Attitude tracking of a multivariable 3-DoF helicopter via decentralized repetitive control

This paper presents a novel strategy for designing a discrete-time decentralized repetitive controller (DRC) for a 3-degree-of-freedom (DoF) helicopter modeled as a multivariable linear system. The proposed design strategy comprises three main steps: (1) decomposing the 3-DoF helicopter model into two independent subsystems, namely an elevation model and a pitch-travel model, (2) designing a state-feedback stabilizing controller for each subsystem, and (3) designing the discrete-time decentralized repetitive controller. Such a repetitive control strategy is intended to enable the 3-DoF helicopter to track repetitive trajectories of the elevation and travel angles perfectly. A numerical example of the 3-DoF Quanser helicopter system for tracking three scenarios (i.e., $\infty$-shape trajectory, diamond-shape trajectory, and diamond-shape trajectory with counterweight mass variation), is simulated to validate the effectiveness of the proposed design. In addition, a comparison is also made to a sliding-mode controller (SMC) and linear-quadratic regulator(LQR)-based proportional–integral–derivative (PID) controller. The results demonstrate that zero-tracking errors are achieved with the proposed design in all scenarios, although the third scenario requires a longer convergence time compared to the first two. Under similar repetitive tasks, the DRC outperforms the SMC and LQR-based PID in terms of tracking accuracies during the steady-state period.