Estimation and control of nonlinear systems using extended high-gain observers

Providing accurate state estimation is important for many systems. This is especially the case for systems whose states may be very difficult or even impossible to measure or require expensive or unreliable sensors. From another prospective, making all the states available simplifies considerably the control design and helps in providing practical and economic solutions to many control problems. The first part of our work involves the design of an observer for a class of nonlinear systems that can potentially admit unstable zero dynamics. The structure of the observer is composed of an Extended High-Gain Observer (EHGO), for the estimation of the derivatives of the output, augmented with an Extended Kalman Filter for the estimation of the states of the internal dynamics. The EHGO is also utilized to estimate a signal that is used as a virtual output to an auxiliary system comprised of the internal dynamics. We demonstrate the efficacy of the observer in two examples; namely, a synchronous generator connected to an infinite bus and a Translating Oscillator with a Rotating Actuator (TORA) system.;In the special case of the system being linear in the states of the internal dynamics, we achieve semi-global asymptotic convergence of the estimation error. We also solve for this class of systems, which may have unstable zero dynamics, the problem of output feedback stabilization. We allow the use of any globally stabilizing full state feedback control scheme. We then recover its performance using an observer-based output feedback control. As a demonstration of the efficacy of this control scheme, we design an output feedback stabilizing control for the DC-to-DC boost converter system.;We also consider the problem of output feedback tracking of possibly non-minimum phase nonlinear systems where the internal dynamics have a full relative degree with respect to a virtual output. In this case, the internal dynamics can be represented in the chain-of-integrators form. This allows the use of a high-gain observer to estimate the states of the internal dynamics, and hence, making all the system states available for the controller. We allow the use of any globally stabilizing full state feedback control and we show that it is possible to recover its stability properties and trajectory performance. Finally, as a demonstration of the design procedure, we solve the problem of output feedback tracking control of flexible joint manipulators where the link angle is the output to be controlled and the motor angle is the measured output. We demonstrate the effectiveness of the proposed scheme in the single link case, and where the zero dynamics are not asymptotically stable.