Development of a Hybrid Optimization Strategy Based on a Bacterial Foraging Algorithm (BFA) and a Particle Swarming Algorithm (PSO) to Tune the PID Controller of a Ball and Plate System

The current systems to be controlled are increasingly complex due to the nonlinearity they have, they vary in time, they present uncertainties in their inputs as well as in their structure; as a consequence, these plants can hardly be optimized using classical control techniques. In this work a hybrid optimization has been developed for any type of PID controller by means of the bio-inspired algorithms BFA and PSO; and with the objective of testing the operation of the proposal, it has been implemented in a Ball and Plate (B&P) system model 33–240 Feedback to evaluate its performance. The control of B&P systems presents two drawbacks at the moment of tuning the optimal parameters of the controller: a) nonlinear plants and b) they have a high degree of uncertainty at the moment of developing the mathematical model, these two considerations can be applied to any type of systems with nonlinear characteristics. The system was modeled using the Euler-Lagrange equations, the maximum values of the gains were determined using the root locus method and the initial values of the PID controller parameters for the heuristic algorithm were determined using the classical control technique of Ziegler Nichols. The optimization was first performed by simulation in MATLAB software and then implemented in the real plant by means of the system's own interface in LabVIEW software. The results of the hybrid BFA-PSO algorithm were compared with the results of the bio-inspired BFA and PSO algorithms allowing to analyze the real performance of each algorithm.