Derivation and Aeroelastic Analysis of a Rotating Airfoil Using Unsteady Loewy Aerodynamic and Flutter Suppression by PID Controller

In this study, we derived the rotating airfoil system of equation considering Loewy aerodynamics. To this end, we define the local coordinate system on airfoil and reference coordinate on the hub. We define the free air velocity vector and the airfoil rotating speed vector according to the reference coordinate. So, the Kinetic and Potential energies are derived based on linear stiffness and linear damping according to the Hamiltonian principle. Wakes behind the rotating blades form into the helix. Therefore, we the equation of motion with Loewy aerodynamic which compensates the wake effects. Stability analysis is performed by the well-known P-K method. Flutter speed and stability boundary are estimated. Comparing the results of stability analysis and the reference validates the applied method. Furthermore, we proposed the PID Control to suppress the flutter speed. the PID controller input and command. The desired time and error tolerance are selected to design PID controller. Unit step response shows that pitch angle response is under-damped. However, step response tracks input well. Besides, disturbance rejection by considering the gain from input to output to remain below the gain value is analyzed.