Robust Control Design : A Polynomial Approach

Our heavy dependence on systems that are automatically controlled is undeniable. Many such systems can be found in nature; others are man-made. A primary component of such systems is a device or mechanism called the controller. In man-made systems, one must first design and then implement such a controller, either as a piece of hardware or as software code in a computer. The process of developing a controller can be dramatically improved if one can generate an appropriate dynamic model of the system under consideration. Robust Control Design: A Polynomial Approach explains how to develop such controllers for system models with uncertainty. In many cases, dynamic models can be expressed in terms of linear, time-invariant equations, or transfer functions. The book presents powerful, new methods for the robust design of system controllers, especially for systems with parameter uncertainty.
The book's approach is based on the Nyquist Theorem, exploiting the properties of polynomials and polynomial value sets. The most promising techniques are those derived from the Finite Nyquist Theorem (FNT) and its corollary, The Finite Inclusions Theorem (FIT). These results reduce the problem of synthesizing a robust controller to an iterative process in which each iteration solves a finite number of linear inequalities in the controller parameters. This formulation facilitates the development of methods for robust D-stabilization and robust multiobjective performance synthesis and can lead to a less conservative design. Furthermore, it provides new insight into the robust control synthesis problem and allows greater flexibility in the choice of controller order. Computationally efficient robust control algorithms can be developed using these results and then implemented in software, thus automating the design process. The focus is on single-input-single-output systems, but the final chapter lays the foundation of robust multivariable design.