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Top1. Introduction
Model predictive control (MPC) is a well-established technology which has become the standard advanced control strategy for tackling constrained control problems typical in process industries. Despite the fact that MPC technology is highly developed in literature on theoretical and practical (T. Badgwell, 2003; M. Nikolaou, 2012) and some recent books (Camacho et, 2007; J. Maciejowski, 2002), a general method to tune MPC controllers is still an open research problem. Lino et al. (1993) have proposed a parameter tuning method considering robust stability based on frequency response analysis. Later, Drogies et al. (1999) have proposed a heuristic tuning method based on expert rules, can be considered as that reported by Rowe et al. (1999). Other authors have proposed an MPC with constraints based on H-infinity loop shaping method. Among other solutions, the heuristic tuning approaches proposed so far are either plain formulas for a variety of the controller parameters based on some characteristic features of the closed-loop system response, for instance, overshoots, rise and settling time. The paper written by Garriga et al. (2010) surveys the major existing ad hoc MPC tuning strategies used in practical real world applications. While ad hoc methods provide valuable guidelines for MPC tuning, they rely upon uniqueness either of the process model or MPC formulation. These methods can become increasingly difficult to implement them, and within this context the trial-and-error tuning approaches are unavoidably adopted. In order to circumvent these shortcomings, there are some research works that stand out in the literature, and these are presented as follows. Gous et al. (2012) formulate a Nelder-Mead search algorithm based tuning problem to find move suppression factors of DMC-type multivariable controllers on account of desired overshoots of the manipulated variables. In addition, the solution of the tuning optimization problem is found by means of a sequential parameters optimization technique. Suzuki et al. (2008) describe an optimal tuning method of MPC to automatically adjust the weights on the relative importance of controlled outputs and the rate of change of inputs. In the attempt to overcome this, the present paper develops an optimal tuning strategy which can be applied to most constrained MPC algorithms. To work around this, the proposed method is formulated in such a way that a set of tunable parameters, composed of both integer variables (e.g. prediction and control horizons) and real variables (move suppression factors, weights on the controlled outputs and targeted inputs etc.) is obtained by minimizing a certain multi-objective performance index in the worst-case conditions to control the process system, thus assuring robustness to the set of optimum tuning parameters in the uncertainty description. Because the optimization problem of the proposed MPC tuning method comprises constrained mixed-integer nonlinear programming, among optimization algorithms used in recent years, may be mentioned evolutionary algorithms (EAs), genetic algorithm (O. Cordon,, 2001), genetic programming (W. Pedrycz,2003) and differential evolution (R. Eberhart, 1995). The most recent is the Particle Swarm Optimization (PSO), The literature shows that this algorithm is more effective in non-linear optimization problems. So, in this paper, we used the PSO approach, which is a quite widespread met-heuristic method of solving this kind of problem.