Continuous Control Set Nonlinear Model Predictive Control of Reluctance Synchronous Machines

In this paper we describe the design and implementation of a current controller for a reluctance synchronous machine based on continuous set nonlinear model predictive control. A simplified experimentally identified grey box model of the flux linkage map is employed in a tracking formulation which is implemented using the high-performance framework for nonlinear model predictive control acados. The resulting controller is validated in simulation and deployed on a dSPACE real-time system connected with a physical reluctance synchronous machine. Experimental results are presented where the proposed implementation can reach sampling times in the range typical for electrical drives and outperforms state-of-the-art classical control strategies.

[1]  Christoph M. Hackl,et al.  A unified theory for optimal feedforward torque control of anisotropic synchronous machines , 2018, Int. J. Control.

[2]  S. Williamson,et al.  Direct finite element design optimisation of the cageless reluctance synchronous machine , 1996 .

[3]  Moritz Diehl,et al.  Recent Advances in Quadratic Programming Algorithms for Nonlinear Model Predictive Control , 2018, Vietnam Journal of Mathematics.

[4]  Moritz Diehl,et al.  ACADO toolkit—An open‐source framework for automatic control and dynamic optimization , 2011 .

[5]  Abdesselam Chikhi,et al.  A Comparative Study of Field-Oriented Control and Direct-Torque Control of Induction Motors Using An Adaptive Flux Observer , 2010 .

[6]  Moritz Diehl,et al.  Auto Generation of Implicit Integrators for Embedded NMPC with Microsecond Sampling Times , 2012 .

[7]  Z. X. Fu,et al.  TORQUE VECTOR CONTROL (TVC) OF AXIALLY-LAMINATED ANISOTROPIC (ALA) ROTOR RELUCTANCE SYNCHRONOUS MOTORS , 1991 .

[8]  M. Diehl,et al.  HPIPM: a high-performance quadratic programming framework for model predictive control , 2020, IFAC-PapersOnLine.

[9]  Christian Feller,et al.  Relaxed Logarithmic Barrier Function Based Model Predictive Control of Linear Systems , 2015, IEEE Transactions on Automatic Control.

[10]  S. Mariethoz,et al.  High-Bandwidth Explicit Model Predictive Control of Electrical Drives , 2012, IEEE Transactions on Industry Applications.

[11]  Shu Yamamoto,et al.  Maximum efficiency drives of synchronous reluctance motors by a novel loss minimization controller considering cross-magnetic saturation , 2009, 2009 IEEE Energy Conversion Congress and Exposition.

[12]  Dragan Nesic,et al.  Optimization-Based Stabilization of Sampled-Data Nonlinear Systems via Their Approximate Discrete-Time Models , 2003, SIAM J. Control. Optim..

[13]  Christoph M. Hackl,et al.  Current PI-funnel control with anti-windup for synchronous machines , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[14]  T. S. Radwan,et al.  A maximum torque per ampere vector control strategy for synchronous reluctance motors considering saturation and iron losses , 2004, Conference Record of the 2004 IEEE Industry Applications Conference, 2004. 39th IAS Annual Meeting..

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

[16]  Thomas A. Lipo,et al.  Field oriented control of synchronous reluctance machine , 1993, Proceedings of IEEE Power Electronics Specialist Conference - PESC '93.

[17]  Andreas Kugi,et al.  Stability and Incremental Improvement of Suboptimal MPC Without Terminal Constraints , 2010, IEEE Transactions on Automatic Control.

[18]  Moritz Diehl,et al.  Inexact Newton-Type Optimization with Iterated Sensitivities , 2018, SIAM J. Optim..

[19]  Gabriele Pannocchia,et al.  Disturbance models for offset‐free model‐predictive control , 2003 .

[20]  Moritz Diehl,et al.  Efficient Zero-Order NMPC with Feasibility and Stability Guarantees , 2019, 2019 18th European Control Conference (ECC).

[21]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[22]  Moritz Diehl,et al.  In-Vehicle Realization of Nonlinear MPC for Gasoline Two-Stage Turbocharging Airpath Control , 2018, IEEE Transactions on Control Systems Technology.

[23]  R. Kennel,et al.  Fundamental saliency based encoderless control for reluctance synchronous machines , 2010, The XIX International Conference on Electrical Machines - ICEM 2010.

[24]  Maarten J. Kamper,et al.  Nonlinear PI current control of reluctance synchronous machines , 2015, ArXiv.

[25]  Christian Kirches,et al.  qpOASES: a parametric active-set algorithm for quadratic programming , 2014, Mathematical Programming Computation.

[26]  Moritz Diehl,et al.  A Lyapunov Function for the Combined System-Optimizer Dynamics in Nonlinear Model Predictive Control , 2020 .

[27]  R. Kennel,et al.  Reducing the parameter dependency of Encoderless Predictive Torque Control for reluctance machines , 2010, 2010 First Symposium on Sensorless Control for Electrical Drives.

[28]  Moritz Diehl,et al.  Lifted implicit integrators for direct optimal control , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[29]  Frank Allgöwer,et al.  A Stabilizing Real-time Implementation of Nonlinear Model Predictive Control , 2007 .

[30]  M. Diehl,et al.  Nominal stability of real-time iteration scheme for nonlinear model predictive control , 2005 .

[31]  X. Xu,et al.  Vector control of a synchronous reluctance motor including saturation and iron loss , 1990, Conference Record of the 1990 IEEE Industry Applications Society Annual Meeting.

[32]  Manfred Morari,et al.  Nonlinear offset-free model predictive control , 2012, Autom..

[33]  Moritz Diehl,et al.  Detecting and Exploiting Generalized Nonlinear Static Feedback Structures in DAE Systems for MPC , 2019, 2019 18th European Control Conference (ECC).

[34]  Moritz Diehl,et al.  Contraction Estimates for Abstract Real-Time Algorithms for NMPC , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).

[35]  Daniel E. Quevedo,et al.  Model Predictive Control for Power Electronics Applications , 2018, Handbook of Model Predictive Control.

[36]  Moritz Diehl,et al.  Real-Time Optimization for Large Scale Nonlinear Processes , 2001 .

[37]  H. J. Ferreau,et al.  An online active set strategy to overcome the limitations of explicit MPC , 2008 .

[38]  Stefan Almér,et al.  Model Predictive Control in the Multi-Megawatt Range , 2016, IEEE Transactions on Industrial Electronics.

[39]  Moritz Diehl,et al.  Exploiting convexity in direct Optimal Control: a sequential convex quadratic programming method , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[40]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

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

[42]  R.E. Betz,et al.  Control of synchronous reluctance machines , 1991, Conference Record of the 1991 IEEE Industry Applications Society Annual Meeting.

[43]  Maarten J. Kamper,et al.  Current control of reluctance synchronous machines with online adjustment of the controller parameters , 2016, 2016 IEEE 25th International Symposium on Industrial Electronics (ISIE).

[44]  Gionata Cimini,et al.  Embedded Model Predictive Control With Certified Real-Time Optimization for Synchronous Motors , 2021, IEEE Transactions on Control Systems Technology.

[45]  Johannes P. Schlöder,et al.  Newton-Type Methods for the Approximate Solution of Nonlinear Programming Problems in Real-Time , 2003 .

[46]  Kenneth R. Muske,et al.  Disturbance modeling for offset-free linear model predictive control , 2002 .

[47]  Moritz Diehl,et al.  Towards a modular software package for embedded optimization , 2018 .

[48]  Moritz Diehl,et al.  Efficient NMPC for nonlinear models with linear subsystems , 2013, 52nd IEEE Conference on Decision and Control.

[49]  G. Pannocchia,et al.  Offset-free MPC explained: novelties, subtleties, and applications , 2015 .

[50]  Christoph M. Hackl,et al.  Non-identifier Based Adaptive Control in Mechatronics , 2017 .

[51]  Knut Graichen,et al.  A Fixed-Point Iteration Scheme for Model Predictive Torque Control of PMSMs , 2018 .

[52]  Moritz Diehl,et al.  Nonlinear Model Predictive Control of a Human-sized Quadrotor , 2018, 2018 European Control Conference (ECC).

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