基于区间方法的不确定二阶控制系统稳定性的鲁棒性分析

运用区间理论,讨论了二阶控制系统稳定性的鲁棒性。首先,将其转换为一个确定部分和不确定部分。根据控制系统的确定性部分,应用独立模态控制的极点配置方法推导出了反馈矩阵,并把这种反馈控制应用于实际的不确定性系统。基于区间参数导出了区间刚度矩阵和质量矩阵,然后利用矩阵摄动理论和区间扩张理论计算出实际的不确定性闭环系统复特征值上下界。最后讨论了不确定性闭环系统稳定性的鲁棒性,并举例说明了该方法的运用。

Robustness analysis of the stability of the second order control systems with uncertainties using interval method

The uncertain parameters were described by the interval variables. Using the interval theory, the vibration control problem of structures with interval parameters was discussed, which was approximated by a deterministic system. The independent modal space control was used to obtain the modal gains. A method to solve the interval eigenvalues of the closed-loop system was presented. The expressions of the interval stiffness and interval mass matrix were deduced directly from the interval parameters. With matrix perturbation and interval extension theory, the algorithm for estimating the upper and lower bounds of the interval complex eigenvalues was presented. The results were used to estimate the robustness of the stability of the second-order control systems, and finally the method was apply to a example.