Real-time FPGA Implementation of Direct MPC for Power Electronics

B. Stellato and P. J. Goulart

@inproceedings{SG:2016a,
  author = {B Stellato and P. J. Goulart},
  title = {Real-time FPGA Implementation of Direct MPC for Power Electronics},
  booktitle = {IEEE Conference on Decision and Control},
  year = {2016},
  pages = {1471-1476},
  url = {https://doi.org/10.1109/CDC.2016.7798474},
  doi = {10.1109/CDC.2016.7798474}
}

Common approaches for direct model predictive control (MPC) for current reference tracking in power electronics suffer from the high computational complexity encountered when solving integer optimal control problems over long prediction horizons. Recently, an alternative method based on approximate dynamic programming showed that it is possible to reduce the computational burden enabling sampling times under 25 mus by shortening the MPC horizon to a very small number of stages while improving the overall controller performance. In this paper we implemented this new approach on a small size FPGA and validated it on a variable speed drive system with a three-level voltage source converter. Time measurements showed that only 5.76 mus are required to run our algorithm for horizon N = 1 and 17.27 mus for N = 2 while outperforming state of the art approaches with much longer horizons in terms of currents distortion and switching frequency. To the authors knowledge, this is the first time direct MPC for current control has been implemented on an embedded platform achieving comparable performance to formulations with long prediction horizons.

Optimal Control of Switching Times in Switched Linear Systems

B. Stellato, S. Ober-Blöbaum and P. J. Goulart

@inproceedings{SG:2016b,
  author = {B. Stellato and S. Ober-Blöbaum and P. J. Goulart},
  title = {Optimal Control of Switching Times in Switched Linear Systems},
  booktitle = {IEEE Conference on Decision and Control},
  year = {2016},
  pages = {7228-7233},
  url = {https://doi.org/10.1109/CDC.2016.7799384},
  doi = {10.1109/CDC.2016.7799384}
}

Switching time optimization arises in finite-horizon optimal control for switched systems where, given a sequence of continuous dynamics, we minimize a cost function with respect to the switching times. In this paper we propose an efficient method for computing optimal switching times in switched linear systems. We derive simple expressions for the cost function, the gradient and the Hessian which can be computed efficiently online without performing any integration. With the proposed method, the most expensive computations are decomposed into independent scalar exponentials which can be efficiently computed and parallelized. Simulation results show that our method is able to provide fast convergence and handle efficiently a high number switching times.

High-Speed Direct Model Predictive Control for Power Electronics

B. Stellato and P. J. Goulart

@inproceedings{SG:2016,
  author = {B. Stellato and P. J. Goulart},
  title = {High-Speed Direct Model Predictive Control for Power Electronics},
  booktitle = {European Control Conference},
  year = {2016},
  pages = {129-134},
  url = {https://doi.org/10.1109/ECC.2016.7810275},
  doi = {10.1109/ECC.2016.7810275}
}

Common approaches for direct model predictive control (MPC) for current reference tracking in power electronics suffer from the high computational complexity encountered when solving integer optimal control problems over long prediction horizons. We propose an efficient alternative method based on approximate dynamic programming, greatly reducing the computational burden and enabling sampling times under 25 microseconds. Our approach is based on the offline minimization of an infinite horizon cost function estimate which is then applied to the tail cost of the MPC problem. This allows us to reduce the controller horizon to a very small number of stages improving overall controller performance. Our proposed algorithm is validated on a variable speed drive system with a three-level voltage source converter.