Optimal design of an adaptive robust proportional-integral-derivative controller based upon sliding surfaces for under-actuated dynamical systems

Abstract

This paper presents a novel adaptive robust proportional-integralderivative (PID) controller for under-actuated dynamical systems via employing the advantages of the PID control and sliding surfaces. The related control gains as adjustable parameters are computed during the control process using gradient descent techniques and the chain derivative rule. Based on the design of control rules, the genetic algorithm optimization is utilized in order to find the optimal values of the learning rates and initial conditions of the control gains. The suggested strategy is implemented successfully to stabilize the cart-pole and ball-beam systems. Lastly, the simulation results demonstrate the efficacy of the proposed controller to control such under-actuated dynamical systems as well as its superiority in comparison with other recently introduced methods.