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

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.