Computationally efficient long-horizon direct model predictive control for transient operation

In this paper we present modifications in the sphere decoder initially introduced in [1] and modified in [2] that allow for its implementation in transient operation. By investigating the geometry of the integer problem underlying direct model predictive control (MPC), a new sphere that guarantees feasibility and includes a significant smaller number of candidate solutions is computed. In a first analysis, the computational complexity can be reduced by up to 99.7% when a variable speed drive system consisting of a three-level neutral point clamped (NPC) voltage source inverter and a medium-voltage induction machine is examined. As also shown, optimality is sacrificed only to a limited extent, thus maintaining the very fast transient response inherent to direct MPC.

[1]  U. Fincke,et al.  Improved methods for calculating vectors of short length in a lattice , 1985 .

[2]  Rolf Findeisen,et al.  Implementation aspects of model predictive control for embedded systems , 2012, 2012 American Control Conference (ACC).

[3]  Joachim Holtz,et al.  The representation of AC machine dynamics by complex signal flow graphs , 1995, IEEE Trans. Ind. Electron..

[4]  Tobias Geyer,et al.  Model predictive control in power electronics: Strategies to reduce the computational complexity , 2013, IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society.

[5]  Tobias Geyer,et al.  Direct Voltage Control of DC–DC Boost Converters Using Enumeration-Based Model Predictive Control , 2014, IEEE Transactions on Power Electronics.

[6]  T. Geyer,et al.  Reformulation of the long-horizon direct model predictive control problem to reduce the computational effort , 2014, 2014 IEEE Energy Conversion Congress and Exposition (ECCE).

[7]  T. Geyer,et al.  Suboptimal search strategies with bounded computational complexity to solve long-horizon direct model predictive control problems , 2015, 2015 IEEE Energy Conversion Congress and Exposition (ECCE).

[8]  Daniel E. Quevedo,et al.  Performance of Multistep Finite Control Set Model Predictive Control for Power Electronics , 2014, IEEE Transactions on Power Electronics.

[9]  Manfred Morari,et al.  Model Predictive Direct Torque Control—Part I: Concept, Algorithm, and Analysis , 2009, IEEE Transactions on Industrial Electronics.

[10]  Moritz Diehl,et al.  An auto-generated real-time iteration algorithm for nonlinear MPC in the microsecond range , 2011, Autom..

[11]  Tobias Geyer,et al.  On the benefit of long-horizon direct model predictive control for drives with LC filters , 2014, 2014 IEEE Energy Conversion Congress and Exposition (ECCE).

[12]  Daniele Micciancio,et al.  The hardness of the closest vector problem with preprocessing , 2001, IEEE Trans. Inf. Theory.

[13]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

[14]  P. Toint,et al.  Global convergence of a class of trust region algorithms for optimization with simple bounds , 1988 .

[15]  Y. Nesterov.  A method for solving the convex programming problem with convergence rate O(1/k^2) , 1983 .

[16]  F. Ana,et al.  A new method for large-scale box constrained convex quadratic minimization problems , 1995 .

[17]  E. L. Lawler,et al.  Branch-and-Bound Methods: A Survey , 1966, Oper. Res..

[18]  M. Morari,et al.  Move blocking strategies in receding horizon control , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[19]  Marc Teboulle,et al.  Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems , 2009, IEEE Transactions on Image Processing.

[20]  Tobias Geyer,et al.  Model predictive control of high power converters and industrial drives , 2016, 2017 IEEE Energy Conversion Congress and Exposition (ECCE).

[21]  Tobias Geyer,et al.  Computationally efficient Model Predictive Direct Torque Control , 2010, 2010 IEEE Energy Conversion Congress and Exposition.

[22]  J. Borwein,et al.  Two-Point Step Size Gradient Methods , 1988 .

[23]  Daniel E. Quevedo,et al.  Performance of Multistep Finite Control Set Model Predictive Control for Power Electronics , 2015 .

[24]  M. Raydan.  On the Barzilai and Borwein choice of steplength for the gradient method , 1993 .

[25]  Babak Hassibi,et al.  On the sphere-decoding algorithm I. Expected complexity , 2005, IEEE Transactions on Signal Processing.

[26]  László Babai,et al.  On Lovász’ lattice reduction and the nearest lattice point problem , 1986, Comb..

[27]  Daniel E. Quevedo,et al.  Fast multistep finite control set model predictive control for transient operation of power converters , 2016, IECON 2016 - 42nd Annual Conference of the IEEE Industrial Electronics Society.

[28]  Ralph Kennel,et al.  Predictive control in power electronics and drives , 2008, 2008 IEEE International Symposium on Industrial Electronics.

[29]  T. Geyer,et al.  Constrained long-horizon direct model predictive control for power electronics , 2016, 2016 IEEE Energy Conversion Congress and Exposition (ECCE).

[30]  T. Geyer,et al.  Computationally efficient sphere decoding for long-horizon direct model predictive control , 2016, 2016 IEEE Energy Conversion Congress and Exposition (ECCE).

[31]  Petros P. Karamanakos,et al.  A Computationally Efficient Model Predictive Control Strategy for Linear Systems With Integer Inputs , 2016, IEEE Transactions on Control Systems Technology.