Extensions in Non-Minimal State-Space and State-Dependent Parameter Model Based Control with Application to a DC-DC Boost Converter

  • Ulrich Hitzemann

    Student thesis: Doctoral ThesisDoctor of Philosophy


    This Thesis is concerned with model-based control, where models of linear non-minimal state-space (NMSS) and nonlinear state-dependent parameter (SDP)form are considered. In particular, the focus is on model-based predictive control(MPC) in conjunction with the linear NMSS model and on proportional-integral-plus (PIP) pole-assignment control in conjunction with the SDP model.

    The SDP-PIP pole-assignment controller is based on a nonlinear SDP model, however, the approach uses a linear pole-assignment controller design technique. This ‘potential paradox’ is addressed in this Thesis. A conceptual approach to realising the SDP-PIP pole-assignment control is proposed, where an additional conceptual time-shift operator is introduced. This allows the SDP-PIP, at each sampling time instance, to be considered as an equivalent linear controller, while operating, in fact, in a nonlinear overall context. Additionally, an attempt to realise SDP-PIP control, where the SDP model exhibits equivalent linear system numerator zeros, is proposed.

    Regarding the NMSS MPC, emphasis is on square, i.e. equal number of inputs and outputs, multi-input multi-output (MIMO) modelled systems, which exhibit system output cross-coupling effects. Moreover, the NMSS MPC in incremental input form and making use of an integral-of-errors state variable, is considered. A strategy is proposed, that allows decoupling of the system outputs by diagonalising the closed-loop system model via an input transformation.
    A modification to the NMSS MPC in incremental input form is proposed such that the transformed system input - system output pairs can be considered individually, which allows the control and prediction horizons to be assigned to the individual pairs separately. This modification allows imposed constraints to be accommodated such that the cross-coupling effects do not re-emerge.

    A practical example is presented, namely, a DC-DC boost converter operating in discontinuous conduction mode (DCM), for which a SDP model is developed. This model is based on measured input-output data rather than on physical relationships. The model incorporates the output current so that the requirements for the load, driven by the converter, is constrained to remain within a predefined output current range. The proposed SDP model is compared to an alternative nonlinear Hammerstein-bilinear structured (HBS) model. The HBS model is, in a similar manner to the SDP model, also based on measured input-output data. Moreover, the differences as well as the similarities of the SDP and HBS model are elaborated. Furthermore, SDP-PIP pole-assignment control, based on the developed SDP model, is applied to the converter and the performance is compared to baseline linear PIP control schemes.
    Date of Award2013
    Original languageEnglish
    Awarding Institution
    • Coventry University
    SupervisorKeith Burnham (Supervisor)

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