Observer-based Approximate Feedback Linearization with Quasi α-degree LQG Controller for Pseudolinear Systems

Abstract

This paper describes an observer-based approximate feedback linearization (AFL) process with a quasi -degree linear–quadratic–Gaussian (quasi -degree LQG) controller for perturbed pseudolinear systems; the systems can be fully linearized by using feedback. The AFL method is based on an exact feedback linearization (EFL) method. A quasi similarity transformation (QST) relationship exists between the two methods. The present study proposes a quasi -degree LQG controller, which includes a quasi -degree LQR type controller and a -degree LQR type observer. Following the separation principle, we designed a quasi -degree LQG controller with an observer system that responds more quickly than the control system. The quasi -degree LQG controller, which uses observer state feedback and output feedback, was introduced to stabilize the pseudolinear systems. A Luenberger-like nonlinear observer was adopted to estimate state variables. The simulation results demonstrated that this control scheme is feasible. Furthermore, the results of this study corroborate previous research results and confirm the QST relationship between AFL and EFL.