Adaptive control of a smart projectile fin with unknown high-frequency gain by piezoelectric actuation

This paper delves into adaptive control of a smart projectile fin with unknown high frequency gain using a piezoelectric bimorph. The hollow projectile smart fin is actuated using a cantilevered piezoelectric bimorph that is completely enclosed within the fin. The model of the smart fin system includes the aerodynamic moment which is a function of the angle of attack of the projectile. The rotation angle of the fin is controlled by deforming the piezoelectric bimorph which is hinged at the tip of the rigid fin. It is assumed that fin parameters as well as the high frequency gain of the model are unknown. Moreover the model includes an unknown bounded time varying aerodynamic disturbance. An adaptive control system using the Nussbaum gain is designed. The structure of the control system is independent of the dimension of the flexible fin model. This is important because the fin model has large number of flexible modes. For the design of the control law, a linear combination of the fin angle and fin angular rate is chosen as the controlled output variable. In the closed loop system, all the signals are bounded and the fin angle tracks the reference trajectory. Simulation results are presented along with the experimental validation done using the subsonic wind tunnel at the University of Nevada, Las Vegas (UNLV). Both simulation and experimental results show that in the closed-loop system, the fin angle is precisely controlled in spite of the uncertainties in the fin parameters and the aerodynamic force.