Gaussian Adaptive PID control with robust parameters considering plant parameter variation with optimization based on bioinspired metaheuristics

Abstract

The purpose of this work is to compare a linear PID to the Gaussian Adaptive PID control (GAPID) regarding their robustness to changes and variation on two different plants. The first one is the second order plant DC-DC Buck converter used as a study plant an analyzed through simulation. The second plant is a DC motor with a beam attached to it. An experimental prototype was built for this second plant to test the GAPID in a a real experiment. The Gaussian function has as adjustment parameters its convavity and the lower and upper bound of the gains. It is a smooth function with smooth derivatives. As a result, it helps avoid problems related to abrupt gains transition, commonly found in other adaptive methods. Because there is no mathematical methodology to set these parameters, two bio-inspired optimization algorithms were used, the Genetic Algorithm (GA) and the Particle Swarm Optimization (PSO). Functions to evaluate the results, called fitness functions, are necessary for the algorithms and were also used as performance comparison. A new variation to the fitness is proposed and the results demonstrate an improvement regarding the overshoot. Results also prove the robustness of the GAPID compared to the linear PID by load and gain sweep tests, achieving fast response (low settling time) and minimal variation, which is not possible to achieve when using the linear PID.