Set-Point Control and Local Stability for Flat Nonlinear Systems Using Model-Following Control

We consider the set-point control problem for nonlinear systems with flat output that are subject to perturbations. The nonlinear dynamics as well as the perturbations are locally Lipschitz. We apply the model-following control (MFC) approach which consists of a model control loop (MCL) for a feedforward generation and a process control loop (PCL) that compensates the perturbations using high-gain feedback. We analyse the resulting closed-loop system and discuss its relation to a standard flatness-based high-gain approach. In particular we analyse the estimated region of attraction provided by a quadratic Lyapunov function. A case study illustrates the approach and quantifies the region of attraction obtained for each control approach. Using the initial condition of the model control loop as tuning parameter for the MFC design, provides that a significantly larger region of attraction can be guaranteed compared to a conventional single-loop high-gain design.