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.
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.
- 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.
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.
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.
- 7.
- 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.
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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Research supported under Australian Research Council’s Discovery Projects funding scheme (project number DP 110103074).
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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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