Exact Linearization and Trajectory Tracking for a 3DOF Helicopter

Abstract

This paper presents the design of a control strategy based on exact feedback linearization and dynamic stabilization for the mathematical model of a benchmark Quanser platform emulating the elevation, pitch, and travel motions of a three-degree-of-freedom (3-DOF) tandem helicopter. The orientation dynamics of the aerial vehicle are described by a set of highly coupled, inherently unstable nonlinear differential equations. Unlike conventional feedback linearization approaches, the core contribution of this work lies in a strategic subsystem decoupling technique combined with a symmetric input transformation and a formal proof of exact linearizability. Once the exact linear canonical representation is derived, optimal Linear Quadratic Regulator (LQR) control gains are synthesized directly within the transformed coordinates. Subsequently, a trajectory tracking scheme is developed for each degree of freedom, simulating aggressive trajectory changes that emulate obstacle-avoidance maneuvers during a mission. Numerical simulations in MATLAB/Simulink demonstrate that the proposed control scheme achieves precise tracking and rapid stabilization while strictly adhering to the physical angular bounds of the experimental platform and operational actuator constraints.