Self-Tuning Control for Bilinear Systems

  • Keith Burnham

    Student thesis: Doctoral ThesisDoctor of Philosophy


    Prompted by the desire to increase the industrial applicability range of self-tuning control, the objective of this work has been to extend the standard linear self-tuning framework to facilitate the design of self-tuning controllers for bilinear systems. Bilinear systems form a well structured class of non-linear systems within which linear systems coexist as a special subclass. They are, therefore, appropriate for modelling a wider range of processes and plant than the restrictive, yet convenient, linear model structures since such models are valid both within the linear subregion and beyond. In addition to extending the self-tuning framework for bilinear systems another significant contribution of the Thesis is the introduction of a cautious least squares estimation procedure which also enhances the existing linear self-tuning schemes.

    In recognition of the inevitable plant/model mismatch problems that accompany the standard linear self-tuning approach, it is pertinent to consider extending the linear self-tuning framework to accommodate the wider class of bilinear systems. Such an extended framework should alleviate the problem of plant/model mismatch whilst at the same time increasing the range of applicability of self-tuning control. An extended form of the linear pole-placement control strategy is investigated and attention is restricted to the class of single-input single-output and multiple-input single output bilinear systems, noting that the more general class of multiple-input multiple-output systems can be represented by a series of interconnected multiple-input single-output subsystems.

    In the development of an appropriate bilinear self-tuning controller, a number of enhancements to the standard estimation algorithms used for linear self-tuning control have been necessitated; this being due mainly to the increased sensitivity of the bilinear approach. Enhancements include; a hybrid form of the variable forgetting factor to facilitate the tracking of slowly varying model parameters; a two-tier adaptive mechanism involving variable forgetting factor reset coupled with covariance matrix reset for both rapid and slow parameter variation; and a cautious least squares parameter estimation scheme for increased robustness.

    The bilinear self-tuning controller and its successive variants are assessed using both simulation studies and real-time laboratory based trials. It is shown that when the bilinear self-tuner is applied to systems exhibiting bilinear characteristics that significant improvements in performance are possible over the use of standard linear schemes incorporating enhanced parameter estimation procedures. Finally, since the resulting self-tuning controller is potentially applicable for a wider range of applications than the linear self-tuning scheme, it is pertinent to consider, as one does for the linear case, the applicability of the bilinear self-tuner to other forms of non-linear systems for which local bilinearity may be assumed.
    Date of Award1991
    Original languageEnglish

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