Sistemas com realimentação por relé: análise e aplicações.

Abstract

This thesis deals with the analysis of a relay based frequency response estimator and its applications to process identification and PID controllers tuning. The identification experiment is based on obtaining a limit cycle at the frequency where the magnitude of the evaluated transfer function is equal to a parameter value, named r. Initially, a time domain analysis of relay feedback systems based on Poincare maps is presented, and necessary and sufficient conditions for the existence and stability of symmetrical unimodal limit cycles are obtained. The results are applied to the relay feedback experiment, in order to obtain closed form expressions for evaluating the existence and stability of symmetrical unimodal limit cycles. It Is shown by simulation examples that the experiment can produce a great variety of phenomena for different settings of the parameter r. For instance, varying the parameter r , even in its safe range, the system can undergo from a stable l i m it cycle to chaotic behavior. A new procedure for the estimation of a first order plus dead-time model using relay tests is presented in the sequel. Based on the time domain analysis of relay feedback systems with time delay, exact expressions for the limit cycle, which relates the dead-time and time constant i n such models are obtained. The advantage of the procedure is that the model fits better i n the frequency range where the process phase angle is between —90° and —180°, in the case of unmodelled dynamics. The results are then used for P I and P ID popular tuning techniques, in order to evaluate the quality of the obtained models. Finally, the relay experiments are applied to iterative P ID controllers tuning based on gain and phase margins specifications. Relay experiments are used to evaluate the stability margins in each step, and the operation is performed in closed loop, without removing the controller. Another advantage of this procedure is the fact that the process frequency response need not be known for the design steps. With some assumptions on the process frequency response characteristics, it is shown that the closed loop remains stable for each controller calculated during the iterations. If no assumptions are made on the process model, a new relay based experiment is presented to detect closed loop instability behavior before modifying the controller parameters. A simulation example is used to illustrate the procedure, and evaluate its properties. The procedure is then applied to tune a P I controller in Nitrate control of a simulated activated sludge treatment plant, a PI controller tuning i n a vanadium-dioxide thin film characterization experiment, and a P ID controller in temperature control of a heat exchanger laboratory scale process. The results point out that with a few iterations a reasonable controller is obtained, such that the robustness specifications are achieved.