A Gain Scheduling Approach of Delayed Control with Application to Aircraft Wing in Wind Tunnel

The objective of this work is to study the equilibrium stability of a switched linear model with time-delayed control and additive disturbances, that in subsidiary represents the control of wing vibrations in the presence of the turbulence disturbances in an aerodynamic tunnel. The state system is modeled as a collection of subsystems, each corresponding to different levels of air velocity in the wind tunnel. The problem is closely related to the gain scheduling approach for stable control synthesis and to the design of stable, switched systems with time-delay control. A state-predictive feedback method is employed to compensate for actuator delay, resulting in closed-loop free delay switching systems both in presence and absence of disturbances. The main contribution of this study is a thorough analysis of system stability in the presence of disturbances. Finally, numerical simulation results are provided to support and complement the findings.