## 1 Introduction  
The performance of a control system is excessively affected by system uncertainties, such as exogenous disturbances, unmodelled dynamics, and parameter perturbations. Simultaneously guaranteeing disturbance rejection and good tracking performance in light of the existence of large uncertainties complicates the design of any controller that aims to address these objectives. Accordingly,anti-disturbance methods with both external-loop controllers and internal-loop estimators have been comprehensively utilized. The precision of such controls mainly depends on the accuracy of the observer in the internal-loop, this type of controller is called \"model-free controller\" in contrast to other controllers that require the dynamics of the system, e.g., disturbance-observers-based control [1]. There have been various observer design philosophies posited, including fuzzy observers, sliding mode observers, unknown input observers, perturbation observers, equivalent input observers, extended state observers, and disturbance observers. Of these observers, the Extended State Observer (ESO) was originally suggested by [PERSON] [2]; it is often favoured because, in terms of design, it requires the minimum information from the system. It estimates the internal states of the system, system uncertainties, and exogenous disturbances, and it can also be used to design a state feedback controller. Based on this, an ESO is considered an essential part of the active disturbance rejection control paradigm. ESO-based control design has thus been widely examined in recent years [3,4]. The basic principle behind the operation of ESO is to augment the mathematical model of the nonlinear dynamical system with an additional virtual state that describes all the unwanted dynamics, uncertainties, and exogenous disturbances, which is termed \"generalized disturbance\". This virtual state, together with the states of the dynamic system, is observed in real-time using the ESO. This form of control design has been applied to a broad range of systems due to its model-independent operation. Initially, each ESO was constructed with nonlinear gains; however, it is more realistic to design and tune the ESO using tuneable linear gains, as proposed in [5]. Two signals, the input and the output of the nonlinear system, thus feed the ESO with information [6]. An ESO-based control system design offers generally good performance due to the simplicity of design of ESO, which offers a need for minimum information, high precision of convergence, and fast-tracking capabilities [7]. In [8], ESO is tested on the nonlinear kinematic model of the Differential Drive Mobile Robot (DDMR). In [9], a general ESO-based control technique for nonchain integrator systems with mismatched disturbances was proposed. Recently, numerous control problems in various fields have also been effectively resolved by utilizing the ESO technique, including permanent magnet synchronous motor(PMSM) control [10], and attitude control of an aircraft [11]. The authors in [12] introduced an ESO-based dynamic sliding-mode control for high-order mismatched uncertainties with applications in motion control systems, and this also presented excellent tracking performance. In [13], an improved nonlinear ESO was proposed which achieved an outstanding performance in terms of smoothness in the control signal which leads to less control energy required to attain the desired performance. Techniques other than classical ones for dealing with measurement noise are proposed in the literature, e.g., authors of [14,15] have proposed a novel class of Adaptive ESOs (AESOs) with time-varying observer gains. As a result, the proposed AESO combines both the advantages of nonlinear extended state observer (NESO) and Linear Extended State Observer (LESO) and provided more extra design flexibility than LESO. Techniques different from ESO based estimation methods like time-delay estimators to estimate the generalized disturbance are proposed in [16,17].