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New approach for main stages of automatic controller tuning, process identification and controller parameters optimization, is proposed. It is based on methods of the three-stage estimation of a plant frequency response and on synthesis of a nonminimum phase transfer function using this response. For the above optimization, new criteria are introduced taking into account an influence of such processes non-linearities acted simultaneously as a backlash and a quantization with hysteresis. A proposed tuning procedure is illustrated by some examples of water level control systems at the IEC Power Boilers.

The paper proposes the method of determining the membership of the object to chaotic systems on the basis of structural risk minimization. It is presented examples that demonstrate the effectiveness of the methodology to model data. The methodology is based on Chebyshev polynomials that can make an informed choice of uniform distribution law or motivated to prefer a different probability density. The main feature of chaotic systems is the presence of a uniform law of distribution, which is typical for systems of the third type - the foundations of modern theory of chaos and self-organization. It is significant that in the theory of chaos and self-organization at short time intervals τ always be uneven distribution. However, it is impossible to keep the system for a long time in this state.

The article presents features of modelling of complex systems – complexity. Specific systems of third type have no repetitions of distribution functions (and their measures), no repetitions of initial states (but the probability theory requires initial states to be repeated and experiences should be repeated many times), no certainties in prediction of the future state of a complex system, i.e. sys-tem is constantly changing and unpredictable. There is a question: what should we work with such systems, how to describe and predict them? Deterministic and stochastic approaches are useless. I.R. Progogine thought that such unique systems are not objects of the science. It is very important that the chaos that demonstrates regulation of tremor, tapping, heart rate beats, myograms and electroencephalograms does not suit to Lorenz attractor, or model chaos in chaos theory (because there are no certain initial states and parameters of quasi-attractors of the same subject (a human) cannot be repeatable). In models of traditional chaos these parameters are repeatable, the Lyapunov exponents can be calculated and autocorrelation functions coincide). But in our case everything is opposite: the autocorrelation functions are unstable, the Lyapunov exponents cannot be calculated, and there are no models. The authors suggest calculating volumes of quasi-attractors.