Robust model predictive control of shimmy vibration in aircraft landing gears with probabilistic uncertainty

This paper considers robust model predictive control (RMPC) methods for linear parameter varying (LPV) system which has both probabilistic uncertain and time-varying parameters. The parameters are considered to be measured on-line. In this regard, the aircraft landing gear system is considered as a LPV system whose parameters variation can affect both stability and performance. By transforming this system into a convex combination of linear time-invariant vertices form with the tensor-product (TP) model transformation method, the landing gear system is represented as a polytopic linear parameter-varying system. A computationally efficient RMPC law is formulated for this system which guarantees closed-loop robust stability and performance. The control signal is calculated on-line by carrying out the convex optimization involving Linear Matrix Inequalities (LMIs) in MPC. The proposed controller can effectively suppress the shimmy vibration of the landing gear with variable taxiing velocity and wheel caster length, also with the probabilistic uncertain torsional spring stiffness.