Adaptive Estimation and Control Algorithms for Certain Classes of Actuator Misalignment Uncertainties

摘要

When designing a control system, the actuators are often assumed to be perfectly aligned. In practice, small actuator misalignments can potentially cause an otherwise stable closed-loop system under ideal conditions to perform poorly, or worse, even become unstable. Consequently, adaptive observers would need to be introduced that build estimates for the unknown misalignments and thereby aid toward recovering closed-loop stability and performance. In this paper, we consider two particular classes of actuator misalignments wherein control inputs applied along the ideal x and y control axes are independently misaligned. The analysis is complicated by nonlinearities due to geometric differences between in-plane and out-of-plane misalignments; accordingly, new sets of nonlinear adaptive observers are introduced for both the in-plane and out-of-plane misalignment problems that guarantee that the estimates of the misaligned axes remain unit vectors throughout the estimation process. Furthermore, a Lyapunov-like stability analysis is performed to show convergence of the misalignment estimates to their true values for a wide range of initial conditions. Additionally, a double-integrator dynamic system executing translational motion in 3D-space and endowed with three independent inputs is considered wherein the control vector is misaligned by the same aforementioned of actuator misalignments studied in this paper. A novel control system is developed that ensures perfect asymptotic tracking of prescribed reference trajectories. Moreover, the structure of the proposed adaptive observers is such that the resulting control signal remains continuous and bounded. Detailed proofs and numerical simulations are presented to help illustrate the technical aspects of the work.