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While proportional-integral-derivative (PID) control is the most applicable controller in industry, it does not provide important qualities, such as stability in case of uncertainties, being robust to disturbances, and optimal control inputs. To address the issue, this paper presents adaptive robust PID control subject to supervisory decoupled sliding mode control for an inverted pendulum system optimized by using a genetic algorithm optimization. Decoupled sliding mode control is a variable structure control method having appropriate features, such as good tracking performance and robustness with regard to disturbances. To this end, decoupled sliding mode control as a supervisory controller is utilized in accordance with PID control to deliver necessary control inputs and enhance the performance of the controller. Effectual methods such as the transfer function which resulted in having minimum chattering in the controller is employed in this paper. An adaptation mechanism is used to update the proportional, derivative, and integral gains of PID control. Then, the parameters of the controller are ascertained by using a genetic algorithm. The results and analysis prove the proper performance of the controller via providing an optimal smooth control input, proper tracking performance, and the elimination of the chattering problem.

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In this paper, a cart-type inverted pendulum is controlled using combining of two methods of approximate feedback linearization and sliding mode control. Both position of the cart and angular position of the pendulum are stabilized. Obtained control gains are optimized by a hybrid algorithm based on the particle swarm optimization and genetic algorithm.