An embedded scalable linear model predictive hardware-based controller using ADMM

Model predictive control (MPC) is a popular advanced model-based control algorithm for controlling systems that must respect a set of system constraints (e.g. actuator force limitations). However, the computing requirements of MPC limits the suitability of deploying its software implementation into embedded controllers requiring high update rates. This paper presents a scalable embedded MPC controller implemented on a field-programmable gate array (FPGA) coupled with an on-chip ARM processor. Our architecture implements an Alternating Direction Method of Multipliers (ADMM) approach for computing MPC controller commands. All computations are performed using floating-point arithmetic. We introduce a software/hardware (SW/HW) co-design methodology, for which the ARM software can configure on-chip Block RAM to allow users to 1) configure the MPC controller for a wide range of plants, and 2) update at runtime the desired trajectory to track. Our hardware architecture has the flexibility to compromise between the amount of hardware resources used (regarding Block RAMs and DSPs) and the controller computing speed. For example, this flexibility gives the ability to control plants modeled by a large number of decision variables (i.e. a plant model using many Block RAMs) with a small number of computing resources (i.e. DSPs) at the cost of increased computing time. The hardware controller is verified using a Plant-on-Chip (PoC), which is configured to emulate a mass-spring system in real-time. A major driving goal of this work is to architect an SW/HW platform that brings FPGAs a step closer to being widely adopted by advanced control algorithm designers for deploying their algorithms into embedded systems.

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

[2]  J. Richalet,et al.  Model predictive heuristic control: Applications to industrial processes , 1978, Autom..

[3]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[4]  Eric C. Kerrigan,et al.  FPGA implementation of an interior point solver for linear model predictive control , 2010, 2010 International Conference on Field-Programmable Technology.

[5]  A. Richards,et al.  Decentralized model predictive control of cooperating UAVs , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[6]  Brett Ninness,et al.  FPGA Implementation of an Interior-Point Solution for Linear Model Predictive Control , 2011 .

[7]  Viktor K. Prasanna,et al.  Sparse Matrix-Vector multiplication on FPGAs , 2005, FPGA '05.

[8]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[9]  U. Ammann,et al.  Model Predictive Control—A Simple and Powerful Method to Control Power Converters , 2009, IEEE Transactions on Industrial Electronics.

[10]  J. Bokor,et al.  Model predictive control in urban traffic network management , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[11]  Alberto Bemporad,et al.  Predictive Control for Linear and Hybrid Systems , 2017 .

[12]  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).

[13]  Jan M. Maciejowski,et al.  Embedded ADMM-based QP solver for MPC with polytopic constraints , 2015, 2015 European Control Conference (ECC).

[14]  Christopher D. Gill,et al.  An FPGA-Based Plant-on-Chip Platform for Cyber-Physical System Analysis , 2014, IEEE Embedded Systems Letters.

[15]  Eric C. Kerrigan,et al.  An FPGA implementation of a sparse quadratic programming solver for constrained predictive control , 2011, FPGA '11.

[16]  Guoyan Li,et al.  The Hardware Design and Implementation of a Signal Reconstruction Algorithm Based on Compressed Sensing , 2012, 2012 Fifth International Conference on Intelligent Networks and Intelligent Systems.

[17]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[18]  Helfried Peyrl,et al.  FPGA implementation of an interior point method for high-speed model predictive control , 2014, 2014 24th International Conference on Field Programmable Logic and Applications (FPL).

[19]  Zainal Ahmad,et al.  MODEL PREDICTIVE CONTROL (MPC) AND ITS CURRENT ISSUES IN CHEMICAL ENGINEERING , 2012 .

[20]  B. Anderson,et al.  Linear Optimal Control , 1971 .

[21]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[22]  Stephen P. Boyd,et al.  A Splitting Method for Optimal Control , 2013, IEEE Transactions on Control Systems Technology.