On frequency response analysis of GPIO

The Generalized Proportional Integral Observer (GPIO), which is a generalized high order Extended State Observer (ESO), has drawn much attention from both the industry and academia recently. This paper explores the characteristics of GPIO for the linear, time-invariant (LTI) plants using the frequency response method. It shows that the high order GPIO not only estimates the total disturbance and its derivatives, but also contributes to the closed-loop system type. Theoretical analysis and simulation results agree in that different GPIO orders have little impact on the tracking performances and the control signal, but more augmented state variables in the GPIO can lead to stronger disturbance rejection and smaller sensitivity function, at the cost of decreasing stability margins, increasing sensitivity to measurement noises and increasing the computational complexity. The conclusions could be useful for the practitioners and researchers who need clarity in the GPIO order selections.