Optimal adaptive state feedback control for a three degree-of-freedom series-type double inverted pendulum system by using particle swarm optimisation

Abstract

ABSTRACT This research tries to stabilise a three degree-of-freedom series-type double inverted pendulum system by employing an adaptive state feedback control approach optimised by a particle swarm optimisation (PSO) algorithm. To this end, the dynamical equations are derived via Lagrangian method and linearised by utilising approximation approaches. Then, the state feedback scheme is implemented to control the system states, that is, the angle and angular velocity of the first and second poles as well as the position and velocity of the cart. In order to timely regulate the control gains, the adaptation rules based on the gradient descent method and sliding surface relations are applied. The particle swarm optimisation algorithm is implemented to optimally tune the design parameters of the controller based on a proper objective function defined as summation of integrals of absolute values of the system errors. The time responses of the angles of the poles and the position of the cart clearly depict the feasibility and efficiency of the introduced control strategy to stabilise the system from different initial conditions to the final desired values.