Identificação de modelos de Hammerstein multivariáveis com não linearidades estáticas ou quase estáticas fortes - Luís Henrique dos Santos (2024)
Models describe essential characteristics of systems, enabling analysis and prediction of behaviors that would be expensive, risky or even impractical. Given the complexity of the processes, which are sometimes multivariable, a suitable representation is the linear state space model that can handle multiple inputs and multiple outputs in a compact way. However, every practical system has some degree of nonlinearity, so the more nonlinear the effect, the less useful the linear model is in terms of global representativeness. In view of this, it is noted that nonlinear models are necessary when one wishes to operate the process in wide ranges, especially when non-linearities are strong. In the scope of this dissertation, strong nonlinearities are those that have at least one point in their domain where the derivative is not defined. Despite presenting considerable advances in recent decades, the literature related to the use of subspace methods for the purpose of obtaining state space models for multivariable nonlinear systems is scarce, especially when dealing with strong nonlinearities. Motivated by this context, this dissertation aims to present two distinct methodologies for identifying systems with strong nonlinearities: one for static nonlinearities and the other for quasi-static nonlinearities, more specifically hysteresis. An interesting structure to represent nonlinear processes is the Hammerstein model, composed of a nonlinear static subsystem followed by a linear dynamic one. From the perspective of processes whose nonlinearities are static, the work defines a neural network that has accurate adjustment capacity and a state space system suitable for the multivariable case to compose the Hammerstein model. Taking these characteristics into account, an approach was developed to identify a neuro-fuzzy multivariable Hammerstein model through a non-iterative procedure, associated with subspace methods. One of the advantages is that it is not necessary to choose the structure as in autoregressive models. In turn, from the perspective of processes that have nonlinearity in the form of hysteresis, a two-step methodology was presented to identify multivariable systems. Unlike other works found in the literature, the nonlinearity is first estimated and then the linear dynamic portion is estimated. Thus, additional restrictions are avoided, such as the impossibility of direct inversion that occurs when the identified system has a non-minimum phase. The proposed Hammerstein model is composed of a generalized rate-dependent Prandtl-Ishlinskii model followed by another in state space. The functionality of both identification methodologies was verified in four simulations, all multivariable, presenting an introductory example and a more complex example for each of the methodologies. The models obtained followed the process, even with the presence of measurement noise and dynamic coupling.