Robust Adaptive Control of a Class of Nonlinear Strict-feedback Discrete-time Systems with Exact Output Tracking

10.1016/j.automatica.2009.07.025Automatica45112537-2545ATCA

Nonlinear Flight Control Design Using Backstepping Methodology

The subject of nonlinear flight control design using backstepping control methodology is investigated in the dissertation research presented here. Control design methods based on nonlinear models of the dynamic system provide higher utility and versatility because the design model more closely matches the physical system behavior. Obtaining requisite model fidelity is only half of the overall design process, however. Design of the nonlinear control loops can lessen the effects of nonlinearity, or even exploit nonlinearity, to achieve higher levels of closed-loop stability, performance, and robustness. The goal of the research is to improve control quality for a general class of strict-feedback dynamic systems and provide flight control architectures to augment the aircraft motion. The research is divided into two parts: theoretical control development for the strict-feedback form of nonlinear dynamic systems and application of the proposed theory for nonlinear flight dynamics. In the first part, the research is built on two components: transforming the nonlinear dynamic model to a canonical strict-feedback form and then applying backstepping control theory to the canonical model. The research considers a process to determine when this transformation is possible, and when it is possible, a systematic process to transfer the model is also considered when practical. When this is not the case, certain modeling assumptions are explored to facilitate the transformation. After achieving the canonical form, a systematic design procedure for formulating a backstepping control law is explored in the research. Starting with the simplest subsystem and ending with the full system, pseudo control concepts based on Lyapunov control functions are used to control each successive subsystem. Typically each pseudo control must be solved from a nonlinear algebraic equation. At the end of this process, the physical control input must be re-expressed in terms of the physical states by eliminating the pseudo control transformations. In the second part, the research focuses on nonlinear control design for flight dynamics of aircraft motion. Some assumptions on aerodynamics of the aircraft are addressed to transform full nonlinear flight dynamics into the canonical strict-feedback form. The assumptions are also analyzed, validated, and compared to show the advantages and disadvantages of the design models. With the achieved models, investigation focuses on formulating the backstepping control laws and provides an advanced control algorithm for nonlinear flight dynamics of the aircraft. Experimental and simulation studies are successfully implemented to validate the proposed control method. Advancement of nonlinear backstepping control theory and its application to nonlinear flight control are achieved in the dissertation research

Nonlinear control and its application to active tilting-pad bearings

The drawbacks of active magnetic bearings are arousing interest in the adaptation of mechanical bearings for active use. A promising mechanical bearing candidate for active operation is the tilting-pad bearing. In this research, we introduce an active tilting-pad bearing with linear actuators that translate each pad. The use of feedback in determining the actuator forces allows for the automatic, continuous adjustment of the pad position during the machine operation. In this work, we develop the dynamic model of the active bearing system such that the actuator forces are the control inputs. The hydrodynamic force is modeled as a spring/damper-like force with unknown damping and stiffness coefficients. Whereas in the literature, the damping and stiffness effects are normally considered linear, here, motivated by a numerical study based on the Reynolds equation, we use a nonlinear model for the stiffness force. An adaptive controller is designed to asymptotically regulate the rotor to the bearing center. The proposed control design is applicable to both the linear and nonlinear stiffness models. Simulations and experiments show that the active strategy improves the bearing performance in comparison to its traditional passive operation. Further, the experiments indicate the nonlinear stiffness-based controller slightly improves the active bearing regulation performance relative to the linear-based one. To the best of our knowledge, this dissertation is the first to report the experimental demonstration of an active tilting-pad bearing using feedback control. Since the model of the active tilting-pad bearing has a parametric strict-feedback-like form, the second part of this dissertation is dedicated to constructing new nonlinear control tools for this class of systems. Specifically, we consider the regulation and tracking control problems for multi-input/multi-output parametric strict-feedback systems in the presence of additive, exogenous disturbances and parametric uncertainties. For such systems, robust adaptive controllers usually cannot ensure asymptotic tracking or even regulation. In this work, under the assumption the disturbances are C2 with bounded time derivatives; we present a new C0 robust adaptive control construction that guarantees the output/tracking error is asymptotically driven to zero. Numerical examples illustrate the main results, including cases where the disturbances do not satisfy the aforementioned assumptions

A family of asymptotically stable control laws for flexible robots based on a passivity approach

A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility