严格区域稳定的模型参考自适应控制器设计

Design of model reference adaptive controller with strict local stability

针对模型参考自适应控制的区域稳定性问题,采用Lyapunov直接法分析参数收敛与系统跟踪误差之间的关系。通过对系统误差项与参数估计项之间能量转移过程的描述,说明常规的区域稳定自适应控制器尚未充分考虑因估计参数振荡引起系统失稳的可能性。为此,提出一种简洁有效的区域稳定控制器设计方案,根据系统跟踪误差大小动态引入增益动态调整的鲁棒控制项,有效消除了控制中潜在的不稳定因素。基于SISO非线性系统的仿真研究验证了所提方案的有效性。

Considering the local stability problem of model reference adaptive control(MRAC), the relation between parameter convergence and system tracking error is analyzed by using Lyapunov direct method. The description of the energy transition process between system error term and parameter estimate term indicates that the traditional locally stable MRAC controller does not consider the possibility of system instability sufficiently due to the adaptive parameter surge. A simple and effective design of locally stable MRAC controller is proposed. It eliminates the potential unstable factor by dynamically adding a robust control term, whose gain is adjusted dynamically according to the system tracking error. The simulation studies on SISO nonlinear system verify the effectiveness of the proposed scheme.