Gain scheduling of aircraft pitch attitude and control of discrete, affine, linear parametrically varying systems

This research is motivated by gain scheduling, a technique which has been successfully applied to many nonlinear control problems. In flight controls, the wide variations in the characteristics of the aircraft dynamics throughout the flight envelope make gain scheduling a particularly suitable design strategy. This research consists of two parts: (1) aircraft pitch attitude scheduling scheme designs, and (2) control of a class of linear parametrically varying (LPV) systems.; In the first part, the classical gain scheduling technique and the single quadratic Lyapunov function (SQLF) based LPV technique are investigated. In the classical gain scheduling design, the $H\infty$ mixed sensitivity GS/T method is chosen for local linear time invariant (LTI) designs to provide robustness to unmodeled dynamics and parametric uncertainties. Following a model reduction procedure that exploits the optimal controller structure, LTI controllers designed at the selected equilibrium points are reduced to second order controllers and realized in a feedback path configuration. Such controllers are shown to retain the superior robust performance at each flight condition, while having a low order that is amenable to scheduling. A gain-scheduling law is developed and simulation results verify that the closed-loop performance specifications are met. In the LPV design, the mixed sensitivity S/KS/T design setup is used. An approximation to the original LPV controller using the linear fractional transformation (LFT) representation is constructed. Our design exhibits potential applications of the LPV technique to commercial aircraft gain scheduling designs.; In the second part, we consider a class of discrete, affine, linear parametrically varying (DALPV) systems. For this type of systems, the parameters are assumed to vary in a polytope and the state space matrices are assumed to depend affinely on the varying parameters. A sufficient condition is derived to analyze the stability and the $\ell \infty$ to $\ell \infty$ performance of a DALPV system. For an open-loop DALPV system, a procedure is proposed to design a gain-scheduled controller such that the closed-loop system is asymptotically stable and achieves a certain level of $\ell \infty$ to $\ell \infty$ performance.