Robust Nonlinear Control System Design For Hypersonic Flight Vehicles

This thesis develops a new nonlinear robust control design procedure which addresses some of the challenges associated with the control of uncertain nonlinear system and applies the proposed method to tracking control of an Air-breathing Hypersonic Flight Vehicle (AHFV). The AHFV is a highly nonlinear system and the combination of nonlinear dynamics, parameter uncertainty and complex constraints make the flight control design a challenging task for this type of vehicle. The main contribution of this thesis lies in the fact that it presents a robust feedback linerization based strategy which solves the control issue of a class of nonlinear systems subject to parametric uncertainty. The method is effectively applied to the tracking control of an AHFV. It is also demonstrated that the proposed approach can be used to design a single robust controller for a large flight envelope rather than using several gain scheduled controllers. This research, firstly presents three different approaches to develop linearized uncertainty models for a class of nonlinear systems using a robust feedback lnearization method. The feedback linearization approach to linearize the nonlinear dynamics has some advantages over the point linearization (Jacobian linearization) method. However, the feedback linearization method only linearizes the nominal model of a system and in the presence of uncertainty in the model the exact linearization is not possible. In this thesis, we present a robust approach to deal with the nonlinearities arising from the uncertainties in the system and use a nonlinear AHFV model to demonstrate the effectiveness of the method. Besides parametric uncertainty, due to the presence of body-integrated propulsion system, and the flexible modes, the nonlinear model of AHFV does not possess full relative degree. Any attempt to feedback linearize this nonlinear model will result into having input term in low order derivatives of the system output. In this research, we strategically remove the coupling and flexible effects from the nonlinear model and simplify the model in such a way that the full relative degree condition is satisfied. In the development of linearized uncertainty model for an AHFV the conventional feedback linearization approach is used to remove the known nonlinearities from the simplified system model and the nonlinearities arising from the uncertainties are treated in three different ways. In the first method, nonlinear uncertainties are linearized using Taylor expansion at an arbitrary point by considering a structured representation of uncertainties. This lienarization approach approximates the actual nonlinear uncertainty by considering only the first order terms and neglecting all the higher order terms. For the linearized model, a minimax Linear Quadratic Regulator (LQR) controller combined with feedback linearization law is proposed to fulfill the velocity and altitude tracking requirements of an AHFV. In the second method, an unstructured uncertainty representation is considered and a minimax Linear Quadratic Gaussian (LQG) controller combined with feedback linearization law is proposed for the same tracking requirements. In the third, method the nonlinear uncertainty terms are linearized at an arbitrary point using the generalized mean value theorem. The main advantages of using this approach are that upper bound on the uncertainties can be obtained by both structured and unstructured uncertainty representations and there is no need to ignore higher order uncertainty terms. The uncertain linearized models obtained from this method are followed by guaranteed cost and minimax LQR controllers combined with feedback linearization law. Rigorous simulations using actual nonlinear model for all the above methods are presented in the thesis to analyze the effectiveness of these controllers. These simulations have considered several cases of uncertainties for a step change in the reference commands. In order to see the robustness properties of the proposed robust scheme a Monte-Calro based simulation is also presented by considering the given bound on the uncertain parameters. Also, in order to demonstrate the effectiveness of the approach for a large flight envelope, several simulations are performed to observe the tracking response for the given reference trajectories in a large flight envelope.

In the past two decades, there has been a renewed and sustained effort devoted to modeling the dynamics of air-breathing hypersonic vehicles, for both simulation and control design purposes. The highly nonlinear characteristics of flight dynamics in hypersonic regimes and the consequent significance variability of the response with the operating conditions requires the development of innovative flight control solutions, hence the development of suitable model of the vehicle dynamics that are amenable to design, validation and rapid calibration of control algorithms. In this dissertation, a control-oriented and a simulation model of a generic hypersonic vehicle were derived to support the design and calibration of model-based flight controllers. A nonlinear robust adaptive controller was developed on the basis of the control-oriented model, that was shown to provide stable trajectory tracking in higher fidelity computer simulations. The first stage of this research was the development of a control design model (CDM) for the 6-degree-of-freedom dynamics of an air-breathing hypersonic aircraft based on an available high-fidelity first principle model. A method that incorporates the theory of compressible fluid dynamics and system identification methods, was proposed and implemented. The development of the CDM is based on curve fit approximation of the forces and moments acting on the vehicle, making the model suitable for control design. Kriging and Least Squares methods were used to find the most appropriate curve-fitted model of the aerodynamic forces for both the control design and the control simulation models. It was shown that the 6-DOF model can be both categorized as an under-actuated mechanical system, as well as an over-actuated system with respect to a chosen in- put/output pair of interest. An important contribution of this work is the development of a nonlinear adaptive controller for the 6-DOF control design model. The controller was endowed with a modular structure, comprised of an adaptive inner-loop attitude controller and a robust nonlinear outer-loop controller of fixed structure. The purpose of the outer- loop controller is to avoid the typical complexity of solutions derived from adaptive backstepping methods. A noticeable feature of the outer-loop controller is the presence of an internal model unit that generates the reference for the angle-of-attack, in spite of parametric model uncertainty. Airspeed, lateral velocity, vehicle's heading and altitude were considered as regulated outputs of the system. Simulation results on the control simulation model show the effectiveness of the developed controller in spite of significant variation in the flight parameters.

Abstract: This thesis presents the design of two nonlinear robust controllers for an air-breathing hypersonic vehicle model. To overcome the analytical intractability of a dynamical model derived from first principles, a simplified control-oriented model is used for control design. The control-oriented model retains most of the features of the original model, including non-minimum phase characteristic of the flight-path angle dynamics and strong couplings between the engine and flight dynamics, whereas flexibility effects, included in the simulation model, are regarded as a dynamic perturbation. In adopting reduced-complexity models for controller design, the issue of robustness with respect to model uncertainty must be carefully addressed and included at the design level. Dynamic inversion-based design methods do not lend themselves easily to quantitative robustness analysis, due to the complexity of the inverse model of the plant. In this work, a nonlinear sequential loop-closure approach is adopted to design two different dynamic state-feedback controllers that provide stable tracking of velocity and altitude reference trajectories. The approach considered utilizes a combination of adaptive and robust design methods based on both classical and recently developed nonlinear design tools. Simulation results indicate that the proposed methodology may constitute a feasible approach towards the development of robust nonlinear controllers that satisfactorily address the issue of model uncertainty for this type of application.

Abstract: This dissertation presents the design of two nonlinear robust controllers for an air-breathing hypersonic vehicle model capable of providing stable tracking of velocity and altitude (or flight-path angle) reference trajectories. To overcome the analytical intractability of a dynamical model derived from first principles, a simplified control-oriented model is used for control design. The control-oriented model retains the most important features of the model from which it was derived, including the non-minimum phase characteristic of the flight-path angle dynamics and strong couplings between the engine and flight dynamics. The first control design considers as control inputs the fuel equivalence ratio and the elevator and canard deflections. A combination of nonlinear sequential loop-closure and adaptive dynamic inversion has been adopted for the design of a dynamic state-feedback controller. An important contribution given by this work is the complete characterization of the internal dynamics of the model has been derived for Lyapunov-based stability analysis of the closed-loop system, which includes the structural dynamics. The results obtained address the issue of stability robustness with respect to both parametric model uncertainty, which naturally arises in adopting reduced-complexity models for control design, and dynamic perturbations due to the flexible dynamics. In the second control design a first step has been taken in extending those results in the case in which only two control inputs are available, namely the fuel equivalence ratio and the elevator deflection. The extension of these results to this new framework is not trivial since several issues arise. First of all, the vehicle dynamics are characterized by exponentially unstable zero-dynamics when longitudinal velocity and flight-path angle are selected as regulated output. This non-minimum phase behavior arises as a consequence of elevator-to-lift coupling. In the previous design the canard was strategically used to adaptively decouple lift from elevator command, thus rendering the system minimum phase. Moreover, the canard input was also employed to enforce the equilibrium at the desired trim condition and to provide a supplementary stabilizing action. As a result, when this control input is not assumed to be available, the fact that the system needs to be augmented with an integrator (to reconstruct the desired equilibrium) and the non-minimum phase behavior have a strong impact on the control design. In these preliminary results the flexible effects are not taken into account in the stability analysis but are considered as a perturbation and included in the simulation model. The approach considered utilizes a combination of adaptive and robust design methods based on both classical and recently developed nonlinear design tools. As a result, the issue of robustness with respect to parameter uncertainties is addressed also in this control design. Simulation results on the full nonlinear model show the effectiveness of both controllers.

Air-breathing hypersonic vehicles are emerging as a method for cost-efficient access to space. Great strides have recently been made in the field of hypersonic vehicles, however the unique dynamics of the vehicles present challenges for control design. In this thesis, a nonlinear controller for a hypersonic vehicle model is designed using the Indirect Manifold Construction approach. The high fidelity hypersonic vehicle model considered in this thesis includes many of the challenging effects of hypersonic flight. The main challenge to control design is the vehicle's unstable internal dynamics. This non-minimum phase behavior prevents the use of many standard forms of nonlinear control techniques. The nonlinear controller developed in this thesis following the Indirect Manifold Construction approach uses a hierarchical control design to force outputs to commanded values while ensuring the internal dynamics of the system remain stable. The nonlinear controller is shown to be effective in simulation. The closed loop system is also shown to be stable through a Lyapunov based stability analysis.

This book contains the original peer-reviewed research papers presented at the 6th China Aeronautical Science and Technology Conference held in Wuzhen, Zhejiang Province, China, in September 2023. Topics covered include but are not limited to Navigation/Guidance and Control Technology, Aircraft Design and Overall Optimisation of Key Technologies, Aviation Testing Technology, Airborne Systems/Electromechanical Technology, Structural Design, Aerodynamics and Flight Mechanics, Advanced Aviation Materials and Manufacturing Technology, Advanced Aviation Propulsion Technology, and Civil Aviation Transportation. The papers presented here share the latest findings in aviation science and technology, making the book a valuable resource for researchers, engineers and students in related fields.

Abstract: This thesis describes control oriented modelling, i.e. the development of a model which is amenable to control design, of an air-breathing hypersonic vehicle and nonlinear control design based on the constructed model. The full simulation model, or truth model, includes intricate couplings between the engine dynamics and the flight dynamics, along with complex interplay between the flexible and rigid modes of the vehicle. Furthermore, this model is found to be unstable and non-minimum phase with respect to the variables to be controlled. By replacing the complex force and moment functions with curve fitted approximations, neglecting certain weaker couplings, resorting to dynamic extension at the input side, and neglecting slower portions of the system dynamics, a control oriented model with full vector relative degree with respect to the regulated output is obtained. Standard dynamic inversion can then be applied to this model, resulting in approximate linearization of the input/output map of the truth model. A robust outer loop control is then designed using LQR with integral augmentation in a model reference scheme. Simulation results demonstrate that this technique achieves excellent tracking performance even in the presence of small plant parameter variations. The fidelity of the truth model is then increased by including additional flexible effects which render the original control design ineffective. A more elaborate control approach with an additional actuator is then employed to compensate for these new flexible effects, and simulation results which include mild plant parameter variations are presented.

This book includes original, peer-reviewed research papers from the ICAUS 2022, which offers a unique and interesting platform for scientists, engineers and practitioners throughout the world to present and share their most recent research and innovative ideas. The aim of the ICAUS 2022 is to stimulate researchers active in the areas pertinent to intelligent unmanned systems. The topics covered include but are not limited to Unmanned Aerial/Ground/Surface/Underwater Systems, Robotic, Autonomous Control/Navigation and Positioning/ Architecture, Energy and Task Planning and Effectiveness Evaluation Technologies, Artificial Intelligence Algorithm/Bionic Technology and Its Application in Unmanned Systems. The papers showcased here share the latest findings on Unmanned Systems, Robotics, Automation, Intelligent Systems, Control Systems, Integrated Networks, Modeling and Simulation. It makes the book a valuable asset for researchers, engineers, and university students alike.

Aerospace vehicles are by their very nature a crucial environment for safety-critical systems. By virtue of an effective safety control system, the aerospace vehicle can maintain high performance despite the risk of component malfunction and multiple disturbances, thereby enhancing aircraft safety and the probability of success for a mission. Autonomous Safety Control of Flight Vehicles presents a systematic methodology for improving the safety of aerospace vehicles in the face of the following occurrences: a loss of control effectiveness of actuators and control surface impairments; the disturbance of observer-based control against multiple disturbances; actuator faults and model uncertainties in hypersonic gliding vehicles; and faults arising from actuator faults and sensor faults. Several fundamental issues related to safety are explicitly analyzed according to aerospace engineering system characteristics; while focusing on these safety issues, the safety control design problems of aircraft are studied and elaborated on in detail using systematic design methods. The research results illustrate the superiority of the safety control approaches put forward. The expected reader group for this book includes undergraduate and graduate students but also industry practitioners and researchers. About the Authors: Xiang Yu is a Professor with the School of Automation Science and Electrical Engineering, Beihang University, Beijing, China. His research interests include safety control of aerospace engineering systems, guidance, navigation, and control of unmanned aerial vehicles. Lei Guo, appointed as "Chang Jiang Scholar Chair Professor", is a Professor with the School of Automation Science and Electrical Engineering, Beihang University, Beijing, China. His research interests include anti-disturbance control and filtering, stochastic control, and fault detection with their applications to aerospace systems. Youmin Zhang is a Professor in the Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, Québec, Canada. His research interests include fault diagnosis and fault-tolerant control, and cooperative guidance, navigation, and control (GNC) of unmanned aerial/space/ground/surface vehicles. Jin Jiang is a Professor in the Department of Electrical & Computer Engineering, Western University, London, Ontario, Canada. His research interests include fault-tolerant control of safety-critical systems, advanced control of power plants containing non-traditional energy resources, and instrumentation and control for nuclear power plants.

The research during the third reporting period focused on fixed order robust control design for hypersonic vehicles. A new technique was developed to synthesize fixed order H(sub infinity) controllers. A controller canonical form is imposed on the compensator structure and a homotopy algorithm is employed to perform the controller design. Various reduced order controllers are designed for a simplified version of the hypersonic vehicle model used in our previous studies to demonstrate the capabilities of the code. However, further work is needed to investigate the issue of numerical ill-conditioning for large order systems and to make the numerical approach more reliable. Calise, A. J. Unspecified Center NAG1-1451...