×

Embedded MPC controller based on interior-point method with convergence depth control. (English) Zbl 1354.93049

Summary: 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 2 ms on an embedded platform.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93C55 Discrete-time control/observation systems
93C05 Linear systems in control theory
90C20 Quadratic programming

Software:

mctoolbox
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Qin, A survey of industrial model predictive control technology, Control Eng. Practice 11 (7) pp 733– (2003) · doi:10.1016/S0967-0661(02)00186-7
[2] Bemporad, The explicit linear quadratic regulator for constrained systems, Automatica 38 (1) pp 3– (2002) · Zbl 0999.93018 · doi:10.1016/S0005-1098(01)00174-1
[3] Johansen, Hardware synthesis of explicit model predictive controllers, IEEE Trans. Control Syst. Technol. 15 (1) pp 191– (2007) · doi:10.1109/TCST.2006.883206
[4] Bemporad, Suboptimal explicit receding horizon control via approximate multiparametric quadratic programming, J. Optim. Theory Appl. 117 (1) pp 9– (2003) · Zbl 1044.90080 · doi:10.1023/A:1023696221899
[5] Summers, A multiresolution approximation method for fast explicit model predictive control, IEEE Trans. Autom. Control 56 (11) pp 2530– (2011) · Zbl 1368.93416 · doi:10.1109/TAC.2011.2146990
[6] Johansen, Approximate explicit constrained linear model predictive control via orthogonal search tree, IEEE Trans. Autom. Control 48 (5) pp 810– (2003) · Zbl 1364.93396 · doi:10.1109/TAC.2003.811259
[7] Ferreau, An online active set strategy to overcome the limitations of explicit MPC, Int. J. Robust Nonlinear Control 18 (8) pp 816– (2008) · Zbl 1284.93100 · doi:10.1002/rnc.1251
[8] Zeilinger, Real-time suboptimal model predictive control using a combination of explicit MPC and online optimization, IEEE Trans. Autom. Control 56 (7) pp 1524– (2011) · Zbl 1368.93417 · doi:10.1109/TAC.2011.2108450
[9] Wright , S. J. Applying new optimization algorithms to model predictive control Fifth Int. Conf. Chemical Process Control 1996
[10] Rao, Application of interior-point methods to model predictive control, J. Optim. Theory Appl. 99 (3) pp 723– (1998) · Zbl 0973.90092 · doi:10.1023/A:1021711402723
[11] Bartlett, Quadratic programming algorithms for large-scale model predictive control, J. Process Control 12 (7) pp 775– (2002) · doi:10.1016/S0959-1524(02)00002-1
[12] Domahidi , A. A. U. Zgraggen M. N. Zeilinger M. Morari C. Jones Efficient interior point methods for multistage problems arising in receding horizon control Proc. 51st IEEE Conf. Dec. Control 2012
[13] Patrinos, A global piecewise smooth Newton method for fast large-scale model predictive control, Automatica 47 (9) pp 2016– (2011) · Zbl 1231.65110 · doi:10.1016/j.automatica.2011.05.024
[14] Patrinos, An accelerated dual gradient-projection algorithm for embedded linear model predictive control, IEEE Trans. Autom. Control 59 (1) pp 18– (2014) · Zbl 1360.93400 · doi:10.1109/TAC.2013.2275667
[15] He , M. K. V. Ling Model predictive control on a chip IEEE Int. Conf. Contr. Autom. 1 528 532
[16] Wills, Fast linear model predictive control via custom integrated circuit architecture, IEEE Trans. Control Syst. Technol. 1 (20) pp 59– (2012)
[17] Jerez , J. L. G. A. Constantinides E. C. Kerrigan K. V. Ling Parallel MPC for real-time FPGA-based implementation Proc. 18th IFAC World Congr. 1338 1343 2011
[18] Jerez, Model predictive control for deeply pipelined field-programmable gate array implementation: algorithms and circuitry, IET Control Theory Appl. 6 (8) pp 1029– (2012) · doi:10.1049/iet-cta.2010.0441
[19] Lu, Convergence analysis and digital implementation of a discrete-time neural network for model predictive control, IEEE Trans. Ind. Electron 61 (12) pp 7035– (2014) · doi:10.1109/TIE.2014.2316250
[20] Currie , J. A. Prince-Pike D. I. Wilson Auto-code generation for fast embedded Model Predictive Controllers IEEE 19th Int. Conf. Mechatronics and Machine Vision in Practice (M2VIP) 116 122 2012
[21] Patrinos P. A. Guiggiani A. Bemporad Fixed-point dual gradient projection for embedded model predictive control European Control Conf. (ECC) 3602 3607 2013
[22] Wang, Fast model predictive control using online optimization, IEEE Trans. Control Syst. Technol. 18 (2) pp 267– (2010) · doi:10.1109/TCST.2009.2017934
[23] Nocedal, Numerical Optimization (1999) · Zbl 0930.65067 · doi:10.1007/b98874
[24] Vouzis, A system-on-a-chip implementation for embedded real-time model predictive control, IEEE Trans. Control Syst. Technol. 17 (5) pp 1006– (2009) · doi:10.1109/TCST.2008.2004503
[25] Chen, Convergence depth control for interior point methods, AICHE J. 56 (12) pp 3146– (2010) · doi:10.1002/aic.12225
[26] Lau , M. S. S. P. Yue K. V. Ling J. M. Maciejowski A comparison of interior point and active set methods for FPGA implementation of model predictive control Proc. European Control Conf. 157 161 2009
[27] Goldberg, What every computer scientist should know about floating-point arithmetic, ACM Comput. Surv. (CSUR) 23 (1) pp 5– (1991) · doi:10.1145/103162.103163
[28] Higham, Accuracy and stability of numerical algorithms (2002) · Zbl 1011.65010 · doi:10.1137/1.9780898718027
[29] Kothare, Robust constrained model predictive control using linear matrix inequalities, Automatica 32 (10) pp 1361– (1996) · Zbl 0897.93023 · doi:10.1016/0005-1098(96)00063-5
[30] Jerez, Embedded online optimization for model predictive control at megahertz rates, IEEE Trans. Autom. Control 59 (12) pp 3238– (2014) · Zbl 1360.93235 · doi:10.1109/TAC.2014.2351991
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.