ARRUDA, G. H. M.; http://lattes.cnpq.br/7628771206086042; ARRUDA, Gustavo Henrique Machado de.
Resumen:
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.