Optimal PID controller design of an inverted pendulum dynamics: A hybrid pole-placement & firefly algorithm approach

Abstract

The solution of control for inverted pendulum is a challenging problem and many control techniques have been tested on this bench mark problem to test the efficacy of the designed control law. In this note an attempt has been made to stabilize a linear dynamics of inverted pendulum by designing an optimal PID controller that guarantees the given time-domain performance specifications. To accomplish the task a hybrid pole-placement and firefly optimization control algorithm has been evolved. To apply the control algorithm, initially the upper bound of the controller gain is computed using Routh-Hurwitz criteria and later the lower bound of the controller gain is found out using pole-placement technique. Once the ranges of controller gains are obtained, the optimized value of the gains are found using firefly optimization technique.