The problem of controlling fast, unstable, and nonminimum-phase systems is considered. With standard predictive control, the time required for optimization is typically larger than the sampling interval that is needed for stabilization of the fast dynamics. On the other hand, due to the nonminimum-phase behavior, control based on input-output feedback linearisation leads to unstable internal dynamics. In this paper, a cascade structure is proposed, with control based on input-output feedback linearisation forming the inner loop and predictive control the outer loop. Assuming high-gain feedback for the inner loop, a stability analysis of the global scheme is provided based on singular perturbation theory. The approach is illustrated via the simulation of an inverted pendulum system.
The problem of controlling nonlinear nonminimum-phase systems is considered, where standard input-output feedback linearization leads to unstable internal dynamics. This problem is handled here by using the observability normal form in conjunction with input-output linearization. The system is feedback linearized upon neglecting a part of the system dynamics, with the neglected part being considered as a perturbation. A linear controller is designed to accommodate the perturbation resulting from the approximation. Stability analysis is provided based on the vanishing perturbation theory.
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