The analysis element recognizes changes in the system parameters by comparing the response of the physical system to the response of a model of the column flotation unit. A neural network model of column flotation has been developed and tested for this purpose. The neural network has four input nodes, six middle nodes, and two output nodes. It computes the grade and recovery of a column flotation unit based on the following parameters: (1) flow rate of the slurry into the column, (2) percent solids in the feed slurry, (3) amount of collector, and (4) the air flow rate. A schematic of the neural network model is shown in Figure 15.3.

Figure 15.3  The neural network model of column flotation consists of four input nodes, six middle nodes, and two output nodes. Its accurate calculation of grade and recovery allows the analysis element to effectively determine when and to what extent the column flotation system has changed.

Figure 15.4 shows the effectiveness of the neural network model of column flotation. This figure shows the neural network model’s predicted response for a column flotation unit. Notice that the neural network model predicts accurately except in the extreme cases.

Figure 15.4  The neural network model of column flotation accurately predicts the response of a real-world system.

As demonstrated in the two preceding chapters, once an effective model of the system has been developed, the analysis element’s job of determining when and to what extent the column flotation system has changed becomes a curve-fitting problem. The curve-fitting problem is solved using a genetic algorithm for tuning the model parameters as described in earlier chapters. The coding scheme and fitness function employed in the analysis element for the column flotation controller are the same as outlined previously. When the GA has completed its task of locating the correct values of the parameters in the physical system, it has solved a system characterization problem. At this point, enough information will have been computed concerning the column flotation unit that the control strategy can be updated by the learning element.

15.3.3 Learning Element

The learning element alters the control element in response to changes in the problem environment. It does so by altering the rules and membership functions employed by the FC of the control element. Since the parameters in the problem environment that get changed do not appear in the FC rule set, the only way to account for these conditions (outside of completely revamping the rule base) is to alter the membership functions employed by the FC. A learning element that utilizes a GA to locate efficient rules and membership functions used in an FC that controls a column flotation unit has been developed. The architecture is currently in place, but must be modified in accordance with the control and analysis elements.

15.4 Review/Preview

The application of the adaptive control system architecture introduced in Chapter 14 to a column flotation unit was discussed. The control system has not yet been completed. The strategy employed by the adaptive system uses GAs to fashion three components necessary for a robust, comprehensive adaptive process control system: (1) a control element to manipulate the problem environment, (2) an analysis element to recognize changes in the problem environment, and (3) a learning element to adjust the control strategy.

Chapters 13, 14, and 15 of this book provided an indication of the robust nature of the architecture developed for achieving adaptive process control. Additionally, it is the authors’ hope that the reader has generated some original ideas on ways to improve the results presented. In the next three chapters of this book, we intend to address some issues we were forced to face while we were developing working systems. In Chapter 16 we will address the issue of fuzzy controllers as “approximate controllers.” We will consider the development of an FC for controlling a chaotic system in which achieving precise results are a must. In Chapter 17 we will consider what happens to FCs as the number of condition variables increases. We will consider an application completed for the U.S. Army in which a GA was used to design a FC for helicopter flight control. In Chapter 18 we will consider an alternative to the expert system approach we have presented thus far in the book. We will consider an adaptive system that has gown out of the GA literature called classifier systems. We will introduce a conventional classifier system, and discuss the extension of such a system by allowing for the fuzzification of its rules.

References

Agar, G.E., Huls, B. J., & Hyma, D.B., (Eds.) (1991). Column ’91. Montreal: The Canadian Institute of Mining and Metallurgy and Petroleum.

Finch, J.A., & Doby, G.S. (1990). Column flotation. Toronto: Pergamon Press.

Herbst, J.A., & Rajamani, K. (1989). Models for the dynamic optimization of mineral processing plant performance. In K. Sastry and M. Fuerstenau (Eds.). Challenges in Mineral Processing, Denver, CO: Society for Mining, Metallurgy, and Exploration, 709–739.

Karr, C.L. (1991). Genetic algorithms for fuzzy logic controllers. AI Expert, 6, 26–33.

Karr, C.L., Gentry, E.J., & Stanley, D. A. (1995). An adaptive system for process control (Report of Investigations number 9563). Washington, DC: U.S. Department of the Interior, Bureau of Mines.

Luttrell, G.H., Adel, G.T., & Yoon, R.H. (1987). Modeling of column flotation. Society for Mining, Metallurgy, and Exploration Annual Meeting, Preprint number 87–130.

Sastry, K.V.S. (1978). Beneficiation of mineral fines, problems and research needs. Report of a workshop held at Sterling Forest, New York, 78–84.

Sastry, K.V.S., & Lofftus, K. (1988). Mathematical modeling and computer simulation of column flotation. Column Flotation ’88, Denver, CO: Society for Mining, Metallurgy, and Exploration, 57–63.

Ynchausti, R.A., Herbst, J.A., & Hales, L. B. (1988). Unique problems and opportunities associated with automation of column flotation cells. Column Flotation ’88, Denver, CO: Society for Mining, Metallurgy, and Exploration, 27–33.

Zadeh, L.A. (1973). Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man, and Cybernetics, SMC-3,28–44.