Learning Based Adaptation of Proportional Derivative Controller for a Novel Rotary Slosh Dynamics Model

The disturbance in the free liquid surface caused by the movement of a partially filled liquid container is referred to as sloshing. A wide variety of application fields, such as liquid cargo carriers, liquidized natural gas and petroleum storage tanks, the beverage industry, rocket engine fuel tanks, molten metal transfer in steel plants, spacecraft trajectory or attitude manoeuvres, etc frequently experience the sloshing phenomenon. Rotary slosh develops in a partially filled liquid container as a result of 2-dimensional movement of the container. In order to solve the rotary slosh minimization problem, this paper proposes an adaptation of proportional derivative (PD) controller parameters using deep reinforcement learning (DRL) framework. In this paper, for the first time a novel rotary slosh dynamics model is proposed. A spherical pendulum on cart is used to represent the rotary slosh when the cart with partially filled liquid container is moving on a specified path in a 2-D plane. A DRL-based adaptation of PD controller parameters is proposed in order to produce near-optimal performance even with unknown perturbations in the system model. The decision making of the proposed DRL-based PD controller for the rotary slosh minimization problem is verified in a Python simulation environment, and its performance with unknown perturbations is compared with conventional PD controller approach to validate the performance and robustness of the controller due to the learning based framework.