The article focuses on developing a TWSBR (Two-Wheeled Self-Balancing Robots) controller aimed at enhancing the performance of underperforming robotic systems, particularly in maintaining stability and precision during movements. It underscores the importance of a novel control approach to address specific performance metrics such as balance, agility, and responsiveness. The paper outlines the establishment of a non-linear system model to capture the intricate dynamics of robotic movements. It briefly discusses the incorporation of non-linearity within the model, potentially involving factors like frictional forces or dynamic load variations. This non-linear framework helps in addressing inherent complexities, thereby improving the performance of two-wheeled robotic systems, especially in scenarios requiring precise balance and regulation. The paper evaluates the performance of various controllers, such as LQR (Linear Quadratic Regulator), ANN (Artificial Neural Network), and PID (Proportional-Integral-Derivative), within the context of the TWSBR system. This analysis provides insights into the effectiveness of different control approaches in improving system stability and precision.

The structure of the interconnected electric power system and the increasing quality of energy have led to an increased importance of Automatic Generation Control, or AGC. The tie line powers and frequency must be maintained within the permitted standard values. This work applies to Automatic Generation Control in a nonlinear model of an interconnected electric power system using a fractional order sliding mode controller. Three sections of a nonlinear interconnected electric power system are controlled by a fractional order sliding mode controller. The block diagram of the power plant model system considers the nonlinearities that are physical limits, such as governor dead band and generation rate constraints. In the presence of various load changes (sudden load change frequency), parameter uncertainty (variation), and the existence of physical constraints, the control’s goal is to manage the frequency deviation (load frequency error) and tie-line power deviation (tie-line power error) of the interconnected power system. Three sections of an interconnected power system with nonlinearities are used to simulate the fractional order sliding mode controller (FOSMC). These designs display the best performance of the suggested FOSMC controller, with numerical values for tie line power deviation of 2.9765e-5p.u. and frequency deviation of 6.8912e-4Hz. The suggested system has reduced nominal values as compared to SMC for the frequency deviation of 2.0762e-3Hz and tie line power deviation of 1.21754e-3p.u., as well as for PID controller frequency deviation of 3.5918e-3Hz and ti line power deviation of 1.5602e-3p.u. These comparisons further demonstrate that, even in the presence of parameter variation, load changes, and nonlinearities in the system, FOSMC performs the best, with reduced undershoot (5.4823e-4), overshoot (1.5545e-4), rising time (1.00042e-8), and settling time (2.688). MATLAB/Simulink has been used to create and simulate the controllers for the system model.