Robust Nonlinear Control System Design for Hypersonic Flight Vehicles

Abstract

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.