Optimal Active Disturbance Rejection Control for Second Order Systems

This study addresses the control of second-order dynamic systems in the presence of uncertainties and disturbances using an optimized Active Disturbance Rejection Control (ADRC) approach. To achieve practical implementation, a Reduced-Order Generalized Proportional Integral (GPI) observer is introduced to estimate potentially time-varying grouped disturbances within a second-order system The optimized ADRC method is developed by incorporating the information generated by the reduced-order GPI Observer (GPIO) into the output prediction. This approach aims to achieve an optimal tracking performance, particularly in scenarios characterized by disturbances and uncertainties. For numerical validation, simulations were conducted on three distinct second-order system models: a power converter, Direct Current (DC) motor, and nonlinear two-tank system. The simulation results underscore the robustness of the proposed control solution compared to a Proportional Integral Derivative (PID) controller designed using the pole assignment method and a traditional GPI controller. The proposed ADRC approach ensures precise reference tracking even in the presence of disturbances and parametric uncertainty, thereby demonstrating its effectiveness in practical applications.