Approaches to nonlinear output feedback control using observers.

摘要

The construction of an observer-based output feedback controller for nonlinear systems is investigated. It incorporates an observer to reconstruct the states from available measurements, and a nonlinear state-feedback controller which utilizes the reconstructed states to determine the control action. Four distinct methods are studied for the construction of a nonlinear observer.; The first method requires differentiating the control equation to give a dynamic control law. This allows the solution of one unknown state from the algebraic control equation. It is successfully applied to a penicillin fermenter.; The second method is based on nonlinear output injection. The nonlinear system is transformed into a linear reference system augmented with nonlinear output injection. The necessary conditions for the existence of this observer is too restrictive for general applications.; The third method considers a more general reference system similar to the Thau observer by adding a nonlinear term of the transformed variable to the nonlinear output injection form. However, Thau's approach provides a very conservative condition for the observer stability. A maximal Lyapunov function is generated numerically instead to determine the system's region of asymptotic stability.; Finally, an adaptive observer is considered for identifying unknown system states and parameters. It is applicable to a larger class of nonlinear systems since the transformations can be functions of unmeasured states. A critically damped observer subsystem is obtained by choosing the observer gains properly. It is shown how the choice of transformation affects the observer's performance.; The observer based on nonlinear output injection, the Thau observer and the adaptive observer are used with a feedback linearizing controller for an exothermic reactor where only temperature measurements are available. The observer based on nonlinear output injection can be constructed only for a first order reaction, while the other two apply to an arbitrary order. For the case of the adaptive observer, unknown reaction rate is also assumed. The open-loop first-order reaction system exhibits extreme parametric sensitivity, ignition and extinction behavior, and nonlinear oscillations at certain operating conditions when subject to measured time-varying feed temperature. Simulations of the controlled system at these operating conditions demonstrate satisfactory global closed-loop response.