Robust adaptive nonlinear PID controller using radial basis function neural network for ballbots with external force

This paper presents a new adaptive nonlinear proportional integral derivative radial basis function neural network (NPID-RBFNN) for ballbots with external force. The proposed controller is designed based on a hybrid of a nonlinear proportional integral derivative (NPID) control, radial basis function neural networks (RBFNN), and balancing composite motion optimization (BCMO). The hybrid NPID-RBFNN controller offers a light-weight computation, chattering-reduction, while providing high robustness against model uncertainties and external disturbance. Therefore, it provides excellent features to control ballbots against the counterpart approaches such as the conventional PID, conventional NPID, which preserves low robustness against disturbances, or sliding mode control (SMC), which provides higher chattering. The BCMO is used to determine the gain values that best fit the system, and RBFNN is learned continuously during the ballbot movement to balance the system in the most stable and smooth way. The NPID-RBFNN controller is proven to be stable through the Lyapunov approach. The simulation and experiment results show that the NPID-RBFNN controller is a robust method for controlling the ballbot system’s motion in applications with external force.