A Generalized Absolute Stability Approach to Dealing with Saturation Nonlinearities: Analysis, Design and Applications to Magnetic Bearing Systems

University Of Virginia Main Campus, Charlottesville VA

Investigators

Abstract

Saturation nonlinearities are ubiquitous in engineering systems. In control systems, every physical actuator is subject to maximum and minimum saturation limits. In between these maximum and minimum limits, the input-output characteristic of a physical actuator is often neither precisely linear nor exactly known. Thus, in the analysis and design of many high performance control systems, it is inadequate to model the actuator characteristic by a standard saturation function. A straightforward approach to accounting for the nonlinearities and uncertainties in the actuator characteristic is to formulate the analysis and control design problem as the classical absolute stability problem, where the actuator characteristic is assumed to be within a linear sector. Such an approach to dealing with actuator nonlinearities leads to severe conservativeness as the two straight lines, the boundaries of a linear sector, cannot tightly bound the actuator characteristic. The proposed research will develop a generalized absolute stability approach to the analysis and control design of linear systems in the presence of actuator nonlinearities. In comparison with the classical absolute stability theory, the main innovation of this proposed approach is that it allows the actuator nonlinearities to reside in between two nonlinear curves, rather than two straight lines. The initial investigation by the PIs has shown that the proposed approach drastically improves the results that can be obtained by the classical absolute stability theory. The proposed research is expected to lead to a set of powerful tools for various aspects of analysis and control design, including the assessment of closed-loop performance under a given feedback law and the design of feedback laws for stabilization, disturbance rejection and output regulation. An integrated part of the project is to experimentally verify the obtained theoretical results on some magnetic bearing/suspension systems in our laboratory. The proposed research will have a strong societal impact by advancing magnetically suspended flywheel energy storage technology and by providing efficient control design for magnetically suspended artificial heart pumps. Other broader impacts of this research include the development of closer interaction among the control theory, the magnetic bearings, and the medical science research communities and curriculum enhancement at the graduate and undergraduate levels.