A Simplified Approach to Multivariable Model Predictive Control

Authors

  • Michael Short

Keywords:

Real-time and embedded control, predictive control, multivariable control.

Abstract

The benefits of applying the range of technologies generally known as Model Predictive Control (MPC) to the control of industrial processes have been well documented in recent years. One of the principal drawbacks to MPC schemes are the relatively high on-line computational burdens when used with adaptive, constrained and/or multivariable processes, which has warranted some researchers and practitioners to seek simplified approaches for its implementation. To date, several schemes have been proposed based around a simplified 1-norm formulation of multivariable MPC, which is solved online using the simplex algorithm in both the unconstrained and constrained cases. In this paper a 2-norm approach to simplified multivariable MPC is formulated, which is solved online using a vector-matrix product or a simple iterative coordinate descent algorithm for the unconstrained and constrained cases respectively. A CARIMA model is employed to ensure offset-free control, and a simple scheme to produce the optimal predictions is described. A small simulation study and further discussions help to illustrate that this quadratic formulation performs well and can be considered a useful adjunct to its linear counterpart, and still retains the beneficial features such as ease of computer-based implementation.

References

E.F. Camacho and C. Bordons, Model Predictive Control: 2nd Edition. Springer-Verlag London, 2004.

M. Morari and J. H. Lee, “Model predictive control: past, present and future,” Computers and Chemical Engineering, vol. 23, no. 4/5, pp. 667-682, 1999.

D.R. Saffer II and F.J. Doyle III, “Analysis of linear programming in model predictive control,” Computers and Chemical Engineering, vol. 28, pp. 2749-2763, 2004.

Y.P. Gupta, “A simplified predictive control approach for handling constraints through linear programming,” Computers in Industry, vol. 21, no. 3, pp. 255-265, 1993.

R.A. Abou-Jeyab, Y.P. Gupta, J.R. Gervais, P.A. Branchi and S.S. Woo, “Constrained multivariable control of a distillation column using a simplified model predictive control algorithm,” Journal of Process Control, vol. 11, pp. 509-517.

F. Zhao and Y.P. Gupta, “A simplified predictive control algorithm for disturbance rejection,” ISA Transactions, vol. 44, pp. 187-198, 2005.

M. Abu-Ayyad and R. Dubay, “Real-time comparison of a number of predictive controllers,” ISA Transactions, vol. 46, pp. 411-418, 2007.

G.C. Kember, R. Dubay and S.E. Mansour, “On simplified predictive control as a generalization of least-squares dynamic matrix control,” ISA Transactions, vol. 44, 345-352.

Y.P. Gupta, “Solution of low-dimensional constrained model predictive control problems,” ISA Transactions, vol. 43, pp. 499-508.

G.C. Buttazzo, Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications, Spinger-Verlag, New York, 2005.

C.H. Papadimitriou and K. Stieglitz, Combinatorial Optimization: Algorithms and Complexity, Dover Publications Inc., England, 2000.

A. Bjorck, Numerical Methods for Least Squares Problems, SIAM Publishing, Philadelphia, USA, 1996.

G.H. Golub and C.F. Van Loan, Matrix Computations: 3rd edition, Baltimore: Johns Hopkins University Press, 1996.

W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, 1992.

J. Sherman and W. Morrison, “Adjustment of an inverse matrix corresponding to a change in one element of a given matrix,” Annals of Mathematical Statistics, vol. 21, no. 1, pp. 124-127, 1950.

K.J. Astrom and B. Wittenmark, Adaptive Control: 2nd Edition, Addison Wesley, 1995.

B. Schofield, “On Active Set Algorithms for Solving Bound-Constrained Least Squares Control Allocation Problems,” In: Proceedings of the 2008 American Control Conference, Seattle, Washington, USA, June 2008.

Z. Luo and P. Tseng, “On the linear convergence of descent methods for convex essentially smooth minimization,” SIAM Journal of Control and Optimization, vol. 19, no. 3, pp. 368–400, 1992.

M. Bierlaire, Ph.L. Toint and D. Tuyttens, “On iterative algorithms for linear least squares problems with bound constraints,” Linear Algebra and its Applications, vol. 143, pp. 111–143, 1991.

B. Roefel and B.H. Betlem, Advanced practical process control, Springer-Verlag, Berlin, 2004.

D. Chen and D.E. Seborg, “PI/PID Controller Design Based on Direct Synthesis and Disturbance Rejection,” Industrial Engineering Chemistry Research, vol. 41, no. 19, pp. 4807-4822, 2002.

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Published

2015-01-01

How to Cite

[1]
M. Short, “A Simplified Approach to Multivariable Model Predictive Control”, Int. j. eng. technol. innov., vol. 5, no. 1, pp. 19–32, Jan. 2015.

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Articles