Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Tracking Model Predictive Control

  • Daniel Limon
  • Teodoro AlamoEmail author
Living reference work entry

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DOI: https://doi.org/10.1007/978-1-4471-5102-9_3-2

Abstract

The main objective of tracking model predictive control is to stabilize the plant satisfying the constraints and steering the tracking error, that is, the difference between the reference and the output, to zero. In order to predict the expected evolution of the tracking error, some assumptions on the future values of the reference must be considered. Since the reference may differ from expected, the tracking problem is inherently uncertain.

The most common case is to assume that the reference will remain constant along the prediction horizon. These predictive control schemes are typically based on a two-layer control structure in which, provided the value of the reference, first an appropriate target equilibrium point is computed, and then an MPC is designed to regulate the system to this target. Under certain assumptions, closed-loop stability can be guaranteed if the initial state is inside the feasibility region of the MPC. However, if the value of the reference is changed, then there is no guarantee that feasibility and stability properties of the resulting control law hold. Specialized predictive controllers have been designed to deal with this problem. Particularly interesting is the so-called MPC for tracking, which ensures recursive feasibility and asymptotic stability of the setpoint when the value of the reference is changed.

The presence of exogenous disturbances or model mismatches may lead to the controlled system to exhibit offset error. Offset-free control can be achieved by using disturbance models and disturbance estimators together with the tracking predictive controller.

Keywords

Reference tracking Loss of recursive feasibility MPC for tracking Offset-free control 
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Notes

Acknowledgements

The authors would like to thank the support received by the MINECO-Spain and FEDER Funds under project DPI2016-76493-C3-1-R.

Bibliography

  1. Angeli D, Amrit R, Rawlings JB (2012) On average performance and stability of economic model predictive control. IEEE Trans Autom Control 57:1615–1626MathSciNetCrossRefGoogle Scholar
  2. Bemporad A, Casavola A, Mosca E (1997) Nonlinear control of constrained linear systems via predictive reference management. IEEE Trans Autom Control 42:340–349MathSciNetCrossRefGoogle Scholar
  3. Camacho EF, Bordons C (2004) Model predictive control, 2nd edn. Springer, New YorkzbMATHGoogle Scholar
  4. Chisci L, Zappa G (2003) Dual mode predictive tracking of piecewise constant references for constrained linear systems. Int J Control 76:61–72MathSciNetCrossRefGoogle Scholar
  5. Ferramosca A, Limon D, Alvarado I, Alamo T, Camacho EF (2009) MPC for tracking with optimal closed-loop performance. Automatica 45:1975–1978MathSciNetCrossRefGoogle Scholar
  6. Findeisen R, Chen H, Allgöwer F (2000) Nonlinear predictive control for setpoint families. In: Proceedings of the American control conferenceCrossRefGoogle Scholar
  7. Limon D, Alvarado I, Alamo T, Camacho EF (2008) MPC for tracking of piece-wise constant references for constrained linear systems. Automatica 44:2382–2387MathSciNetCrossRefGoogle Scholar
  8. Limon D, Ferramosca A, Alamo T, Gonzalez AH (2012) Model predictive control for changing economic targets. Paper presented at the IFAC conference on nonlinear model predictive control 2012 (NMPC’12). Noordwijkerhout, 23–27 Aug 2012Google Scholar
  9. Limon D, Pereira M, Muñoz de la Peña D, Alamo T, Jones CN, Zeillinger MN (2016) MPC for tracking periodic references. IEEE Trans Autom Control 61:1123–1128MathSciNetCrossRefGoogle Scholar
  10. Limon D, Ferramosca A, Alvarado I, Alamo T (2018) Nonlinear MPC for tracking piece-wise constant reference signals. IEEE Trans Autom Control 63:23735–3750MathSciNetCrossRefGoogle Scholar
  11. Maeder U, Morari M (2010) Offset-free reference tracking with model predictive control. Automatica 46(9):1469–1476MathSciNetCrossRefGoogle Scholar
  12. Maeder U, Borrelli F, Morari M (2009) Linear offset-free model predictive control. Automatica 45:2214–2222MathSciNetCrossRefGoogle Scholar
  13. Magni L, Scattolini R (2005) On the solution of the tracking problem for non-linear systems with MPC. Int J Syst Sci 36(8):477–484MathSciNetCrossRefGoogle Scholar
  14. Magni L, Scattolini R (2007) Tracking on non-square nonlinear continuous time systems with piecewise constant model predictive control. J Process Control 17: 631–640CrossRefGoogle Scholar
  15. Magni L, De Nicolao G, Scattolini R (2001) Output feedback and tracking of nonlinear systems with model predictive control. Automatica 37:1601–1607CrossRefGoogle Scholar
  16. Muske K (1997) Steady-state target optimization in linear model predictive control. Paper presented at the 16th American control conference, Alburquerque, 4–6 June 1997Google Scholar
  17. Olaru S, Dumur D (2005) Compact explicit MPC with guarantee of feasibility for tracking. In: Conference decision and control and European control conference 2005, pp 969–974Google Scholar
  18. Pannocchia G (2004) Robust model predictive control with guaranteed setpoint tracking. J Process Control 14:927–937CrossRefGoogle Scholar
  19. Pannocchia G, Bemporad A (2007) Combined design of disturbance model and observer for offset-free model predictive control. IEEE Trans Autom Control 52:1048–1053MathSciNetCrossRefGoogle Scholar
  20. Pannocchia G, Kerrigan E (2005) Offset-free receding horizon control of constrained linear systems. AIChE J 51:3134–3146CrossRefGoogle Scholar
  21. Pannocchia G, Rawlings JB (2003) Disturbance models for offset-free model-predictive control. AIChE J 49:426–437CrossRefGoogle Scholar
  22. Pereira M, Muñoz de la Peña D, Limon D, Alvarado I, Alamo T (2017) Robust model predictive controller for tracking changing periodic signals. IEEE Trans Autom Control 62:5343–5350MathSciNetCrossRefGoogle Scholar
  23. Rao CV, Rawlings JB (1999) Steady states and constraints in model predictive control. AIChE J 45:1266–1278CrossRefGoogle Scholar
  24. Rawlings JB, Mayne DQ, Diehl MM (2017) Model predictive control: theory, computation and design, 2nd edn. Nob-Hill Publishing, MadisonGoogle Scholar
  25. Rossiter JA, Kouvaritakis B, Gossner JR (1996) Guaranteeing feasibility in constrained stable generalized predictive control. IEEE Proc Control Theory Appl 143:463–469CrossRefGoogle Scholar
  26. Wan Z, Kothare MV (2003) An efficient off-line formulation of robust model predictive control using linear matrix inequalities. Automatica 39:837–846MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Departamento de Ingeniería de Sistemas y Automática, Escuela Técnica Superior de IngenieríaUniversidad de SevillaSevillaSpain

Section editors and affiliations

  • James B. Rawlings
    • 1
  1. 1.Dept. of Chemical EngineeringUniversity of CaliforniaSanta BarbaraUSA