Algebraic and spectral identification techniques with applications in mechatronics and economics

The analysis of harmonic signals spans a wide range of applications which stem from different disciplines like Mechatronics or Economics. This thesis deals with the problem of harmonic signals identification by means of system identification and time series analysis techniques.;The novel algebraic derivative technique has been used to develop algorithms capable of estimating the parameters of harmonic signals in on-line environments. One important advantage of such technique is that estimation is accomplished in a time interval inferior to the signal period. Simulations and experimental vibratory data coming from flexible arms prototypes have been used to validate the algebraic estimators. In addition, these results have been compared to Adaptive Notch Filters (ANF) recently found in the literature. Moreover, open-loop and closed-loop adaptive controllers were implemented taking advantage of these algebraic identification procedures. These adaptive controllers are well suited to face the problem of payload mass changes in flexible manipulators.;The knowledge acquired in the analysis of flexible structure vibrations has been used to study other harmonic signals which come from economic scenarios. In particular, the problem of forecasting load demand and price of electric energy in deregulated markets is studied. These time series were chosen because of their strong periodic pattern, i.e., they have daily and weekly seasonality and even an annual cycle. Frequency domain techniques were used with models developed in a State Space framework. This State Space framework allows to extract unobservable components like the trend, seasonal or irregular terms. Additionally, frequency domain estimation yields automatic predictions without necessity of a re-identification of models. These results improve other typical methodologies in time series analysis. The same model and State Space framework is adapted in this thesis to produce mid and long term forecasts of electricity time series.;Finally, both the ANF filters and the algebraic estimators of periodic signals are used to explore the business cycle from a standard economic indicator in a novel way, i.e. by considering the period of such a cycle as varying in time.