Design and performance tradeoffs of high-gain observers with applications to the control of smart material actuated systems

The study of high-gain observers has typically involved properties that are asymptotically recovered as the gain is pushed higher. In any practical implementation of high-gain observers one will ultimately encounter performance tradeoffs associated with the choice of gain. These include tradeoffs between fast reconstruction of the system states, better rejection of modeling uncertainty, and closed-loop stability versus amplification of measurement noise, large transient response amplitude, and computational cost in the discrete-time case. We propose several high-gain observer designs and examine their effectiveness at dealing with these tradeoffs.; We examine the tradeoff between closed-loop stability and large observer transient response by considering a time-varying high-gain observer that is of the form of an extended Kalman filter (EKF). We highlight an important feature of the Riccati equation with respect to the observer transient and show closed-loop asymptotic stability for a particular class of nonlinear systems under EKF feedback. We compare the performance of the time-varying extended Kalman filter against a fixed-gain high-gain observer in terms of closed-loop stability and transient response.; To balance the tradeoff between state reconstruction speed during the observer transient with amplification of measurement noise at steady-state we propose a high-gain observer that switches between two gain values. This scheme is able to quickly recover the system states during large estimation error and reduce the effect of measurement noise in a neighborhood of the origin of the estimation error. We argue boundedness of the trajectories of the closed-loop system.; Since closed-loop stability for sampled-data systems using high-gain observers follows for sufficiently small sampling periods, there is a tradeoff between elevated sampling rates and closed-loop performance. We consider a multirate sampled-data output feedback control design in order to relax the tradeoff between computational cost and closed-loop stability. This scheme employs control update rates that are fixed by a state feedback design with a sufficiently fast measurement sampling rate. We prove practical stabilization for the closed-loop system under multirate output feedback. We also argue stability with respect to a set in the presence of bounded disturbances.; For smart material actuated systems, the existence of significant hysteresis nonlinearity inherent in smart materials along with difficulties in measuring system states points to output feedback control designs employing hysteresis compensation. We apply our multirate output feedback scheme to a shape memory alloy actuated rotary joint by combining the observer with a hysteresis inversion controller. The rotary joint is modeled as a hysteresis operator of Preisach type combined with a dynamic system. Experimental results of the proposed scheme are reported.; This dissertation attempts to address certain criticisms of high-gain observers and thus may be of interest to both control theoreticians and practicing engineers.