Adaptive Output Feedback Control for an Aeroelastic Generic Transport Model: A Parameter Dependent Riccati Equation Approach

Abstract

This paper presents the application of an adaptive output feedback control design for an aeroelastic genetic transport model. The adaptive design uses a novel parameter dependent Riccati equation approach. The adaptive controller is intended to augment a nominal, fixed g ain, observer based output feedback control law. Although the formulation is in the setting of model following adaptive control, the realization of the adaptive controller does not require implementing the reference model. In this regard, the cost of implementing the adaptive controller, above that of a fixed gain control law, i s far less than that of other methods. In addition, it is applicable to output feedback adaptive control design for non-minimum phase plants. I. Introduction Research in adaptive output feedback control of uncertain nonlinear systems is motivated by the many emerging applications that employ novel actuation devices for active control of flexible structures and fluid flows. These applications include actuators such as piezo-electric films and s ynthetic jets, which are typically nonlinearly coupled to t he plant dynamics they are intended to control. Models for these applications vary from accurate low frequency models to models that crudely approximate the true dynamics even at low frequencies. Examples of applications include active damping of flexible structures, control of aeroservoelasti c aircraft, and active control of flows. Adaptive control can be used to satisfy performance requirements in the presence of large scale parameter uncertainty, and improved safety in the event of actuator failure. The adaptive output feedback approach used in this paper is taken from Ref. 1. It assumes that a state observer is employed in the nominal controller design. The observer design is modified and employed in the adaptive part of the design. This is combined with a novel adaptive weight update law. The weight update law ensures that estimated states follow both the reference model states and the true st ates so that both state estimation errors and state tracking errors are bounded. Although the formulation is in the setting of model following adaptive control, the realization of the adaptive controller uses the observer of the nominal controller in place of the reference model to generate an error signal. Thus the only components that are added by the adaptive controller are the realizations of the basis functions and the weight adaptation law. The realization is even less complex than that of implementing a model reference adaptive controller in the case of state feedback. The stabi lity analysis employs a Lyapunov candidate function that entails the solution of a parameter dependent Riccati equation (rather than a Lyapunov equation) to show that all error signals are uniformly ultimately bounded (UUB). It is shown how the upper limit for the Riccati equation parameter is employed in the design of the adaptive law, and also influen ces the ultimate bounds for the state estimate error and the adapted weight error.