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Predictive Control in Power Electronics and Drives: Basic Concepts, Theory, and Methods

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Advanced and Intelligent Control in Power Electronics and Drives

Part of the book series: Studies in Computational Intelligence ((SCI,volume 531))

Abstract

In this chapter we revise basic principles and methods of model predictive control with a view towards applications in power electronics and drives. The simplest predictive control formulations use horizon-one cost functions, which can be related to well-established dead-beat controllers. Model predictive control using larger horizons has the potential to give significant performance benefits, but requires more computations at each sampling instant to solve the associated optimization problems. For particular classes of system models, we discuss practical algorithms, which make long-horizon predictive control suitable for power electronics applications.

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Notes

  1. 1.

    Note that the weighting functions should be chosen such that \( V( \cdot , \cdot ) \) depends on the decision variables contained in \( {\mathbf{u^{\prime}}}(k) \), see (7).

  2. 2.

    It is important to remark that in the case that \( B \in {\mathbb{R}}^{n \times n} \), with B nonsingular, we have that \( B^{\dag } = B^{ - 1} \). Thus, the control law (14) is a particular case of (15).

  3. 3.

    Alternatively, one can also penalize the size of the increments of the control input via a term of the form \( (u(k) - u(k - 1))^{T} R(u(k) - u(k - 1)) \).

  4. 4.

    When considering linear time-invariant (LTI) systems, inverse behavior is equivalent to non-minimum phase behavior, i.e. systems with zeros in the right half-plane of the Laplace domain.

  5. 5.

    Note that (37) contains the third term \( x^{T} (k){\mathbf{S}}^{T} {\mathbf{S}}x(k) \). Since this term is constant and independent of \( {\mathbf{u}}(k) \), it can be omitted in the cost function without affecting the result of the optimization problem.

  6. 6.

    For the cost function the constant term in (37) has been neglected. The inequality constraints can be derived by substituting (35) into the state constraints and adding the input constraints.

  7. 7.

    To simplify the notation, in (50, 50b, 50c) we dropped \( \alpha \beta \) from the vectors \( i_{s} ,\,\psi_{r} \) and \( v_{s} \).

  8. 8.

    The notation \( {\mathbf{H}}_{(i,1:i)} \) refers to the first i entries of the i-th row of \( {\mathbf{H}} \); similarly, \( {\mathbf{u}}_{1:i} \) are the first i elements of the vector \( {\mathbf{u}} \). Note that the matrix \( {\mathbf{H}} \) is time-invariant and does not change when running the algorithm. Therefore, \( {\mathbf{H}} \) can be computed once offline before the execution of the algorithm.

  9. 9.

    Note that, \( E_{\text{sw}} \) is a function of the inverter current i, which in turn is either a state variable or a linear combination of the state vector x.

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Acknowledgments

Research supported under Australian Research Council’s Discovery Projects funding scheme (project number DP 110103074).

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Authors and Affiliations

  1. School of Electrical Engineering and Computer Science, The University of Newcastle, Callaghan, NSW, 2308, Australia

    Daniel E. Quevedo & Ricardo P. Aguilera

  2. ABB Corporate Research, ABB Switzerland Ltd, Power Electronic Systems, Segelhofstrasse 1 K, 5405, Baden-Dättwil, Switzerland

    Tobias Geyer

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  1. Daniel E. Quevedo
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  2. Ricardo P. Aguilera
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  3. Tobias Geyer
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Correspondence to Daniel E. Quevedo .

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Editors and Affiliations

  1. Institute of Electrical Machines, Drives and Measurements, Wrocław University of Technology, Wrocław, Poland

    Teresa Orłowska-Kowalska

  2. Department of Energy Technology Power Electronic Systems, Aalborg University, Aalborg East, Denmark

    Frede Blaabjerg

  3. Department of Electronics Engineering, Universidad Técnica Federico Santa María, Valparaíso, Chile

    José Rodríguez

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Quevedo, D.E., Aguilera, R.P., Geyer, T. (2014). Predictive Control in Power Electronics and Drives: Basic Concepts, Theory, and Methods. In: Orłowska-Kowalska, T., Blaabjerg, F., Rodríguez, J. (eds) Advanced and Intelligent Control in Power Electronics and Drives. Studies in Computational Intelligence, vol 531. Springer, Cham. https://doi.org/10.1007/978-3-319-03401-0_5

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