Introduction to Feedback Linearisation

Abstract

Feedback linearisation is perhaps the most important nonlinear control design strategy developed during the last few decades [5]. The main objective of the approach is to algebraically transform a nonlinear dynamic system into a linear dynamic system by using a static state feedback and a nonlinear coordinate transformation based on a differential geometric analysis of the system. By eliminating nonlinearities in the closed loop system, conventional linear control techniques can be applied. Our presentation of relative degree, normal forms, zero dynamics and feedback linearisation for nonlinear control affine systems given in Section 3.1 follows the notation that is used in the mainstream nonlinear control literature [5, 56]. The method of input-output feedback linearisation for nonlinear MIMO control affine systems, which is central in this book, is presented in Section 3.1.3. Other linearisation techniques, such as exact linearisation and Volterra linearisation, are reviewed in Section 3.2. Finally, two feedback linearisation techniques that are applicable to systems that are not control affine are briefly presented in Section 3.3.KeywordsRelative DegreeFeedback LinearisationCharacteristic MatrixZero DynamicDynamic Neural NetworkThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.