Gain-Scheduling Composite Nonlinear Feedback Control for a Set of 2nd Order Linear Parameter-Varying Systems

We present in this paper gain-scheduling composite nonlinear feedback (CNF) control for a set of second-order linear parameter-varying (LPV) systems that capture commonly used plant models in automatic control. The selected three parameter-varying plant models are double integrator with a gain, a series connection of an integrator and a first order system, and a second-order system without integration. We assume that the parameters of the plant models depend on an exogenous scheduling signal, which is unknown a priori, but it is measurable online and available for feedback control. The resulting model-based parameter-varying CNF controller assigns certain predefined properties for the closed-loop control system, which can be explained using linear time invariant (LTI) control theory. We demonstrate the proposed control structure with a simulation-based design example, in which a plant model is updated through a slowly varying scheduling signal, and, at the same time, the closed-loop system is commanded towards desired reference values. Our simulation results indicate that the closed-loop control system yields satisfactory tracking performance under parameter-varying conditions.