline ADHDP and HDP controllers can already cope with some changes in the plant dynamics without adapting themselves. The online experiments further show that the HDP controller outperforms the ADHDP controller in adapting to changed plant dynamics. The HDP controller is more sensitive to measurement noise than the ADHDP controller, but can be used with a wider range of initial flight conditions.

Flight Envelope Clearance of Atmospheric Re-entry Module with Flight Control

The paper concerns the flight envelope clearance of a six-degree-of-freedom (6 DOF) re-entry vehicle with flight control, i.e. the analysis of the vehicle’s dynamic stability in its flight envelope. A brief description is given about the controller, which is based on the nonlinear dynamic inversion technique combined with the classical PID control. The objectives of the control system are to track the reference attitude angles and to keep the vehicle spinning at the desired speed. The clearance methods aim to test the stability robustness of the control system in the presence of model uncertainties. The two methods used in this work, i.e. the structured singular values and the interval analysis, allow one to robustly certify compact regions of uncertainty affecting the nominal model. By application of the method to analyse the control system’s stability, we show that in this way we can eliminate the drawback of classical Monte-Carlo based robust stability analysis methods which may fail to detect instabilities due to critical combinations of system parameters. Moreover, we can also perform worst-case simulations of the dynamical system in question.

Online Adaptive Critic Flight Control using Approximated Plant Dynamics

A relatively new approach to adaptive flight control is the use of reinforcement learning methods such as the adaptive critic designs. Controllers that apply reinforcement learning methods learn by interaction with the environment and their ability to adapt themselves online makes them especially useful in adaptive and reconfigurable flight control systems. This paper is focused on two types of adaptive critic design, one is action dependent and the other uses an approximation of the plant dynamics. The goal of this paper is to gain insight into the theoretical and practical differences between these two controllers, when applied in an online environment with changing plant dynamics. To investigate the practical differences the controllers are implemented for a model of the general dynamics F-16 and the characteristics of the controllers are investigated and compared to each other by conducting several experiments in two phases. First the controllers are trained offline to control the baseline F-16 model, next the dynamics of the F-16 model are changed online and the controllers will have to adapt to the new plant dynamics. The result from the offline experiments show that the controller with the approximated plant dynamics has a higher success ratio for learning to control the baseline F-16 model. The online experiments further show that this controller outperforms the action dependent controller in adapting to changed plant dynamics

Virtual Reality Modeling Simulation of the Re-Entry Motion of an Axialsymmetric Vehicle

This work started during the stability analysis of the Delft Aerospace Re-entry Test demonstrator (DART) which is a small axisymmetric ballistic re-entry vehicle. The dynamic stability evaluation of an axisymmetric re-entry vehicle is especially concerned on the behaviour of its angle of attack during the flight through the atmosphere. The variation in the angle of attack is essential for prediction of the trajectory of the vehicle and for heating requirement of the structure of the vehicle. The concept of the total angle of attack and the windward meridian plane are introduced. The position of the centre of pressure can be a crucial point in the stability of the vehicle. Although the simpleness of an axisymmetric shape, the re-entry of such a vehicle is characterised by several complex phenomenologies that were analysed with the aid of the flight simulator and of a 3D virtual reality modeling simulator.

Re-entry flight controller design using nonlinear dynamic inversion

This paper discusses the application of Nonlinear Dynamic Inversion to the design of a flight controller for atmospheric re-entry. The subject of the research is a re-entry vehicle in study at the Control and Simulation Division of the Faculty of Aerospace Engineering. This vehicle is a so-called small wingless lifting body, which produces lift by the body itself flying with an high angle of attack. It will have fully automated re-entry and landing, and it will be used in emergency situations. The vehicle will have a small crew, and therefore several constraints in terms attitude control arise. Common control approaches did not show satisfactory results in dealing with this type of application, mainly due to the fact that re-entry is characterized by a large flight envelope. Thus, linear control is not an option is such a case; instead, a nonlinear control approach should be used. The proposed control technique is Nonlinear Dynamic Inversion, whose concept has attracted research interest in years, with the increase of computational capability of onboard computers. MATLAB/SIMULIK was the environment chosen for the development and implementation of the NDI flight controller. The inversion of the vehicles dynamics was divided in two main phases: the inversion of the equations of motion; and the inversion of the aerodynamic database. The vehicles actuators were studied and assigned to generate the attitude commands imposed by the controller. In order to solve the problem of the lack of one actuator during part of the re-entry flight, input-output linearization was performed using well-know techniques. Numerical simulation tests and analyses were conducted to verify the correctness and performance of the controller. The final attitude controller was tested by using reference pre-computed trajectories. Further validation was performed by means of comparison between the NDI controller and other available controllers. The final evaluation of the tests results lead to the conclusion that the NDI controller was able to control the attitude maneuvers of the Lifting Body Re-entry Vehicle. Moreover, this controller was able to generically respect the constraints imposed in terms of maximum acceptable heat flux and g-load.