Linear programming predictive control with actuator saturation: Experimental robustness and performance results

Abstract

Linear programming optimization is widely used in several application areas. One possible application of this optimization technique, which has not received sufficient attention, is process control. In particular, the standard structure of linear programming optimization problems allows formulating optimal predictive control schemes with the additional advantage of facilitating the handling of actuator saturation. Actuator saturation appears in many engineering applications and there are several control approaches dealing with this problem. In this article, a very simple predictive control scheme based on linear programming optimization for actuator saturation control is proposed. The main characteristics of the presented scheme are simplicity and practical robustness/performance tuning parameters. First, the simplest possible output-feedback linear programming predictive controller is proposed as a starting point. Next, through several practical observations inspired in classical control engineering, a series of modifications to the basic controller structure are proposed. These modifications aim at effectively increasing the performance and robustness of the control algorithm. The experimental results confirm that the proposed control algorithm can operate effectively under the presence of perturbations, something which is currently not widely reported in the literature for linear programming actuator saturation predictive control.

Keywords

Linear programming actuator saturation experimental setup

Get full access to this article

View all access options for this article.

References

Ghate

Smith

. A linear programming approach to nonstationary infinite-horizon Markov decision processes. Oper Res 2003; 61(2): 413–425.

Castro

Teles

. Comparison of global optimization algorithms for the design of water-using networks. Comput Chem Eng 2013; 52: 249–261.

Zhang

Han

Zhu

. Stability and stabilization of positive switched systems with mode-dependent average dwell time. Nonlinear Anal Hybrid Syst 2013; 9: 42–55.

Kapila

Grigoriadis

. Actuator saturation control. New York: Marcel Dekker Inc., 2002.

Goodwin

Seron

De Doná

. Constrained control and estimation: an optimisation approach. London: Springer-Verlag, 2005.

Bemporad

Borrelli

Morari

. Model predictive control based on linear programming—the explicit solution. IEEE T Automat Contr 2002; 47(12): 1974–1985.

Mayne

Rawlings

Rao

. Constrained model predictive control: stability and optimality. Automatica 2002; 36(6): 789–814.

Zeman

Rohal’-Ilkiv

. Robust min-max model predictive control of linear systems with constraints. In: IEEE international conference on industrial technology, vol. 2, 10–12 December 2003, pp.930–935. Maribor, Slovenia: IEEE.

Zeilinger

Jones

Morari

. Real-time suboptimal model predictive control using a combination of explicit MPC and online optimization. IEEE T Automat Contr 2011; 56(7): 1524–1534.

10.

Ghaemi

Sun

Kolmanovsky

. Robust control of constrained linear systems with bounded disturbances. IEEE T Automat Contr 2012; 57(10): 2683–2688.

11.

Gomma

Owens

. Stability analysis for generalized predictive control (GPC) and time varying weighting generalized predictive control (TGPC). In: IEEE international conference on control applications, vol. 4, 2–4 September 2004, pp.3706–3711. Taipei, Taiwan: IEEE.

12.

Young

Hyun

. Weighted receding horizon predictive control and its related GPC with guaranteed stability. In: IEEE 32nd conference on decision and control, vol. 2, 15–17 December 1993, pp.1316–1321. Texas, USA: IEEE.

13.

Amezquita

Liceaga

. A simple non-windup linear programming predictive controller. In: IEEE electronics, robotics and automotive mechanics conference, 25–28 September 2007, pp.100–105. Morelos, Mexico: IEEE.

14.

Bazaraa

Jarvis

Sherali

. Linear programming and network flows. New York: John Wiley & Sons, 2009.

15.

Shanno

Weil

. Linear programming with absolute-value functionals. Oper Res 1971; 19(1): 120–124.

16.

Ogata

. Discrete-time control systems. 2nd ed. Englewood Cliffs, NJ: Prentice Hall, 1995.

17.

Dong

. Stability gain interval of Dahlin control system. In: IEEE sixth world congress on intelligent control and automation, 21–23 June 2006, vol. 1, pp.486–489. Dalian, China: IEEE.

18.

Zhang

Sun

. Robust digital controller design for processes with dead times: new results. IEE P Contr Theor Ap 1998; 145(2): 159–164.

19.

Zhou

Doyle

Glover

. Robust and optimal control. Englewood Cliffs, NJ: Prentice Hall, 1995.

20.

Freudenberg

Looze

. Right half plane poles and zeros and design tradeoffs in feedback systems. IEEE T Automat Contr 1985; 30(6): 555–565.

21.

Chang

Tsai

. Adaptive generalised predictive temperature control for air conditioning systems. Control Theor Appl 2011; 5(6): 813–822.

22.

Verhaegen

Verdult

. Filtering and system identification: a least squares approach. New York: Cambridge University Press, 2007.