In this paper, a Novel Active Disturbance Rejection Control (N-ADRC) strategy is proposed that replaces the Linear Extended state observer (LESO) used in Conventional ADRC (C-ADRC) with a Nested LESO. In the nested LESO, the inner-loop LESO actively estimates and eliminates the generalized disturbance. Increasing the bandwidth improves the estimation accuracy which may tolerate noise and conflict with H/W limitations and the sampling frequency of the system. Therefore, an alternative scenario is offered without increasing the bandwidth of the inner-loop LESO provided that the rate of change of the generalized disturbance estimation error is upper bounded. This is achieved by the placing an outer-loop LESO in parallel with the inner one, it estimates and eliminates the remaining generalized disturbance that eluded from the inner-loop LESO due to bandwidth limitations. The stability of LESO and nested LESO is investigated using Lyapunov stability analysis. Simulations on uncertain nonlinear SISO system with time-varying exogenous disturbance revealed that the proposed nested LESO can successfully deal with a generalized disturbance in both noisy and noise-free environments, where the Integral Time Absolute Error (ITAE) of the tracking error for the nested LESO is reduced by 69.87% from that of the LESO.
The performance of a control system is excessively affected by system uncertainties, such as exogenous disturbances, unmodeled dynamics, and parameter perturbations. Guaranteeing simultaneously 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. 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 Han [1]; 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 to be an essential part of the active disturbance rejection control paradigm. ESO-based control design has thus been widely examined in recent years [2]. 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" or "total 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 [3]. Two signals, the input and the output of the nonlinear system, thus feed the ESO with information [4]. 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 [5]. In [6], ESO is tested on the nonlinear kinematic model of the differential drive mobile robot (DDMR). In [7], a general ESObased control technique for non-chain 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 PMSM control [8], and attitude control of an aircraft [9]. The authors in [10] 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 [11], 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. In this paper, a novel ADRC is constructed by connecting a second ESO in parallel with an original ESO (the inner ESO), to construct a nested ADRC (N-ADRC). The advantage of this configuration is that the second ESO estimates and eliminates the remaining total disturbance that passes from the inner-ESO due to bandwidth limitations in real-time. Its excellent performance becomes very evident when considered in terms of measurement noise. To the best of the authors' knowledge, using double ESOs within the same ADRC structure, with applications in highly nonlinear uncertain systems, has not previously appeared in the literature. An outline of this paper's contents and organisation follows. Section II briefly presents the concepts behind active disturbance rejection control (ADRC). A description of the proposed nested ESO and the relevant stability tests are included in section III. The numerical simulations verifying the validity of the proposed configuration are provided in section IV. Finally, the conclusion is given in section V, along with recommendations for future work.
In ADRC, the model of the nonlinear system is extended with an additional virtual state variable, which lumps all of the unwanted dynamics, uncertainties, and disturbances that remain unobserved in the standard system into a single term known as “generalized disturbance”. In addition to estimating the states of the nonlinear system, the ESO performs online estimation and cancellation of this virtual state. In this scenario, the nonlinear system is converted into a chain of integrators, which allows the control system design to be simpler. Fig. 1 demonstrations the structure of a Conventional ADRC, (C-ADRC) which contains three key parts: the Tracki
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