Embedded MPC Controller Based on Interior‐Point Method with Convergence Depth Control

To allow the implementation of model predictive control on the chip, we first propose a primal-dual interior point method with convergence depth control to solve the quadratic programming problem of model predictive control. Compared with algorithms based on traditional termination criterion, the proposed method can significantly reduce the computation cost while obtaining an approximate solution of the quadratic programming problem with acceptable optimality and precision. Thereafter, an embedded model predictive controller based on the quadratic programming solver is designed and implemented on a digital signal processor chip and a prototype system is built on a TMDSEVM6678LE digital signal processor chip. The controller is verified on two models by using the hardware in loop frame to mimic real applications. The comparison shows that the whole design is competitive in real-time applications. The typical computation time for quadratic programming problems with 5 decision variables and 110 constraints can be reduced to less than 2ms on an embedded platform.

[1]  Manfred Morari,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[2]  Manfred Morari,et al.  A Multiresolution Approximation Method for Fast Explicit Model Predictive Control , 2011, IEEE Transactions on Automatic Control.

[3]  Alberto Bemporad,et al.  The explicit linear quadratic regulator for constrained systems , 2003, Autom..

[4]  Tor Arne Johansen,et al.  Hardware Synthesis of Explicit Model Predictive Controllers , 2007, IEEE Transactions on Control Systems Technology.

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

[6]  Dewei Li,et al.  Convergence Analysis and Digital Implementation of a Discrete-Time Neural Network for Model Predictive Control , 2014, IEEE Transactions on Industrial Electronics.

[7]  Manfred Morari,et al.  Efficient interior point methods for multistage problems arising in receding horizon control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[8]  Stephen P. Boyd,et al.  Fast Model Predictive Control Using Online Optimization , 2010, IEEE Transactions on Control Systems Technology.

[9]  Tor Arne Johansen,et al.  Approximate explicit constrained linear model predictive control via orthogonal search tree , 2003, IEEE Trans. Autom. Control..

[10]  Alberto Bemporad,et al.  Fixed-point dual gradient projection for embedded model predictive control , 2013, 2013 European Control Conference (ECC).

[11]  Alberto Bemporad,et al.  An Accelerated Dual Gradient-Projection Algorithm for Embedded Linear Model Predictive Control , 2014, IEEE Transactions on Automatic Control.

[12]  Pantelis Sopasakis,et al.  A global piecewise smooth Newton method for fast large-scale model predictive control , 2011, Autom..

[13]  Manfred Morari,et al.  Real-Time Suboptimal Model Predictive Control Using a Combination of Explicit MPC and Online Optimization , 2011, IEEE Trans. Autom. Control..

[14]  A. Bemporad,et al.  Suboptimal Explicit Receding Horizon Control via Approximate Multiparametric Quadratic Programming , 2003 .

[15]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[16]  Eric C. Kerrigan,et al.  Model predictive control for deeply pipelined field-programmable gate array implementation: algorithms and circuitry , 2012 .

[17]  Zhijiang Shao,et al.  Convergence depth control for interior point methods , 2010 .

[18]  Manfred Morari,et al.  Embedded Online Optimization for Model Predictive Control at Megahertz Rates , 2013, IEEE Transactions on Automatic Control.

[19]  Leonidas G. Bleris,et al.  A System-on-a-Chip Implementation for Embedded Real-Time Model Predictive Control , 2009, IEEE Transactions on Control Systems Technology.

[20]  D. I. Wilson,et al.  Auto-code generation for fast embedded Model Predictive Controllers , 2012, 2012 19th International Conference on Mechatronics and Machine Vision in Practice (M2VIP).

[21]  David Goldberg,et al.  What every computer scientist should know about floating-point arithmetic , 1991, CSUR.

[22]  Minghua He,et al.  Model predictive control on a chip , 2005, 2005 International Conference on Control and Automation.

[23]  Eric C. Kerrigan,et al.  Parallel MPC for Real-Time FPGA-based Implementation , 2011 .

[24]  Johan U. Backstrom,et al.  Quadratic programming algorithms for large-scale model predictive control , 2002 .

[25]  Stephen J. Wright,et al.  Application of Interior-Point Methods to Model Predictive Control , 1998 .

[26]  Brett Ninness,et al.  Fast Linear Model Predictive Control Via Custom Integrated Circuit Architecture , 2012, IEEE Transactions on Control Systems Technology.

[27]  Jan M. Maciejowski,et al.  A comparison of interior point and active set methods for FPGA implementation of model predictive control , 2009, 2009 European Control Conference (ECC).