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首页> 外文期刊>Journal of guidance, control, and dynamics >Kinetic State Tracking for a Class of Singularly Perturbed Systems
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Kinetic State Tracking for a Class of Singularly Perturbed Systems

机译：一类奇摄动系统的动力学状态跟踪

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摘要

The trajectory-following control problem for a general class of nonlinear multi-input/multi-output two time-scale system is revisited. While most earlier works used singular perturbation theory and assumed that an isolated real root exists for the nonlinear set of algebraic equations that constitute the slow subsystem, here, two time-scale systems are analyzed in the context of integral manifolds. It is shown that the singularly perturbed system has a center manifold and, for small values of the slow state, an approximate solution of the nonlinear set of transcendental equations can be computed. Geometric singular perturbation theory is used as the model-reduction technique, and modified composite control design is used to formulate the stabilizing control laws for slow state tracking. The control laws are independent of the scalar perturbation parameter and an upper bound for it, and the closed-loop error signals are determined such that uniform boundedness of the closed-loop system is guaranteed. Additionally, asymptotic stabilization is shown for the nonlinear regulation problem. The methodology is demonstrated through numerical simulation of a nonlinear generic two-degree-of-freedom kinetic model and a nonlinear, coupled, six-degree-of-freedom model of the F/A-18A Hornet. Results demonstrate that the methodology permits close tracking of a reference trajectory while maintaining all control signals within specified bounds.
机译：讨论了一般一类非线性多输入多输出两时标系统的轨迹跟踪控制问题。尽管大多数较早的工作使用奇异摄动理论，并假设构成慢子系统的非线性代数方程组存在孤立的实根，但在此，我们在积分流形的背景下分析了两个时标系统。结果表明，奇异摄动系统具有中心流形，对于慢状态的较小值，可以计算出超越方程组的非线性集合的近似解。将几何奇异摄动理论用作模型简化技术，并使用改进的复合控制设计来制定用于慢状态跟踪的稳定控制律。控制定律与标量摄动参数及其上限无关，并且确定闭环误差信号以确保闭环系统的均匀有界性。此外，针对非线性调节问题显示了渐近稳定。通过对F / A-18A大黄蜂的非线性通用两自由度动力学模型和非线性，耦合，六自由度模型进行数值模拟，论证了该方法。结果表明，该方法可以在保持所有控制信号在指定范围内的同时，密切跟踪参考轨迹。

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