双积分系统阶跃响应快速无超调控制: 一种增益切换非线性PD控制

采用标准PD或PID控制器镇定双积分对象时,系统的阶跃响应必然存在超调:为此,设计了一种可以切换增益的非线性PD控制器,给出了系统阶跃响应无超调的充要条件,以及减小调节时间的方法.采用的切换规律是:当误差的幅值大于设定门限时,设计好的快速PD控制器投入工作,以加快误差的收敛:当误差的幅值小于设定门限时,设计好的强阻尼PD控制器投入工作,以抑制可能出现的超调.通过这两个控制器的配合作用,既能实现阶跃响应无超调,又能有效减小调节时间.仿真验证了该结论.

Fast and nonovershooting control for a double-integral system with step input: nonlinear PD control based on gain-switching

If a standard PD or a PID controller is used to stabilize a double-integral system with step input, a nonovershooting step-response can't be obtained. A novel nonlinear PD controller with gain-switching is presented to deal with this problem. The necessary and sufficient condition of the nonovershooting step-response and the methods to reduce the settling time are given. The designed switching action obeys the following rule: when the amplitude of the tracking error is larger than a threshold value, a fast PD controller is employed to accelerate the convergence of the tracking error; otherwise, a strong-damping PD controller is adopted to restrain the overshoot. The cooperation of the two PD controllers reduces the settling time while rendering a nonovershooting step-response. These theoretical results are confirmed by computer simulations.