输入饱和的双积分系统的复合时间最优控制

Composite TOC Control for Double Integrating Systems with Input Saturation

针对典型的有输入饱和的双积分环节或系统的时间最优控制问题,建立了双积分环节的传递函数和状态空间方程两种数学模型,设计双积分环节的闭环时间最优控制律;对时间最优控制在系统存在干扰和不确定性存在条件下出现的振颤现象进行分析;基于对振颤问题的分析,提出一种对时间最优控制的改进,即一种复合控制方法,当输入作用时,系统先由时间最优控制律控制,当误差达到预定值限,控制律由时间最优控制律切换到另一种线性控制律。采用了比例微分控制律,来解决时间最优控制的振颤问题,响应时间达到最优,并解决振颤问题。

To the issue of time optimal control of double integrating systems with input saturation, the transferring function model and state--space model of double integrating systems are established, and the time optimal controller （TOC） is designed. Unfortunately, it is well known that the classical TOC is not robust with respect to the system uncertainties and measurement noises. Thus, we , in the paper, study the chatter problem by simulation and introduces a nonlinear composite control, method, i. e. , a combination of time optimal control （TOC） and PID control, for double integrating systems with input saturation. The TOC part is designed to enable the time optimization. In order to solve the drawback of TOC, when the error is small to a certain level, it will switch to the PD part to overcome the chatter problem caused by the TOC. Finally, the simulation results, approximate time optimization and fair robustness demonstrate the effectiveness and fea- sibility of the proposed method.