The investigations of input shaping with optimal state feedback for vibration control of a flexible joint manipulator

This paper presents investigations into the development of input shaping with optimal state feedback for trajectory tracking and vibration control of a flexible joint manipulator. A single-link flexible joint manipulator is considered and the dynamic model of the system is derived using the Euler-Lagrange formulation. To study the effectiveness of the controllers, a linear-quadratic regulator (LQR) controller is developed for tip angular position control of a flexible joint manipulator. This is then extended to incorporate input shaper control schemes for vibration reduction of the flexible joint system. The positive zero-vibration-derivative-derivative (ZVDD) and new modified specified negative amplitude zero-vibration-derivative-derivative (SNA-ZVDD) input shapers are then designed based on the properties of the system for vibration control. The new SNA-ZVDD is proposed to improve the robustness capability while increasing the speed of the system response. Simulation results of the response of the flexible joint manipulator with the controllers are presented in time and frequency domains. The performances of the LQR with input shaping control schemes are examined in terms of input tracking capability, level of vibration reduction, robustness and time response specifications. A comparative assessment of the positive ZVDD and modified SNA-ZVDD shapers to the hybrid system performance is presented and discussed.