Rejecting the effects of both input disturbance and measurement noise: A second‐order control system example

Abstract

This article originates from the well-accepted observations in practice: rejection of both input disturbance and measurement noise is practically important for high-precision tracking control, and the classic estimators, such as the uncertainty and disturbance estimator (UDE) and disturbance observer, are proven to be inherently sensitive to measurement noises. Motivated by these observations, we develop a robust control solution and demonstrate the possibility of unifying the design of noise estimator (NE) and UDE for a class of second-order systems. Interestingly, the NE and UDE have three important features in common: (i) the designs are based on system model and reliable state measurement; (ii) a first-order filter is used to ensure that the design is physical realizable, rather than to filter out undesired signals; (iii) the filter parameters are readily determined by an introduced singular perturbation parameter. The performance of UDE is improved when augmented with NE to reject measurement noises. Then, a simple mapping for parameter tuning is presented, by which the estimation performance can be explicitly analyzed using the singular perturbation theory. Comparative simulation and experimental studies show that the proposed NE+UDE-based solution is not only less sensitive to measurement noise than the classic UDE-based control, but also able to deliver superior trajectory-tracking performance over other robust output feedback control approaches.

UDE-Based Dynamic Surface Control for Quadrotor Drone Attitude Tracking under Non-Ideal Actuators

“…Lemma 1. Under the stability conditions (22), system (20) with s 2 , ḟ1 , and ẍ1d as inputs is both globally input-to-state stable (ISS) and bounded-input bounded-state (BIBS) stable.…”

“…Proof of Lemma 1. It is known that A 1 is Hurwitz under the conditions in (22). As is stated in Theorem 4.5 of [42], the unforced system…”

“…In this step, the controller composed of ( 11), (15), and ( 16) is designed for the outermost loop of system (7). The constraints (22) on the control parameters should be satisfied.…”

“…In recent years, this approach has been used successfully in many applications in various fields, such as time-delayed processes [17], vehicle systems without velocity measurements [18][19][20], and multi-vehicle systems [19,21]. In addition, with the aim of simultaneously rejecting system disturbances and velocity measurement noise, a robust control scheme combining a noise estimator (NE) with a UDE was developed in [22] and was shown to provide excellent trajectory tracking performance. However, due to the structural constraints, the mismatched uncertainties and disturbances, e.g., the kinematic couplings and the external disturbance torque in the model of quatortor drone attitude dynamics, cannot be handled by traditional UDE [23].…”

Cascade-modified uncertainty and disturbance estimator–based control of quadrotors for accurate attitude tracking under exogenous disturbance

“…ADRC has received great attention in recent years and has been widely used in quadrotors attitude control, but parameter tuning for ADRC is complex, and also, high-accuracy sensors are required for ADRC because its tracking differentiator (TD) can easily enlarge the sensor noise. 16 A UDE-based controller was first proposed in Ref. 17 and is a model-based disturbance estimation and suppression method that has been widely used in UAV control.…”