###### Abstract
An alternative solution is based on a composite control structure, including a baseline NDI controller for the desired performance specifications of the nominal system and a nonlinear disturbance observer (NDO) for robustness enhancement of the closed-loop system. The fundamental idea of NDO is to bring together all the internal uncertainties, external disturbances, parameter variations, and unmodeled dynamics as lumped disturbances [26], which are always mismatched and cannot be completely counteracted through control input channels [28]. Taking the partially known nonlinear dynamics into account, an appropriately designed NDO can be employed to reconstruct an inverse model of the actual system, and estimate the nonlinear lumped disturbances by using the baseline NDI control input and the system output. As described in ref [25; 28], it is feasible to remove the influence of lumped disturbances from the system output variables in the steady-state and reduce the influence on transient performance with a composite controller involving the NDI and NDO. The NDO employed in this paper is firstly proposed by [PERSON] with rigorous stability analysis of both the NDO and the closed-loop system [29], and then widely applied to the field of flight control, such as the longitudinal autopilot of a missile [30], the longitudinal tracking of an air-breathing hypersonic vehicle [27], the attitude control of a spacecraft [31], etc. It appears that such NDO based control methods can lead to significant improvement of the disturbance rejection ability of an existing controller without scarifying the nominal performance. However, to the authors' knowledge, the existing literatures on NDO based NDI (NDI-DO) control of tailless aircraft are rare. Though a primitive NDI-DO controller has been designed for a tailless aircraft and numerically validated in ref. [32], experimental implementation and flight validation are to be carried out. As is well known, another main weakness of NDI is the requirement of the plant's input distribution matrix to be invertible. However, it is often the case that the input distribution matrix becomes \"almost\" singular for some states and hence may lead to excessively large control activities [33]. As deflection range and rate limitations are inevitably present in physical actuated surfaces, aggressively piloted maneuvers of aircraft may yield actuator saturation and associated degradation of closed-loop performance or even loss of stability [34]. A favorable solution in industry and academia to address the actuator saturation is the so-called anti-windup (AW) techniques, in which an existing controller is augmented with an additional element that only becomes active during saturation [35]. In ref. [25], a classic static AW scheme is added to the baseline controller of a tailless unmanned aerial vehicle (UAV) allowing for windup attenuation and nominal performance recovery in the absence of saturation. This paper extends the work of ref. [25] to the NDI setting and nonlinear case. The remainder of this paper is structured as follows. Section 2 provides the preliminaries including a brief introduction to the tailless aircraft, the experimental setup and the mathematical modeling. In Section 3, the equations of angular motions are reformulated in the form of a nonlinear affine system for application of the NDI control scheme, which is then augmented with an NDO to improve the ability of disturbance rejection and further modified for anti-windup enhancement in the presence of actuator saturation. In Section 4, the designed baseline NDI controller, NDI-DO controller, and anti-windup modified controller (NDI-AW) are validated and compared in the context of nonlinear simulations. In Section 5, both the baseline NDI scheme and the NDI-DO scheme are implemented for free flight tests in the wind tunnel, in which the NDI-DO scheme demonstrates the superior ability of disturbance rejection in contrast with the baseline NDI scheme. Finally, a conclusion is provided in Section 6.