There exists a need to develop better mathematical models for physical processes, but it is also essential to understand that it is impossible to describe real-world industrial processes by exact mathematical models. Pattern recognition based methodology implemented in the architecture of artificial neural networks can be used to model knowledge intensive feedback control systems. The procedure for development and practical design of neural-net based control systems is described and demonstrated by the example of a nonlinear hydraulic system. The results obtained in computer simulations and experiments are presented to illustrate the new approach. J n t r o d wReal-world industrial processes have always been of considerable interest for control theorists and practitioners.These processes are typically characterized with partially understood nonlinear system dynamics, lack of knowledge of true system parameters, noisy measurement subsystems and a great amount of uncertainty in the interactions between the process and its environment. Over the decades, the theorists of classical and modem control have been offering new and sophisticated techniques to cope effectively with some of these difficult problems. However a rigorous mathematical treatment is constrained usually by a set of various assumptions. To ensure applicability of certain theories, it turns out that continuous verification of underlying assumptions has to be enforced, which from the practical viewpoint is often impossible. This is one among the reasons that most of the process industry in the last 40 years has based their automatic control decisions on the actions of a rather simplistic structure of proportional-integral-derivation (PID) controllers.A PID controller has three tunable parameters (gain, reset and rate), that can be used to modify system's behaviour over the wide frequency range. Development of techniques for tuning of the PID constants has a long history. Ziegler and Nichols (1942) estimated tuning constants from the gain required for sustained system oscillations. Cohen and Ceon (1953) and Yuwana and Seborg (1982) suggested the use of the open loop step response to calculate the tuning values. More recently, Astrom and Hagglund (1983) in their "relay method" proposed gain and phase-margin techniques to find the gain, reset and rate parameters. The techniques mentioned above belong to the group of off-line tuning methods.On-line tuning, or self-tuning is based on automatic system identification and self-adjustment of adaptive feedback law. The adaptive controllers, like most other controllers, are Authors are also with AI WARE, Inc., -1 -designed on models that are simpler than the real processes. Self-tuning and model reference adaptive control methods from Astrom, Wittenmark (1973), Clarke, Gawthrop (1979, Wellstead et al. (1979), Forescue et al. (1981, Zervos et al.(1988)l mostly deal with linear systems and specialized algorithms exist for nonlinear systems such as those where unknown parameters enter linearly in the nonlinear mod...

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