Discrete-Time Model Predictive Controller Using Laguerre Functions for Active Flutter Suppression of a 2D wing with a Flap

Abstract

In this paper, a discrete-time model predictive controller using Laguerre orthonormal function-based (LMPC) for active flutter suppression of a two-dimensional wing with a flap is presented. In this work, a linear mathematical state-space model for the pitch, plunge, and flap degrees of freedom under unsteady aerodynamics is derived and used to determine the linear flutter velocity and frequency of the parameters of a selected experimental wing. To verify the model, the open-loop simulation results are compared to an experimental study using the same wing from the literature. The state-space system is then discretized and LMPC with a Kalman filter is designed and tuned using the MATLAB® simulation environment at a selected speed in the linear flutter region. The predictive control advantage of dealing with input constraints in a systematic manner is explored through a quantitative analysis of the response of both constrained and unconstrained LMPC controllers. The results indicate that theoretically both cases can give excellent performance. However, the input trajectory generated by the unconstrained LMPC is very aggressive in a way that it is considered impractical when compared to the physical limits of an experimental actuator from the literature. The potential of LMPC to achieve a reasonable performance at a significantly lower computational cost compared to the classical model predictive controller (MPC) is investigated by measuring the time required by the same computer to compute the control trajectory for both controllers. The data suggest that LMPC requires remarkably low computational power, which makes it an excellent choice for fast aeroelastic applications.