Session: 02-03-03: Dynamic Loads, Wave Propagations, Response, Vibration, Control, and Alleviation of Aerospace Structures and Vehicles

Paper Number: 158227

158227 - Design and Analysis of Optimal Controllers on a 3 Dof Airfoil Model 

Flutter is a critical aeroelastic phenomenon that arises from unstable oscillations of aircraft structures as a result of the extraction of energy from coupled fluid-structure interaction (FSI). The appearance of flutter often requires stiffer wing designs, which can negatively impact aircraft performance by virtue of added weight and reduced flexibility. This study investigates the application of advanced control techniques to mitigate flutter and enhance system stability in a three-degree-of-freedom (3 DOF) aeroelastic airfoil model. By incorporating a Linear Quadratic Regulator (LQR) and state observers, the research aims to delay or prevent the early onset of flutter while maintaining stable system performance. 

The 3 DOF model represents an airfoil with coupled pitch angle (α), vertical displacement (plunge, h), and trailing-edge angle (β). This system is inherently nonlinear due to the torsional stiffness dependency on α. To simplify the controller design, the model is linearized about a chosen steady-state α. This simplification allows a state-space representation to be constructed.  

An LQR controller was developed to provide optimal feedback gains, K, by solving the algebraic Riccati equation (ARE). Quadratic cost functions were used to penalize states and control inputs, prioritizing the stabilization of the pitch angle (α) due to its dominant role in the system. To evaluate the controller's effectiveness, the closed-loop system was tested through nonlinear simulations using a fourth-order Runge-Kutta method with a fixed time-step of 10^(-5) seconds.  

Simulation results demonstrated significant improvement in flutter prevention. Without control, the flutter speed of the system was determined to be 9.0 m/s, characterized by the emergence of positive eigenvalues in the state matrix. Implementation of the LQR controller increased the flutter speed to 22.2 m/s, more than double the initial stable operational range. The closed-loop system exhibited rapid decay of oscillations across all parameters, with the pitch angle converging quickly due to its higher penalty weight in the performance index. Control effort was moderate, with a maximum torque of approximately 5 Nm applied by a servo motor to the trailing edge. 

To further address real-world constraints, where all system states may not be directly measurable, a general state observer was designed. The observer utilized estimated states to enable the performance LQR control under partial-state feedback conditions. Observer poles were placed conservatively, five times faster - more negative - than the closed-loop system poles, to ensure rapid convergence of the estimated states to the actual states. Simulations validated the observer's ability to accurately track system dynamics and maintain the closed-loop performance, despite the lack of full-state feedback. 

The robustness of the control algorithm was further enhanced by implementing a Linear Quadratic Gaussian (LQG) controller, which combines the LQR with a Kalman filter. This approach was implemented to observe the effects of initial input condition disturbances on the airfoil system. The addition of a Kalman filter allows for optimal control in the presence of sensor noise and addresses real-world uncertainties.  

The LQG controller exhibited superior performance compared to the LQR paired with the general state observer. Specifically, the LQG implementation resulted in a less drastic magnitude of oscillatory decay and quicker convergence of the three primary state variables. This smoother dynamic response reflects the Kalman filter's ability to provide more accurate state estimates by accounting for stochastic disturbances and sensor noise. Simulation results under varying initial disturbances and noise conditions confirmed the robustness of the LQG controller.

This research highlights the potential of advanced control methods, particularly LQR, LQG, and observer designs, to address critical challenges in aeroelastic systems. By increasing the flutter speed and ensuring robust stabilization, the proposed control framework offers significant benefits for aircraft safety, operational lifespan, and efficiency. Future work would incorporate more complex aerodynamic models and explore adaptive control strategies to handle varying flight conditions.  

Presenting Author: Amber Jozwiak University of Houston

Presenting Author Biography: Amber Jozwiak is a first year graduate student pursuing dual Master's degree objectives in Aerospace Engineering and Space Architecture at the University of Houston (UH). She works with Dr. Karolos Grigoriadis, Ethan Collins, and other colleagues to investigate control applications on high order airfoil systems to mitigate the phenomenon known as flutter. In association with the Air Force Research Laboratory (AFRL), Amber Jozwiak and fellow researchers at UH seek to find innovative control techniques to make aircraft more safe and fuel efficient. Amber is also an active member and executive officer in the UH chapter of the American Institute of Aeronautics and Astronautics (AIAA) in which she avidly supports rocketry and aeronautic competition teams and spearheads professional development.