Adaptive control design with guaranteed margins for nonlinear plants

Abstract

Adaptive control is one of the technologies that improve both performance and safety as controller parameters can be redesigned autonomously in the presence of uncertainties. Considerable research has been accomplished in adaptive control theory for several decades and a solid foundation has been laid out for stability and robustness of adaptive systems. However, a large gap between theory and practice has been an obstacle to transition theoretical results into applications and it still remains. In order to reduce the gap, this thesis presents a unified framework for design and analysis of adaptive control for general nonlinear plants.An augmented adaptive control architecture is proposed where a nominal controller is designed in the inner-loop with an adaptive controller in the outer-loop. The architecture is completed by addressing three separate problems. The first problem is the design of adaptive control in the presence of input constraints. With a rigorous stability analysis, an algorithm is developed to remove the adverse effects of multi-input magnitude saturation. The second problem is the augmentation of adaptive control with a nominal gain-scheduling controller. Though adaptive controllers have been employed with gain-scheduling to various applications, no formal stability analysis has been developed. In the proposed architecture, adaptive control is combined with gain-scheduling in a specific manner while stability is guaranteed. The third problem is the development of analytic stability margins of the closed-loop plant with the proposed adaptive controller. A time-delay margin is derived using standard Lyapunov stability analysis as an analytic stability margin.The overall adaptive control architecture as well as the analytically derived margins are validated by a 6-DoF nonlinear flight dynamics based on the NASA X-15 hypersonic aircraft. Simulation results show that the augmented adaptive control is able to stabilize the plant and tracks desired trajectories with uncertainties in the plant while instability cannot be overcome only with the nominal controller. The time-delay margins are validated based on a generic transport model and they are compared with margins obtained from simulations studies. We utilize numerical methods to find less conservative time-delay margins.