Advanced controls of highly nonlinear systems for stability and performance with applications to power plant systems

In this dissertation, we develop a number of advanced controls for highly nonlinear systems with emphasis on stability and performance. The proposed nonlinear controllers can be applied to power plant systems for real-time implementation.;First, a finite-time observer design technique is introduced and used to solve the observer design problem for a class of linear time-varying systems which cannot be dealt with via conventional approaches due to the presence of the time-varying terms. This observer design technique is then applied to a second-order boiler system for partial unknown parameters identification. Furthermore, a parameter identification strategy using least square method is presented to obtain all the system parameters in real-time for the adaptive control of the second-order boiler system. We also consider the case when the system has unmeasurable states. A constant controller is first designed and then an output feedback stabilization technique is introduced using a genuinely nonlinear design to improve the convergence rate.;Later, we consider solving the optimal control problem of homogeneous systems by taking advantage of their favorable properties. We provide the necessary and sufficient conditions for the finite-time and infinite-time optimal control problems of the systems with a homogeneous degree of zero. Illustrative examples are presented to validate both conditions. We further investigate the necessary and sufficient conditions for the infinite-time optimal control problem of systems with non-zero homogeneous degree using a time-scaling technique. In addition, in order to solve the nonlinear optimal control problems whose analytic solutions are not solvable, a direct optimal control formulation with pseudospectral discretization methods is introduced and applied to a highly nonlinear boiler-turbine system for real-time optimization.;The significance of this research mainly lies in the improvement of system stability and the optimization of plant operation performance for the inherently nonlinear power plant systems through advanced nonlinear controls. The results in this dissertation have also demonstrated the application potential of nonlinear control and real-time optimal control, which will spur new directions for the research and applications of advanced nonlinear controls in power plants.