Estudo, proposta e avaliação de novas metodologias de sintonia automática de controladores PID baseadas no ensaio do relé realimentado

Abstract

The strong presence of PID (Proportional-Integral-Derivative) controllers in the industry and the difficulties of tuning these controllers have motivated the development of several auto-tuning techniques. The relay feedback methodology is the most important of these techniques. In the present literature, although contemplating a great number of systems, it does not contemplate the auto-tuning of PIDs for oscillatory systems with low damping and several vibration modes. This constitutes the main motivation of this research work. Firstly, this work presents the main auto-tuning methodologies based on the relay feedback test and proposes two new auto-tuning methods of the PID controllers. The first one (complete methodology) adds to the relay test a compensator and an automatic and variable reference signal. The frequency response function of the system is estimated by using the Fast Fourier Transform and the PID gains are obtained by fitting the frequency response of the dynamic system (mechanical system + controller) to a reference response. The second methodology (simplified methodology) just requests two points of the system FRF. Tests are proposed to identify these two points and the PID gains are obtained by solving a system of algebraic equations. The methods are evaluated numerically for various dynamical systems and experimentally on three systems: (i) system with one degree of freedom, (ii) system with three degree of freedom and, (iii) a cantilever beam with piezoelectrics actuators. The work concludes that the proposed methodologies are efficient for a wide spectrum of systems, especially for oscillatory systems with low damping and several vibration modes in the band of interest. Future work points out to the investigation of technological application of low cost Digital Signal Processors and to the investigation of the tuning methodology for complex controllers and applications devoted to multi-input multi-output systems.