Fully Automated Tuning and Implementation of Fractional PID Controllers

Abstract

The advantages and applications of modeling and control of non-integer order linear systems are well known, but the inherent complexity of practical approximations has prevented the generalized appearance in the market of simple devices capable of implementing a fractional order control on a unknown given plant in a reliable way. The purpose of this work is to make a step forward in this sense, looking for a compromise between simplicity and reliability of the system. An automatic method for tuning, design, and implementation of fractional order PIαDμ controllers is presented in this paper. The auto-tuning method is based on plant magnitude and phase measuring at a frequency of interest, obtained by the relay feedback technique. A fractional order PIαDμ controller is designed from these measurements so that specifications of phase margin and robustness to variations of the plant gain are reached. Once the fractional order PIαDμ controller transfer function is obtained, it is discretized applying Pascal Matrix Method, and approximated using continuous fraction expansion of the Tustin Operator, generalized for a general transfer function. Simulation results obtained using the described method on an a priori unknown characteristic servo are presented in this paper.