Pareto optimal design of the decoupled sliding mode controller for an inverted pendulum system and its stability simulation via Java programming

In this paper, firstly, a decoupled sliding mode controller (DSMC) is designed for stabilization of an inverted pendulum system. Secondly, a multi‐objective particle swarm optimization (MOPSO) algorithm is implemented to optimize the DSMC parameters in order to decrease the normalized angle error of the pole and normalized distance error of the cart, simultaneously. The proposed Pareto front for the DSMC problem is validated through comparisons with existing state‐of‐the‐art multi‐objective algorithms. Then, Java programming with applets is presented in order to simulate the stability and educate the internet‐based control.