3- DOF直升机小超调定常性能自适应姿态跟踪控制
Prescribed Performance Adaptive Fixed-Time Attitude Tracking Control of a 3-DOF Helicopter with Small Overshoot
摘要：
针对三自由度直升机的姿态跟踪问题，研究了一种新的指定性能自适应固定时间反推控制策略。首先，设计了一个新的统一障碍函数（UBF），将给定的性能约束系统转化为无约束系统。然后，建立了固定时间（FxT）的反推控制框架，实现姿态跟踪。通过一个新提出的不等式的虚化，构造了一个非奇异的虚拟控制律。此外，FxT微分器的补偿机制，以克服“爆炸的复杂性”的问题。此外，一个修改的自适应律的开发，以近似上界的干扰。为了得到一个更小的保守性和更准确的近似的建立时间，一个改进的FxT稳定性定理的建议。基于该定理，证明了系统的所有信号都是FxT有界的，并且跟踪误差在用户定义的时间内收敛到一个具有小超调的预定域。最后，通过数值仿真验证了所提出控制策略的可行性和有效性。
英文摘要：
In this article, a novel prescribed performance adaptive fixed-time backstepping control strategy is investigated for the attitude tracking of a 3-DOF helicopter. First, a new unified barrier function (UBF) is designed to convert the prescribed performance constrained system into an unconstrained one. Then, a fixed-time (FxT) backstepping control framework is established to achieve the attitude tracking. By virtual of a newly proposed inequality, a non-singular virtual control law is constructed. In addition, a FxT differentiator with a compensation mechanism is employed to overcome the matter of "explosion of complexity". Moreover, a modified adaptive law is developed to approximate the upper bound of the disturbances. To obtain a less conservative and more accurate approximation of the settling time, an improved FxT stability theorem is proposed. Based on this theorem, it is proved that all signals of the system are FxT bounded, and the tracking error converges to a preset domain with small overshoot in a user-defined time. Finally, the feasibility and effectiveness of the presented control strategy are confirmed by numerical simulations.
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