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研究具有输入时滞的线性时不变(LTI)系统的状态反馈控制镇定问题.由于时滞的引入,闭环系统特征方程变成一个超越方程.从时滞系统的特征根求解出发,从特征方程的实部和虚部系数中提取两个与系统矩阵和反馈矩阵相关的向量,其幅值和相角关系正好反映了特征根轨迹穿越虚轴的情况,且得到的判据将时滞参数与系统其他参数进行了分离,可方便地应用于镇定控制器的设计.最后通过仿真实例表明了该算法的正确性和有效性.
The state feedback control stabilization problem of linear time-invariant (LTI) systems with input delay is studied. Due to the introduction of delay, the closed-loop system characteristic equation becomes a transcendental equation. Starting from the eigenvalue solution of the time-delay system, , Two vectors related to the system matrix and the feedback matrix are extracted from the real part and the imaginary part coefficient, and the relationship between the amplitude and the phase angle exactly reflects the situation that the eigen-root locus traverses the imaginary axis. The obtained criterion compares the delay parameter with The other parameters of the system are separated and can be easily applied to the design of the stabilization controller.Finally, the simulation example shows the correctness and effectiveness of the algorithm.