PDD² Sliding Mode Control of a 2-DOF Helicopter System

A proportional-derivative square (PDD<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>) based sliding mode control (SMC) strategy is proposed for a 2 degrees of freedom (DOF) helicopter system, targeting precise attitude regulation and trajectory tracking in the presence of system nonlinearities and external disturbances. The PDD<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>-SMC approach combines the robustness of sliding mode control with the simplicity and effectiveness of PDD<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> control to enhance system stability and response. A Lyapunov-based analysis is conducted to ensure the stability of the system. To validate the effectiveness of the proposed PDD<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>-SMC strategy, simulations are carried out to track the pitch and yaw angles of the 2-DOF helicopter. Results demonstrate that the PDD<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>-SMC scheme achieves improved tracking performance and robustness under varying operating conditions, highlighting its effectiveness for nonlinear aerospace systems.