(444a) Model Predictive Control for Embedded Applications

Model Predictive Control (MPC) refers to a family of control algorithms that compute a sequence of manipulated variables by solving an optimization problem, incorporating explicit knowledge of the plant model and incorporating feedback information. Due to the properties of MPC?its ability to handle nonlinear, constrained, and multivariable systems yet its severe computational requirements?it has primarily been used in the chemical process industries. Thus, while MPC remains an open and growing area of research in systems and control, there are somewhat limited applications reported outside the processes industries. More recently, there has been considerable interest in expanding the applicability of MPC to other domains of engineering which were traditionally considered unsuitable for MPC due to their small physical size and fast dynamics. Applications that can readily benefit from embedded MPC chip range from automotive and avionics [5] to microchemical systems [1, 11], drug-delivery systems [2, 12] and fuel cells [9, 10].

In [10], Wright and Edgar, present the use of Nonlinear MPC for controlling a Water Gas Shift (WGS) reactor, which is essential for the efficient operations of a fuel processor [9]. At that time, the problem was solved on a cascade control configuration of three workstations, which is impossible to be employed for portable devices, powered by fuel cells, due to size and power-consumption restrictions. Nevertheless, the recent advances in the semiconductor technology and in computer architecture, enables today the integration of enough computational power on a chip, to solve efficiently NMPC problems in real time [3].

The objective of this work is twofold; firstly, to give an overview of the platforms that have appeared in the literature for embedding MPC in applications with small physical size, such as fuel processors, and secondly, to present our recent research results towards the same direction. The proposed approaches for embedding MPC span a wide implementation spectrum, ranging from pure software to complete hardware.

A direct solution is to use an off-the-shelf microprocessor which can be programmed to solve an MPC problem [3]. This approach leads to short development time and easy reprogrammability. However, commercial microprocessors are designed for a wide range of applications, and thus usually encompass unnecessary resources (increased arithmetic accuracy, redundant peripherals), which potentially lead to a sizeable implementation platform exhibiting increased power consumption.

The results of designing a FPGA hardware unit tailored to solve a constrained MPC problem are presented in [5]. In this paper, a rapid prototyping environment for FPGAs is used that helps to explore the design space efficiently, and Hardware-In-the-Loop (HIL) simulations were conducted for verifying the functionality and the performance of the design. In [4], synthesis results for implementing explicit MPC [13] on a Field Programmable Gate Array (FPGA) or an Applications-Specific Integrated Circuit are presented. In explicit MPC the optimization problem is solved off-line and during runtime the solutions are only invoked from a local memory. The disadvantage of this approach is that the memory requirements increase superexponentially as the sizes of parameters of the problem increase (number of inputs and outputs, control and prediction horizon), resulting in prohibitive sizes for small scale embedded applications.

Four different processor-array architectures, for the Generalized Predictive Control (GPC), are proposed in [7]. Processor arrays offer certain advantages, such as modularity, reconfigurability, parallelism and pipelineability. However, the particular architecture is limited to unconstrained optimization problems, and, in general, the processor arrays are not scalable to problems of different sizes, thus wasting resources when matrices smaller, than the ones designed for, are used. An Application Specific Integrated Circuit (ASIC) MPC chip is presented in [1], where the control problems of temperature distribution across a wafer and the non-isothermal flow in a microdevice are addressed. It is shown, by emulation, that a reduced precision processor can solve, close to optimally, the aforementioned problems, while proving energy and computational cost savings by taking advantage of the Logarithmic Number System (LNS) [8].

Our approach follows a hardware-software co-design path to produce an architecture that occupies small area, and consequently is power efficient, and is easily reconfigurable to different algorithms [6]. This is achieved by dividing the operations in an MPC algorithm in two parts; one that fits into a general-purpose microprocessor and one into an auxiliary array coprocessor. A profiling study of the algorithm reveals the computationally demanding parts of the algorithm (characterized by substantial matrix operations), which are migrated to the matrix coprocessor, while the rest of the algorithm is executed on the microprocessor, which runs a software program developed in a high-level programming language. The system has been implemented and prototyped on an FPGA. Its functionality has been verified by employing HIL simulations, where the FPGA (executing the MPC algorithm) is connected to a workstation (emulating the behavior of the system under control). The hardware requirements, the performance and a HIL simulation case study will be presented.

[1] L. G. Bleris, J. G. Garcia, M. V. Kothare, and M. G. Arnold, ?Towards Embedded Model Predictive Control for System-on-a-Chip Applications,? in Journal of Process Control, vol. 16, pp. 255?264, March 2006.

[2] R. S. Parker, F. J. Doyle III, and N. A. Peppas, ?A Model-Based Algorithm for Blood Glucose Control in Type I Diabetic Patients,? IEEE Transactionson Biomedical Engineering, vol. 46, pp. 148?156, Feb. 1999.

[3] L. G. Bleris and M. Kothare, ?Implementation of Model Predictive Control for Glucose Regulation on a General Purpose Microprocessor,? in 44th IEEE European Control Conference, ECC 2005, (Seville, Spain), Dec. 12?15 2005.

[4] T. A. Johansen, W. Jackson, R. Schreiber, and P. Tøndel, ?Hardware Architecture Design for Explicit Model Predictive Control,? In proceedings of the Americal Control Conference, (Minneapolis, MN), 14?16 June 2006.

[5] K. Ling, S. Yue, and J. Maciejowski, ?An FPGA Implementation of Model Predictive Control,? In proceedings of the Americal Control Conference, (Minneapolis, MN), 14?16 June 2006.

[6] P. Vouzis, L. Bleris, M. Kothare, and M. Arnold, ?A System-on-a-Chip Implementation for Embedded Real-Time Model Predictive Control,? Submitted to IEEE Transactions on Control Systems Technology (2006).

[7] K. Karagianni, T. Chronopoulos, A. Tzes, N. Kousoulas, and T. Stouraitis, ?Efficient Processor Arrays for the Implementation of the Generalized Predictive-Control Algorithm,? IEE Proceedings ? Control Theory and Applications, vol. 145, pp. 47?54, Jan. 1998.

[8] E. E. Swartzlander and A. G. Alexopoulos, ?The Sign/Logarithm Number System,? IEEE Transactions on Computers, vol. 24, pp. 1238?1242, Dec. 1975.

[9] S. Varigonda, J. Ebom, and S. A. Bortoff, ?Multivariable Control Design for the Water Gas Shift Reactor in a Fuel Processor,? In proceedings of the American Control Conference, (Boston, MA), pp. 840 ? 844, 2004.

[10] G. T. Wright and T. F. Edgar, ?Nonlinear Model Predictive Control of a Fixed-Bed Water-Gas Shift Reactor: An Experimental Study,? Computers & Chemical Engineering, Vol. 18, No. 2, pp. 83 ? 102, Feb. 1994.

[11] L. G. Bleris, J. Garcia, M. G. Arnold, and M. V. Kothare, ?Model Predictive Hydrodynamic Regulation of Microflows?, submitted: Journal of Micromechanics and Microengineering, 2006.

[12] L. G. Bleris, P. Vouzis, M. G. Arnold, and M. V. Kothare, ?Pathways for Optimization-Based Drug Delivery Systems and Devices,? In proceedings of the International Symposium on Advanced Control of Chemical Processes (ADCHEM) 2006, Gramado, Brazil. April 2006.

[13] A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, ?The Explicit Linear Quadratic Regulator for Constrained Systems,? Automatica, vol. 38, No. 1, pp. 3?20, 2002.