Yuz Eissmann, Juan Ignacio

Some nonlinear systems can be represented through linear parameter varying models. In this work, we address the estimation of continuous-time linear parameter varying models in output error form, using a refined instrumental variable method. A distinguished feature of a linear parameter varying model is that it has parameters that depend on an external signal called the scheduling variable. In this paper, we assume that the scheduling variable is noisy, a condition which is often met in practice, but not frequently considered in the literature. On the other hand, there are applications in which the noise-free version of the scheduling variable is smooth. Under such scenario we can simply filter the scheduling variable before estimating the linear parameter model. Nonetheless, there are cases where special smoothing techniques are required. In this study, we consider one of these special cases, and we use the well-known local regression method as smoothing technique. A numerical example based on a Monte Carlo simulation shows the benefits of the proposed approach.

Model estimation of industrial processes is often done in closed loop due, for instance, to production constraints or safety reasons. On the other hand, many processes are time-varying because of aging effects or changes in the environmental conditions. In this study, a recursive estimation algorithm for linear, continuous-time, slowly time-varying systems operating in closed loop, is developed. The proposed method consists in coupling linear filter approaches to handle the time-derivative, with closed-loop instrumental variable (IV) techniques to deal with measurement noise. Simulations show the advantages of using this IV-based method.