Adaptive Estimation and Control Algorithms for Certain Independent Control Axis Misalignments

Actuators are often assumed to be perfectly aligned when designing for a stable closed-loop system. In practice, small actuator misalignments can cause the system to perform poorly, or worse, become unstable. Consequently, adaptive observers can be introduced that build online estimates for the unknown misalignments and recover closed-loop stability. In this paper, the problem where the control axes are independently misaligned in three dimensions is considered. A study of the problem indicates a fundamental geometric difference between in-plane and out-of-plane misalignments. Accordingly, special attention is paid to the case where two axes are independently misaligned. New nonlinear adaptive observers are introduced for both the in-plane and out-of-plane problems that guarantee that the misalignment axis estimates remain unit vectors. Furthermore, a Lyapunov-like stability analysis is performed to show convergence of the misalignment estimates to their true values for a wide range of misalignment angles. In addition, a novel control system is developed for a representative dynamic system containing the aforementioned actuator misalignments that ensures perfect asymptotic tracking of prescribed reference trajectories. Also, an axis decoupling method is described that helps alleviate some of the inherent issues in the estimation problem. Detailed proofs and numerical simulations are presented to help illustrate the technical aspects of the work.