Design, Mathematical Modeling, and Control of an Underactuated 3-DOF Experimental Helicopter

This article covers the design, implementation, mathematical modelling, and control of a multivariable, underactuated, low-cost, three-degrees-of-freedom experimental helicopter system (namely a 3-DOF helicopter). The system is considered an essential benchmark for the development and evaluation of control algorithms and identification methods as it mimics real helicopters and UAVs. The system is multivariable and difficult to control due to its underactuation characteristics. In addition, it presents further challenges in modelling and control analysis in terms of high nonlinearity, coupling, uncertainty, and unmodeled dynamics. In this scene, the system is designed, developed, and operated virtually in SolidWorks using the necessary hardware and software. A new accurate multivariable coupled nonlinear mathematical model is derived and proposed. The model takes into account the complex dynamics and interactions between the system components, providing a more comprehensive representation of the real system compared to previous models. System parameters are then identified using the Sum of the Square Error (SSE) algorithm, and the mathematical model is compared to the practical results in many different scenarios via Simulink. Experimental tests confirmed the mathematical model and robust performance of the implemented experimental 3-DOF helicopter system, as well as the ability of the proposed controller to stabilize the helicopter and track different trajectories in the presence of uncertainties and cross-coupling effects.