Simulation research on PD combined with input-shaping for suppressing the vibration of single-mode flexible mechanical structures

The mechanical structures that belong to a single-flexible mode with a slight damping behave the dynamical performance of long-time damped vibration. A PID controller to control mechanical systems, only designed on the criteria in time domain and frequency domain, may lead to excessive over-shoot and long-time residual vibration. To suppress effectively the residual vibration, input shaping is used in the PD feedback control system. PD combined with input-shaping control is presented for single-mode flexible mechanical structures. The system responses and the actuator efforts of PD combined with input-shaping control system, subject to four typical inputs, are described in general formula. The effect of input shaping on the actuator effort and energy consumption is analyzed quantitatively. Given the condition of the same feedback gains as PD feedback control, compared with PD control, PD combined with input shaping control produces smaller over-shoot and requires less actuator effort, and allows larger vibratory frequency and smaller damping ratio, thus improving the system response speed. Moreover, input shaping suppresses effectively the residual vibration, thereby reducing the settling time and energy consumption of the system. Simulation results show the validity of the control strategy.