In this paper (A preliminary version of the submitted paper appeared in the Proceedings of the 2020 International Conference on Unmanned Aircraft Systems (ICUAS’20), Athens, Greece*), a robust attitude controller is proposed for a small-scale helicopter based on Multi-Variable Super Twisting Algorithm. An interconnected hybrid model of a helicopter is considered consisting of fuselage and rotor which are modeled as a single rigid body and a disc, respectively. For designing a globally defined controller, we consider that attitude dynamics evolves on non-Euclidean space. We assume that the rotor is subjected to unknown disturbances and exact information of the helicopter parameters are unavailable due to parametric uncertainty. A attitude tracking controller using Super Twisting Algorithm based on Second-Order sliding mode technique is proposed to ensure robustness in the presence of both unknown disturbance and parameter variation. A family of strong Lyapunov functions is used to show that the proposed controller drives the closed loop system to the sliding manifold in finite time. For the suitable choice of gain matrices, the reduced order error dynamics becomes almost globally asymptotically stable. We further show that the reduced order error dynamics is almost semi-globally exponentially stable if its trajectories starts from a specific subset. The rate of convergence can be adjusted as required by tuning the controller gains. Numerical simulations are carried out by comparing the proposed controller with the state-of-the art controllers available in the literature.

在这篇论文中（提交论文的初步版本出现在 2020 年国际无人机系统会议（ICUAS'20），希腊雅典*）中，提出了一种用于小型直升机的鲁棒姿态控制器，基于多变量超级扭曲算法。直升机的互连混合模型被认为由机身和旋翼组成，它们分别被建模为单个刚体和圆盘。为了设计一个全局定义的控制器，我们认为姿态动力学是在非欧几里得空间上演化的。我们假设旋翼受到未知干扰，并且由于参数不确定性，直升机参数的准确信息不可用。提出了一种使用基于二阶滑模技术的超级扭曲算法的姿态跟踪控制器，以确保在存在未知扰动和参数变化时的鲁棒性。一系列强李雅普诺夫函数用于证明所提出的控制器在有限时间内将闭环系统驱动到滑动流形。对于增益矩阵的合适选择，降阶误差动态变得几乎全局渐近稳定。我们进一步表明，如果其轨迹从特定子集开始，则降阶误差动态几乎是半全局指数稳定的。通过调整控制器增益，可以根据需要调整收敛速度。通过将所提出的控制器与文献中可用的最先进的控制器进行比较来进行数值模拟。