Industrial Processes With Fuzzy Parameters, Steady-state Hierarchical Optimization Control

With the development of science and technology, more and more large-scale systems with complex structure come forth in real world. It becomes realistic that these systems can be controlled and administrated on the basis of rapid development of computer technology. In order to ensure the condition of large-scale systems in normal operation to be satisfied and find out the method to improve the performances of these systems, the theory of large-scale systems has been established as a result of the requirement of practical applications. The existing theory of large-scale systems (based on the mathematical model), however, falls into straits and faces such serious challenges as the complexity,activity,uncertainty and curse of dimensionality of large-scale systems. Therefore, the experts who are engaged in the study of large-scale systems have strong motivation to break through the traditional theoretical framework of large-scale systems for finding out a new method to deal with these challenges since the end of 1980s. The Chinese famous scientist Xue-Sen Qian has pointed out that the theory of large-scale systems requires innovation. In order to develop a new approach of steady state hierarchical control of large-scale systems, a new method is proposed in this dissertation to optimize the large-scale systems with the uncertainty and model-reality difference, and meantime to obtain some improved results at the same time. (1) The new idea of fuzzy modeling is presented for large-scale industrial processes. The new fuzzy equality model of large-scale industrial processes can be obtained through fuzzifying the coefficients of the process model on the basis of retaining the structural information of original crisp model. The obtained fuzzy model is different from that described by a number of if-then rules based on human experience thoroughly. It is an integrated model as a combination of the crisp models resulted from system identification and the fuzzy numbers embodying the fuzziness of process. (2) The technique to defuzzify the fuzzy equality is developed through the definition of satisficing function according to the theory of fuzzy mathematics. Therefore, the fuzzy programming problem as a result of fuzzifying the coefficients of the process model is transformed to the corresponding crisp programming one. On the basis of these results, the method that integrates the fuzzy programming with the algorithm of steady state hierarchical control of large-scale systems is presented to solve the hierarchical optimizing problem of large-scale systems with fuzzy parameters. (3) The three basic coordination methods: interaction balance method (IBM), interaction prediction method (IPM) and mixed method (MM) of steady state hierarchical optimizing control for large-scale systems based on fuzzy models are developed. As the crisp mixed method can not be used to control large-scale systems with fuzzy models, the new mixed method based on fuzzy model is derived to achieve it. The simulation results show that the IBM based on fuzzy model provides a better objective function of real process, which approaches the value obtained by IBM with feedback, compared with the IBM in open loop case. The IBMF (IBM with feedback) based on fuzzy model requires the greatly lesser number of on-line iterations than that required by the IBMF in close loop case. The IPM based on fuzzy model gives a better objective function of real process than that given by IPM. The IPMF (IPM with feedback) based on fuzzy model can achieve a better objective function of real process with the lesser number of on-line iterations than that achieved by IPMF at the same time. The MM and the MMF (MM with feedback) based on fuzzy model provide the better performances than that provided by the MM and the MMF on objective function of real process and the number of on-line iterations respectively. (4) The study of the dissertation shows that the IBMF with double iterative technique based on fuzzy model is the coordination algorithm that requires the fewest number of on-line iterations (only 4~5 times of on-line iteration in the classical examples) that has been recorded in literatures so far. (5) The fuzzy numbers of rectangular membership function are adopted in the IBM as the model coefficients being variable within a small interval. And the method to optimize such a large-scale systems with fuzzy parameters is presented. (6) The IBM with fuzzy inequality constraints is proposed in accordance with the fact that the models of real process are slowly changing with the time elapsing and the margin of real constraints is allowed when modeling for the realprocesses. The adopted technique to defuzzify the fuzzy inequality constraints is different from that to defuzzify the fuzzy equality ones. (8) The proof of the convergence of the IBM based on fuzzy model is presented through three steps. Firstly, it is proven that the intersection of the defuzzified and the original constraint sets is nonempty and convex. Secondly, the applicable condition of the IBM based on fuzzy model is established. Finally, the convergence of interaction balance method based on fuzzy model is proven by using of the definition of the A-norm of iterative sequence, and the range of iterative gain is found out by which the convergence is guaranteed.