PERIODIC DISTURBANCE REJECTION OF NONLINEAR SYSTEMS

UoM administered thesis: Phd

  • Authors:
  • Xiafei Tang

Abstract

Disturbance rejection is an important topic in control design since disturbances are inevitable in practical systems. To realise this target for nonlinear systems, this thesis brings in an assumption about the existence of a controlled invariant mani- fold and a Desired Feedforward Control (DFC) which is contained in the input to compensate the influence of disturbances. According to the approximation property of Neural Networks (NN) that any periodic signals defined in a compact set can be approximated by NN, the NN-based disturbance approximator is applied to approximate the DFC. Algorithmically, two important types of NN approximators that are Multi-layer Neural Networks (MNN) and Radial Basis Function Neural Networks (RBFNN) are presented in detail.In this thesis, a variety of nonlinear systems in standard canonical form are looked into. These forms are the output feedback form, the extended output feedback form, the decentralised output feedback form and the partial state feedback form. For these systems, four types of uncertainties are mainly considered. The first one is the disturbance that can be eliminated by the DFC. Secondly, the parameter uncertainty is taken into account. To get rid of this uncertainty, the adaptive control technique is employed for the estimation of unknown parameters, e.g. the NN gain matrix. The third one is the nonlinear uncertainty. For the case that nonlinear uncertainties are polynomials, it has a bound consisting of an unknown constant and a function of the regulated error such that this uncertainty can be also treated as the parameter uncertainty. Delay is the last type of uncertainty. Particularly, the delay is supposed to appear in output only. This uncertainty can be eliminated together with the nonlinear uncertainty. To establish the closed- loop stability, a Lyapunov-Krasovskii function is invoked. In addition, due to the requirement of the system structure or the stability analysis, some general control techniques are also involved such like the backstepping control and the high gain control.Throughout the results are illustrated by simulations.

Details

Original languageEnglish
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Supervisors/Advisors
Award date31 Dec 2012