## 1 Introduction
This incremental nonlinear dynamics inversion (INDI) control demonstrates robust characteristics due to less model dependency [11]. Controllers based on incremental dynamics demonstrate robust characteristics in this context. The incremental dynamics-based controller suppresses the disturbances better at higher update frequency [14]. Other requirements for this controller are that the control input should affect the system much higher than the system dynamics and the control effectiveness matrix must be exact [14]. The state derivative information required for incremental dynamics-based controllers poses a problem when it is not measured by onboard sensors, particularly in our case to control rotational motion. The common control state variable for aircraft systems is body rate which can be measured by gyroscopic sensors. The derivative of body rate is not provided in most aircraft systems, as sensors measuring angular acceleration are not widely manufactured nor easily procured compared to cheap and abundant gyroscopic sensors. This indicates that to apply incremental dynamics-based controllers to the rotational control of an aircraft, state derivative must be estimated. The simplest method for calculating derivative terms is numerical differentiation. However, this approach amplifies noise as the sample time decreases, reducing accuracy. Alternatively, first- or second-order low-pass filters can be used, as discussed by [PERSON], [PERSON], and [PERSON] [15] and [PERSON], [PERSON], and [PERSON] [16], who combined this with incremental dynamics-based controllers and gain scheduling. In this research, a first-order low-pass filter is used to obtain the derivative of the body rate. This process requires uncertainty estimation for it to work properly. To address above mentioned concerns, a disturbance observer-based uncertainty estimation is proposed in various related works. The high-order sliding mode disturbance observer (HOSMDO) was proposed in [17] without measuring state derivative terms but requires upper bounds of uncertainties and has an inherent chattering problem. The time delay adaptation method was proposed in [18] but requires system model information. [PERSON] et al., in [19], proposed a Gaussian process regression-based data-driven adaptive controller but the method requires high computational power and state derivative term. Nonlinear disturbance observer (NDO) is proposed by [PERSON] et al. [20] to estimate disturbances and uncertainties in the given nonlinear system. The NDO does not require knowledge of state derivatives to estimate the disturbances. The assumption for the NDO to work properly is that the disturbance should be constant or slowly varying. Among different types of uncertainty estimation, the proposed controller utilized NDO. The incremental dynamics-based controller assumes the system model term as uncertainty, as it affects the state derivative relatively smaller and slower compared to the control model part. This forms the valid assumption for the NDO to work properly. The NDO is also a model-based algorithm but to use NDO in more practical situations, the aerodynamics coefficient required for the NDO was assumed not known except for the direction of the aileron, elevator, and rudder actuator control surfaces. For further uncertainty quantification, investigation approaches as in [21; 22] can also be considered based on the analysis methodology in this research. The motivation for the proposed research stems from the challenges associated with controlling the rotational motion of aircraft due to the uncertainties in aerodynamics, which complicate the implementation of traditional control methods. The necessity arises because the existing linear control approaches, like gain scheduling, demand extensive tuning and struggle to accurately represent nonlinear behaviors across a wide range of operating conditions. Meanwhile, nonlinear controllers, while promising, still face limitations when there are uncertainties in the system model.