Nonlinear Analysis and Control in the Frequency Domain
Hua Jun Chen · 2006
In this thesis, the Nonlinearity-Index ( ) is proposed as a yardstick to distinguish functions and systems as linear or nonlinear. This scale can be used to decide whether a given plant should be modeled as a nonlinear system, and whether a nonlinear control algorithm should be employed. The larger the is, the more confident the engineers can be in justifying the use of nonlinear schemes. The High Order Nonlinearity Approximation ( ) is introduced, based on the , as a form of the plant model. The enlarges the class of nonlinear systems expressible in the so called High Degree Transfer Function ( ), and can simplify the form of . The exisiting nonlinear Internal Model Control method, which relies on the , is augmented by incorporating a fuzzy algorithm that evaluates the . These methods are shown to be effective through simulation studies.