Gain analysis and stability of nonlinear control systems

The complexity of large industrial engineering systems such as chemical plants has continued to increase over the years. As a result, flexible control systems are required to handle variation in the operating conditions. Some of the challenging elements in the design of control systems are nonlinearity, disturbances and uncertainty in the process model. In the classical approach, first the plant model should be linearized at the nominal operating point and then, a robust controller should be designed for the resulting linear system. However, the performance of a controller designed by this method deteriorates when operation deviates from the nominal point. When the distance between the operating region and the nominal operating point increases, this performance degradation may lead to instability.;The core objective of this thesis is to develop new tools to study stability of closed-loop nonlinear systems controlled by local controllers in order to improve design of multiple model control systems. For example, one of the aims of this work is to investigate how to determine the region where closed loop system is stable. A secondary objective is to study the effects of the exogenous signals on stability of such systems.;To achieve these goals, first, new representations for nonlinear systems, called zetaA and zetaAB representations, are proposed. In zetaA and zeta AB representations, initial state contributes to the feedback interconnection as an exogenous input. These representations can be used to develop new tools for non-zero state nonlinear systems based on the input-output theory. The zetaA and zetaAB representations convert a nonlinear system with non-zero initial state into a combination of a memoryless nonlinearity and a linear system with some input signals. The way initial state is handled by these representations provides a novel viewpoint on all aspects of investigating nonlinear systems.;Using these representations, stability of nonlinear systems with non-zero initial states can be investigated by the input-output stability methods. Based on this usage, a new framework is developed for the analysis of stability of systems by the zetaA and zeta AB representations. For local stability, a method developed to find a pair of local areas, namely Delta and Upsilon, where belonging the initial state to Delta implies staying the state inside Upsilon. The methods are also extended to forced systems.;To compute an upper bound on the L1 , L2 and Linfinity norms of a class of nonlinear systems, a new method is proposed based on the zetaA and zetaAB representations. Another Method, which provides tighter bounds, is proposed to find an upper bound on the induced L2 norm. Both methods are only applicable to globally Lipschitz systems. To overcome this restriction, another tool is developed for local conditions, namely, an upper bound on system output is derived for bounded input and initial state. This method is restricted to the Linfinity induced norm.;To measure the distance between local systems in multiple model method, some researchers have suggested to use the gap metric. However, since there are no straight-forward method to compute the nonlinear gap metric and using linear gap metric can not guarantee global stability of the system, the mentioned problem is still unsolved. In this thesis based on zetaA and zetaAB representations, a method is proposed to compute an upper bounds on the gap metric and the corresponding stability margin for a class of nonlinear systems.;The minimum gain of an operator is defined, some of its properties are derived and some computational methods are developed to calculate the minimum gain. Based on the minimum gain of operators, the large gain theorem is stated. The large gain theorem asserts that the feedback loop will be stable if the minimum loop gain is greater than one.;To study disturbance attenuation of a closed loop multitank system, the proposed methods are utilized. It is assumed that a proportional controller is used to control the level of the liquid in one of the tanks. The mathematical model of the open loop system is derived using physics of the plant. The gray box identification method is used to identify the model parameters and the disturbance attenuation of the system is investigated by the proposed method. (Abstract shortened by UMI.)...