Stabilization of Cart Inverted Pendulum System by 2-rate controllers based on PSO technique

This paper proposes a PSO (Particle Swarm Optimization) based tuning rule for 2-rate controllers for the stabilization of cart-inverted pendulum system. In [1] the 2-Rate controller, a special subset of 2-periodic controller, has been designed to achieve poles as well as loop-zero placement leading to an improved gain margin (GM) as compared to its LTI counterpart. In the work of [2], the 2-Rate compensation technique was employed to stabilize the cart inverted pendulum system. However, the controller design approach was based on trial and error method and the GM of the overall system depends on the choice of controller poles and loop-zeros. In order to formalize this problem of selecting the proper locations of the controller poles and loop-zeros, this paper proposes a PSO based approach. The objective is to have an efficient and effective search by a group of particles in the solution space to find out the optimal locations of the controller poles and loop-zeros that yield satisfactory loop robustness.