Identificação de sistemas utilizando modelos em bases de funções ortonormais com atraso.

Abstract

In this work are presented contributions for the identification of SISO (single input, single output) and MIMO (multiple inputs, multiple outputs) systems. First, identification techniques of reduced order models for SISO systems are proposed, that is first order plus time delay (FOPTD) models and second order plus time delay (SOPTD) models. These models are the most common used in the PID controllers project and tuning. The identification experiment is based on the information obtained by the relay feedback experiment, that is based on the critical frequency ωu where the please is -180°. The excitation is composed of a high frequency part (relax) and a low frequency part (pulse). This way, the identified models represent the system in a wider frequency region than those models identified using just the critical point information. In addition, the identified models obtained using the proposed techniques are based on the combined information on the frequency domains. The orthonormal bases function models are presented and they are used as high order system models. But if the time delay is present, the model order is unnecessarily high. This way, the ortonormal bases function models plus time delay (OBF-TD) are defined. These models are combined models of an ortonormal bases function model part and a time delay part. But if model is intended to be used to PID controller tuning, reduced order models as FOPTD or SOPTD models are required. So, it is proposed a reduction model technique using OBF-TD models with or without residue compensation. The residue compensation (information not considered) is necessary if the system order is higher than one (first order) or two (second order). Two propositions are present to verify if the residue compensation on the reduction techinique is necessary because the system order is not necessarily known a priori. The identification techniques proposed for reduced order models and ortonormal bases function models plus time delay are formulated for MIMO systems. For MIMO systems another choice need to be made: the multivariable structure. Several structures are presented and described based on the preliminary information avaliable. These information are the time constants and the time delays. In addition to that, the experimental methodology need also to the chosen: independent or decentralized. With the independent methodology one input is excited at a time and with the decentralized methodology all the inputs are excited at the same time. The main differences between MIMO systems and SISO systems are the presence of interactions and directions. The directionality is very important for ill-conditioned MIMO systems. These directions describe the system gain dependency with respect to the imput combinations. This way, certain combinations results on a higher variation on this context and simulation results based on a simplified high purity distillation columm model are presented.