Robust control of nonlinear systems in the presence of uncertainties

  • Liqun Cong

    Student thesis: Doctoral Thesis


    Any mathematical model that is adopted for the purposes of design is, at best, an approximation to reality. However, despite the existence of such mismatch between the plant and its model, the engineering system should still be stable and achieve some prespecified performance. Different robustness measure bounds and synthesis techniques have been developed. A promising area is the so-called deterministic theory, where the uncertainties incorporated in the system are described only in terms of the bounds on their possible size, and the objective is to find a class of controller which can achieve some prescribed behaviour for all possible variations of the uncertainties within the prescribed bounds. This has found wide applications in such areas as robotics and aircraft control.

    The results presented here cover various novel techniques, which can be roughly divided into two categories according to the concepts on which the techniques are based. One category uses feedback linearisation, in which, besides a basic feedback linearisation controller proposed for the nominal part of the system, additional control effort is introduced to compensate the uncertainties in the system. The other category uses a variable structure controller which is developed for the nominal part of the system, whilst a variable feedback gain is employed to attenuate the effect of the uncertainties. Both techniques can be applied to effectively deal with systems in the presence of nonlinearity and uncertainty, and some stability theory can be developed.

    The techniques developed here are concerned with both robust stability control design and robust tracking control design for SISO and MIMO nonlinear uncertain systems where closed loop stability can be guaranteed and robustness is shown.

    For illustrative purposes, a second order system, with uncertain pole location and non-minimum phase properties, is adopted to demonstrate the performance of the techniques. Some applications are also included in the thesis, and it is shown that the techniques developed here are an improvement on previously developed methods.
    Date of AwardAug 1993
    Original languageEnglish

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