Offset-free nonlinear Model Predictive Control with state-space process models

Open access

Abstract

Offset-free model predictive control (MPC) algorithms for nonlinear state-space process models, with modeling errors and under asymptotically constant external disturbances, is the subject of the paper. The main result of the paper is the presentation of a novel technique based on constant state disturbance prediction. It was introduced originally by the author for linear state-space models and is generalized to the nonlinear case in the paper. First the case with measured state is considered, in this case the technique allows to avoid disturbance estimation at all. For the cases with process outputs measured only and thus the necessity of state estimation, the technique allows the process state estimation only - as opposed to conventional approach of extended process-and-disturbance state estimation. This leads to simpler design with state observer/filter of lower order and, moreover, without the need of a decision of disturbance placement in the model (under certain restrictions), as in the conventional approach. A theoretical analysis of the proposed algorithm is provided, under applicability conditions which are weaker than in the conventional approach. The presented theory is illustrated by simulation results of nonlinear processes, showing competitiveness of the proposed algorithms.

[1] K.J. Astrom and B. Wittenmark: Computer Controlled Systems. Prentice Hall, Upper Saddle River, 1997.

[2] J. Birk andM. Zeitz: Extended Luenberger observer for non-linear multivariable systems. Int. J. of Control, 47(6), (1988), 1823-1835.

[3] T. L. Blevins, G. K. McMillan, W. K. Wojsznis and M. W. Brown: Advanced Control Unleashed. The ISA Society, Research Triangle Park, NC, 2003.

[4] T. L. Blevins, W. K. Wojsznis and M. Nixon: Advanced Control Foundation. The ISA Society, Research Triangle Park, NC, 2013.

[5] E.F. Camacho and C. Bordons: Model Predictive Control. Springer Verlag, London, 1999.

[6] A. H. Gonzalez, E. J. Adam and J. L. Marchetti: Conditions for offset elimination in state space receding horizon controllers: A tutorial analysis. Chemical Engineering and Processing, 47 (2008), 2184-2194.

[7] M. Ławryńczuk: Computationally Efficient Model Predictive Control Algorithms: A Neural Network Approach, Studies in Systems, Decision and Control, 3. Springer Verlag, Heidelberg, 2014.

[8] M. Ławryńczuk: Nonlinear state-space predictive control with on-line linearisation and state estimation. Int. J. of Applied Mathematics and Computer Science, 25(4), (2015), 833-847.

[9] J.M. Maciejowski: Predictive Control. Prentice Hall, Harlow, England, 2002.

[10] U. Maeder, F. Borelli and M. Morari: Linear offset-free model predictive control. Automatica, 45 (2009), 2214-2222.

[11] U. Maeder and M. Morari: Offset-free reference tracking with model predictive control. Automatica, 46 (2010), 1469-1476.

[12] M. Morari and U. Maeder: Nonlinear offset-free model predictive control. Automatica, 48 (2012), 2059-2067.

[13] K.R. Muske and T.A. Badgwell: Disturbance modeling for offset-free linear model predictive control. J. of Process Control, 12 (2002), 617-632.

[14] G. Pannocchia and A. Bemporad: Combined design of disturbance model and observer for offset-free model predictive control. IEEE Trans. on Automatic Control, 52(6), (2007), 1048-1053.

[15] G. Pannocchia and J.B. Rawlings: Disturbance models for offset-free model predictive control. AIChE J., 49(2), (2003), 426-437.

[16] S.J. Qin and T.A. Badgwell: A survey of industrial model predictive control technology. Control Engineering Practice, 11 (2003), 733-764.

[17] V. Rao and J. B. Rawlings: Steady states and constraints in model predictive control. AIChE J., 45(6), (1999), 1266-1278.

[18] J. B. Rawlings and D. Q. Mayne: Model Predictive Control: Theory and Design. Nob Hill Publishing, Madison, 2009.

[19] J.A. Rossiter: Model-Based Predictive Control. CRC Press, Boca Raton - London - New York - Washington, D.C., 2003.

[20] P. Tatjewski: Advanced Control of Industrial Processes. Springer Verlag, London, 2007.

[21] P. Tatjewski: Advanced control and on-line process optimization in multilayer structures. Annual Reviews in Control, 32 (2008), 71-85.

[22] P. Tatjewski: Supervisory predictive control and on-line set-point optimization. Int. J. of Applied Mathematics and Computer Science, 20(3), (2010), 483-496.

[23] P. Tatjewski: Disturbance modeling and state estimation for offset-free predictive control with state-spaced process models. Int. Journal of Applied Mathematics and Computer Science, 24(2), (2014), 313-323.

[24] P. Tatjewski: Offset-free nonlinear predictive control with measured state and unknown asymptotically constant disturbances. In K. Malinowski, J. Józefczyk, and J.Światek, (Eds) Aktualne problemy automatyki i robotyki (Actual problems in automation and robotics), pages 288-299. Akademicka Oficyna Wydawnicza (Academic Publisher) EXIT, Warszawa, 2014.

[25] P. Tatjewski: Sterowanie zaawansowane procesów przemysłowych (Advanced Control of Industrial Processes), Second, revised edition (e-book, in Polish). Akademicka Oficyna Wydawnicza (Academic Publisher) EXIT, Warszawa, 2016.

[26] P. Tatjewski: Offset-free nonlinear model predictive control. In W. Mitkowski, J. Kacprzyk, K. Oprzedkiewicz, and P. Skruch, (Eds), Trends in Advanced Intelligent Control, Optimization and Automation, Proc. of 19th Polish Control Conference, Advances in Intelligent Systems and Computing 577, pages 33-44. Springer, 2017.

[27] P. Tatjewski and M. Ławryńczuk: Soft computing in model-based predictive control. Int. J. of Applied Mathematics and Computer Science, 16(1), (2006), 7-26.

[28] L. Wang: Model Predictive Control System Design and Implementation using MATLAB. Springer Verlag, London, 2009.

Archives of Control Sciences

The Journal of Polish Academy of Sciences

Journal Information


IMPACT FACTOR 2016: 0.705

CiteScore 2016: 3.11

SCImago Journal Rank (SJR) 2016: 0.231
Source Normalized Impact per Paper (SNIP) 2016: 0.565

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 141 141 20
PDF Downloads 44 44 8