| Analysis of Essentially Nonlinear Systems (1998) | |||||||||||
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| The objective of the research supported by AFOSR was development of new techniques for rigorous and efficient computer-aided analysis and design of essentially nonlinear systems. Applications of these techniques will include stability analysis of fighter aircraft control algorithms in the case of gain scheduling and actuator rate and amplitude saturation. A number of useful analysis and design tools was developed with the support of the AFOSR grant. A new framework was proposed for the problem of auto-oscillations induced by a relay feedback. For the problem of stabilization of linear time-invariant systems with bounded control, a simple method of designing a stabilizing output feedback is proposed, based on "scheduling" a single-parameter family of controllers, so that the higher gain controllers are used closer to the origin. A number of contributions to the method of Integral Quadratic Constraints (IQC) has been made, enhancing the handling of important nonlinear blocks, such as saturation, relay, and hysteresis. In particular, a new set of IQC is derived for a class of "rate limiters", modelled as a series connections of saturation-like memoryless nonlinearities followed by integrators. In addition, more flexible version of the general IQC analysis framework is presented, and the IQC analysis software also made a significant step forward after the package iqc-beta was introduced. The issue of designing aggressive globally stabilizing controllers in some benchmark mechanical systems was addressed, and a methodology for robustness analysis of forced and self-induced oscillations in nonlinear systems has been developed. | |||||||||||
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