This paper presents one possible application of generalized quasi-orthogonal functional networks in the sensitivity analysis of complex dynamical systems. First, a new type of first order (k = 1) generalized quasi-orthogonal polynomials of Legendre type via classical quasi-orthogonal polynomials was introduced. The short principle to design generalized quasi-orthogonal polynomials and filters was also shown. A generalized quasi-orthogonal functional network represents an extension of classical orthogonal functional networks and neural networks, which deal with general functional models. A sequence of the first order (k = 1) generalized quasi-orthogonal polynomials was used as a new basis in the proposed generalized quasi-orthogonal functional networks. The proposed method for determining the parameter sensitivity of complex dynamical systems is also given, and an example of a complex industrial system in the form of a tower crane was considered. The results obtained have been compared with different methods for parameter sensitivity analysis.

Hammerstein-Wiener systems present a structure consisting of three serial cascade blocks. Two are static nonlinearities, which can be described with nonlinear functions. The third block represents a linear dynamic component placed between the first two blocks. Some of the common linear model structures include a rational-type transfer function, orthogonal rational functions (ORF), finite impulse response (FIR), autoregressive with extra input (ARX), autoregressive moving average with exogenous inputs model (ARMAX), and output-error (O-E) model structure. This paper presents a new structure, and a new improvement is proposed, which is consisted of the basic structure of Hammerstein-Wiener models with an improved orthogonal function of Müntz-Legendre type. We present an extension of generalised Malmquist polynomials that represent Müntz polynomials. Also, a detailed mathematical background for performing improved almost orthogonal polynomials, in combination with Hammerstein-Wiener models, is proposed. The proposed approach is used to identify the strongly nonlinear hydraulic system via the transfer function. To compare the results obtained, well-known orthogonal functions of the Legendre, Chebyshev, and Laguerre types are exploited.

In cable production, it is imperative to control speed and tension. This paper proposes a web tensile force regulation between input and output pulling caterpillar devices. The web tensile force is controlled indirectly using a PI controller based on feedback information about tensile force using a tensile observer. This paper also deals with the regulation speed of the input-pulling caterpillar device and the speed and torque (current) of output pulling caterpillar device and deals with the effect of line speed on the temperature change at the extruder zones. The input and output-pulling caterpillar devices are connected by the web material that is processed on them. The input and output-pulling caterpillar devices are connected by the web material that is processed on them. The task was realized using a PLC Micrologix 1200 controller and SIMOREG DC drives, which regulate the input caterpillar's speed and output caterpillar's torque. The identification of separately excited DC motors parameters was made. Models for the input, output caterpillars and web zone were simulated in Matlab and Simulink. The controllers of the current loop, velocity loop, and tension loop are all integral isolated PI regulators. Speed signal is obtained by tacho generator. In practical realization, tensile force is observed directly from the Simoreg DC converter, eliminating the tension sensor. The tensile force controller is realized with the PI controller, which was realized with PLC. Setting optimal parameters is performed using ITAE criteria. The ITAE function is calculated using a complex Simpson's quadrature formula.