Contributions to LPV modeling and gain-scheduled control applied to mechatronic systems. - Neves, Gabriel Pereira das (2021)
This thesis proposes contributions for modeling and control of a class of nonlinear systems using linear parameter-varying (LPV) models. As a first contribution, two modeling techniques specialized in the generation of LPV models with polynomial dependence on the parameters (called LPV parameters) are proposed. If the parameters are related to states or inputs, the model is called quasi-LPV. The first technique, based on Taylor series expansion, produces a more accurate model around an operating point when compared to classical linearization techniques. The second approach is based on a polynomial interpolation algorithm and yields a family of linear models within a pre-established operating range, being especially suitable for dealing with reference tracking problems. The second contribution of the thesis is a set of conditions for gain-scheduled control of LPV or quasi-LPV systems. Stabilization, H2 and H control design conditions by state and output feedback static and full-order dynamic are proposed, being solved in terms of linear matrix inequalities and search on a scalar parameter confined in the range (1, 1). All classes of controllers can present gains with arbitrary degree polynomial dependence on the LPV parameters, in general providing less conservative results as the degrees increase. In order to validate the contributions of this thesis, the proposed modeling and control techniques are applied in some mechatronic systems, considering simulations and practical experiments.