bond graph dynamic modeling and stabilization of a quad-rotor helicopter
Four-rotor/quad-rotor helicopters are emerging as a popular unmanned aerial vehicle configuration because of their simple construction, easy maintenance and high payload capacity. A quadrotor is an under-actuated mechanical system with six degrees of freedom and four lift-generating propellers arranged in cross configuration. Maneuvers are executed by varying the speed of the propellers, which causes moments that affect attitude control; and by varying thrust, which affects altitude control. This makes stabilization challenging. This work presents a dynamic model of such a vehicle using bond graphs. Both an open loop unstable model and a closed loop stable model using different controllers are demonstrated in this paper. The Newton-Euler formalism with body fixed coordinates is used to model the dynamics of the platform. Rotor drag torque is assumed proportional to thrust of the rotor. The graphical nature and explicit power flow paths inherent in the bond graph formalism facilitated model construction and troubleshooting. Existing commercial bond graph software allowed simultaneous modeling and control implementation. The model results for different maneuvers and combinations of propeller thrust agree with existing theoretical results. Open loop simulation shows an uncontrolled revolving effect with increasing linear speed which results in instability of the system. The closed loop PID-controlled result nicely demonstrates the stabilization of the system from an initial roll, pitch, yaw and altitude to the desired steady state configuration.
bond graph in aerospace stabilization of quad-rotor helicopters quad-rotor helicopter dynamics