On Active Disturbance Rejection Control in Presence of Measurement Noise

High-gain nature of extended state observer (ESO), which forms an integral part of active disturbance rejection control (ADRC) technique, results in the following limitations: (1) Sensitivity to high-frequency measurement noise which limits closed-loop performance in practical applications. (2) Escalation of observer gains up-to a power $\bm{n+1}$ of observer bandwidth, which complicates numerical implementation when system order $(\bm{n})$ or observer bandwidth is large. To overcome these limitations, a low-power higher-order ESO (LHESO) is proposed in the present work for practical application of ADRC scheme in noisy environment. Moreover, a recently proposed cascade ESO (CESO), designed for noise suppression, is analyzed in the frequency-domain to reveal an underlying similarity with higher-order ESO, which is not reported in literature. Presented analysis justifies the performance improvement obtained over conventional ESO and provides a guideline for selecting the number of cascade levels based on the expected nature of disturbance. Case study performed on a DC-DC boost converter illustrates the practical advantages of proposed scheme over CESO in terms of improved immunity to high-frequency measurement noise, precise regulation in presence of time-varying disturbance, low observer gains that facilitate numerical implementation and ease of tuning due to a single observer parameter.