Frequency-Domain Analysis of Nonlinear Active Disturbance Rejection Control via the Describing Function Method

Active disturbance rejection control (ADRC) is a new design concept that shows promising power in dealing with the uncertainties of control systems. However, most of the previous work has been numerical time-domain development and frequency-domain analysis for the linear framework. This paper focuses on the frequency-domain analysis of the nonlinear ADRC behavior using the describing function method and characterizes the effect of the fal nonlinearity parameter on the performance of the closed-loop system. Both the describing function of the nonlinearity and the transfer function description of the system's linear portion are derived. The stability, dynamic stiffness, and tracking performance are analyzed for a second-order single-input single-output plant. The analysis results show that the nonlinearity parameter plays a crucial role in the system performance. The nonlinear ADRC has higher control efficiency than the linear ADRC but reduces the stability margin of the system. Using the fast tool servo case, simulations and hardware experiments are conducted, and the results further support the analysis.