RESUMEN
The problem of stabilizing dynamic systems with unknown or uncertain equilibrium states is studied. Derivative control schemes are proposed for both state and output feedback for the local stabilization at the true equilibrium states. The case where norm-bounded uncertainties are present in the system model is considered to derive robust stability conditions in linear matrix inequality form. The proposed control solutions drive the closed-loop system exponentially to its equilibrium states as shown via simulation on the chaotic Rössler and Lorenz attractors, when the equilibrium states are unknown and model uncertainties are present. A practical example involving a magnetic levitation system, in which two disks are to be levitated at an unknown magnetic equilibrium, demonstrates the effectiveness of the output derivative feedback controller.
RESUMEN
The adaptive correction of uncertain equilibrium states in feedback controlled systems is studied in this paper, with application to the active control of compressor surge with uncertainty in the characteristic curves. Adaptive compensation methods are introduced to correct for the uncertainty in the equilibrium state in both the state and the output feedback control cases, using information from the feedback control signal to determine the true equilibrium of the nonlinear plant. In particular, our proposed solutions overcome the odd-number condition, or parity condition, which appears as a recurring limitation in comparable solutions reported in the literature. Conditions for the existence of the adaptive solutions are presented, and the stability of the closed-loop system is demonstrated. The effectiveness of the proposed adaptation mechanism is verified using a high fidelity mathematical model of a compression system, commissioned to test active surge control methods by active magnetic bearings.