Steady state hierarchical optimizing control for large-scale industrial processes with fuzzy parameters

This paper presents a new method for steady state hierarchical optimizing control of large-scale industrial processes. The several classical steady state coordination mechanisms are applied to the case that the model coefficients of each subprocess of a large-scale industrial process are replaced by fuzzy numbers. Hence, each subprocess model is converted into fuzzy form and then the original crisp programming problem with equality and inequality constraints is transformed to the fuzzy programming problem with fuzzy equality and crisp inequality constraints in each local decision unit. The final solutions are obtained by solving the general mathematical programming problem after the fuzzy equality constraints are converted into crisp inequality constraints. The developed method is mainly used to deal with the model-reality difference caused by either the model coefficients of subprocess being not known accurately or the model itself being slow varying during normal operation. Three main types of coordination for processes with fuzzy parameters are derived in this paper: interaction balance method (IBM), interaction prediction method (IPM), and mixed method (MM). Simulation results of two examples show that 1) the proposed method can deal with model-reality difference efficiently, 2) the convergence speed of the on-line coordination for fuzzy parameter processes is faster than that of corresponding coordination for crisp parameter processes, and 3) the objective function of real processes can be improved by using the proposed method compared with the classical case. Furthermore, the studies show that the interaction balance method with global feedback (IBMF) based on double iterative technique for processes with fuzzy parameters is the coordination algorithm that requires the fewest number of on-line iterations so far.