Optimal nonlinear PID TSK3DCMAC controller based on balancing composite motion optimization for ballbot with external forces

Abstract

This paper proposes an innovative approach to address the challenges of dynamic balance and external disturbances in ballbot systems, overcoming the limitations of conventional Proportional Integral Derivative (PID) controllers and their variants in handling highly nonlinear dynamics and external forces. Traditional PID controllers and their variants often have difficulty adapting to complex, real-time dynamic systems, leading to performance degradation under varying conditions. A nonlinear PID controller-based Takagi–Sugeno–Kang 3D Cerebellar Model Articulation Controller (TSK3DCMAC) is introduced to overcome these shortcomings. The proposed controller is developed utilizing a combination of nonlinear PID control, TSK3DCMAC, and the Balancing Composite Motion Optimization (BCMO) algorithm. The TSK3DCMAC is iteratively trained during the ballbot's motion to ensure the system balance in a very steady and seamless manner. Furthermore, the BCMO algorithm is utilized to obtain the optimal gains for precisely modeling the system. The stability of NPID-TSK3DCMAC law is analyzed using the Lyapunov technique. The simulation and experimental results highlight the effectiveness of the NPID-TSK3DCMAC controller. Without external force, it reduces the mean squared error (MSE) by 45.84 % and 99.87 % and the mean absolute error (MAE) by 25.68 % and 63.91 % compared to the PID and NPID controllers, respectively. With external force, it further surpasses the NPID controller by 64.94 % in MSE and 17.67 % in MAE, demonstrating its robustness and precision under varying conditions. Simulation and experiment results reveal that the proposed approach has robustness and effectively regulates the motion of the ballbot system despite external disturbances. This indicates a promising solution for applications requiring precise/agile motion control and stability under varying external conditions.